sympy integral

integral.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "d1 = Symbol('D_1', real=True, positive=True)\n",
    "d2 = Symbol('D_2', real=True, positive=True)\n",
    "d3 = Symbol('D_3', real=True, positive=True)\n",
    "t = Symbol('t', real=True, positive=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABJkAAAAyBAMAAAANcBcmAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nWJ1//wdRKTLrMuGvHwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$0.2 \\left(e^{t \\left(4 D_{1} + 7 D_{2} + 7 D_{3}\\right)} + e^{t \\left(7 D_{1} + 4 D_{2} + 7 D_{3}\\right)} + e^{t \\left(7 D_{1} + 7 D_{2} + 7 D_{3}\\right)} + 2 e^{t \\left(6 D_{1} + 6 D_{2} + 6 D_{3} + 2 \\sqrt{D_{1}^{2} - D_{1} D_{2} - D_{1} D_{3} + D_{2}^{2} - D_{2} D_{3} + D_{3}^{2}}\\right)}\\right) e^{- 8 t \\left(D_{1} + D_{2} + D_{3}\\right)}$$"
      ],
      "text/plain": [
       "    ⎛                                                                         \n",
       "    ⎜                                                                         \n",
       "    ⎜ t⋅(4⋅D₁ + 7⋅D₂ + 7⋅D₃)    t⋅(7⋅D₁ + 4⋅D₂ + 7⋅D₃)    t⋅(7⋅D₁ + 7⋅D₂ + 7⋅D\n",
       "0.2⋅⎝ℯ                       + ℯ                       + ℯ                    \n",
       "\n",
       "          ⎛                          _________________________________________\n",
       "          ⎜                         ╱   2                     2             2 \n",
       "₃)      t⋅⎝6⋅D₁ + 6⋅D₂ + 6⋅D₃ + 2⋅╲╱  D₁  - D₁⋅D₂ - D₁⋅D₃ + D₂  - D₂⋅D₃ + D₃  \n",
       "   + 2⋅ℯ                                                                      \n",
       "\n",
       "⎞⎞                     \n",
       "⎟⎟                     \n",
       "⎠⎟  -8⋅t⋅(D₁ + D₂ + D₃)\n",
       " ⎠⋅ℯ                   "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C2 = 1 / 5 * exp(-8 * t * (d1 + d2 + d3)) * (\n",
    "    exp(t * (4 * d1 + 7 * d2 + 7 * d3)) + exp(t * (7 * d1 + 4 * d2 + 7 * d3)) +\n",
    "    exp(t * (7 * d1 + 7 * d2 + 7 * d3)) + 2 * exp(t * (\n",
    "        6 *\n",
    "        (d1 + d2 + d3\n",
    "         ) + 2 * sqrt(d1**2 + d2**2 + d3**2 - d1 * d2 - d1 * d3 - d2 * d3))))\n",
    "C2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAACDUAAABpCAMAAAAXt3qLAAAAP1BMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADFBd4eAAAAFHRS\nTlMAmc0i3e8yEESru4l2VOOLZpPz+Zy/zysAAAAJcEhZcwAADsQAAA7EAZUrDhsAACAASURBVHgB\n7V2Ntqugjq611Vr13s6M7/+skwCBgMG/arftiWuds62GkHwghBDgctFLEVAEFAFFYA0C1Rriz9O+\nXp/PU3P8KgTqJhL35BU6klV/KAKKgCLwdQjcTy1xdz21eCrcGRB4RJXk3BX6DHipDIqAIqAIvIHA\nqRvZx71+QzVN+o8g0HFvw6kr9D9SIKqmIqAI/DACZ25k67u6m3+46u2n2pXNY22t0EXksdhPNuWk\nCCgCisBPIbC1kf0ECA0fQ34iQ83jOxEomU9qW4Uub4dZqF3btR7WtngW3+8/+yGVfkgVX8l++iYq\nMND0+dPanlS5bY3sR5SphnJ9PsWg168hMF8LmH25qUKXw31DXZuXCyheYDL0ZP62kEvz9U6NH1Lp\nh1RZVBu/nigqMNCmH75epS9UYFMj+xk9r9TWsuy6gv0QbsuPm56/MXpkUJ5AodUiVIMfwG+p0PVt\neDAEdr29IWcS7wZWwyZjeFeR3mX2Qyr9kCrvlup3pI8K7HKpW7Ua/qDgtjSynxGzlFwN1cyQsDms\n9c8o/RujR6bcCRTaIMK1IxW2VOhmOMzYrAeMzbn3Vjxs88rjLBTC4Ni/P6TSD6lybJmfhXtcYJdL\nV6vV8Adls6WR/YyYW8LTyo97f39j9MhK9AQKbRDh5euxv2E6zdzWg+naZ6i2vbaehRsL1+zJ8bCN\n4d+n+iGVfkiVv68Xn5AgKbCqv6jV8Anckzw2NLKGQ109vFM4YbnTz7sfPi5nWBzoaihZyx8k+onR\nY1DncjmBQl6EfsazFOQOA/gFFbq82sgPWqHTDgsShbxW3dm5kxury/x+FauzEP+QSj+kyllqx7Fy\nJAUGMUNqNeyP+KPppp2v8+1leZe6y/5qHK3yyz30KIXx38OszE8b/ZBbnXU1VM01BLKHBP7OvSd1\nBNhqh+OrGYZn0zyfje/SZkePQhrKeeIVkYz+5tPk34yY+AdCmhMoZEUIGHtxMzd3Kt75Cn0pqqqr\ni9pbvddBiKDJ5LP2sR0cMQu4nYnMWZvB5+l/SKUfUuXz9eAvcowL7AVNsFoNu5dDda8f09Oo841s\nNVCDHIlnR3eZlxHlth8voTq0JqwsbfQD/9ZNH4cn/q6+T/cM9r1Tx8EWOS6u3kgYrG3yGii3BaPH\nURov2GXiVSBK7vJp8m8SFuznKM0JFLIi5M1AJr659SsT5Ard3cixABFUMB1aXljnfZdreJrFpt92\nIjZ8gy+W7yaG84l65tiYp15P8UMqfVCVo0tlfTl+Y4qowGqs6EI38Y2KnUnmYtrRAKL+72ZxQ0u4\nmcVUwuI2elvWPTwcNfqebrKPeU5bDRf+3sJW8wY+tPbV4FrlwnVQC0aPozReZgipT9iFV9m7fJr8\nG8dMaLxGaQ5WaI0I7dIesKPWQ6jQdZuaQc9LyQp3oCLIAv7GC5xu8WsoLg+wwB/BgHmDbz6pgG+e\neMubH1Lpc6ocXipbSvL70vAC64u2LYZCcoV/n2InkrhhbaMs1v/Jjxc8PdhquEkGz9N2InGj72Vt\np+oPtwp8CnbD31vYgqEAZBihZ6+Opk4eg8kvIiOi5G+ahr2eeMWo4tt8mvwbx0FovNI0Ryu0RoRa\ndh3EcOCvnlbcjCp0WfBYRJMS1uc+mBF5qNWAa4Vxv4byCeZude37Hm+OvAR8983uh1T6nCqHl8q+\nZXxWblGBgZDlt8cWnxDoeathvlUuK3lsZKyG3Mv3sRgEg6ceapQlafR9XmPvhH8Fe4ixboI99rfm\nvVPHwNZzCcrA+0mj2tI4theNHpM0PlO4mXjFyaL7fJr8G8dAaLySNIcrtEqEazRNhEqEPjfc4S4I\nbr4oqdBlc6WJpAAhDE8qRneo1XDpYEAEWVe4j9TdhGEGQQ65E/DdOZ8fUuljqhxfKjsX8knZ8QKD\nPdSeQzP+vk8q+neIVRX3ewEtVt12XQut7+N67/o2TNCjFth4wvP2VbSNHaqXxauFKDQiLqFckJCY\nmFtgWKHV4F+ir2jf0uNeY8y7gEa3v14wxiJp9FE6vDojf6xMkNpaDT0ggf4K0s4kNP/he6uOhe1V\nDLfC64Qmrrv82v4HArNs9BinIU7m78SriI7/yKfJv3HphcYrTnO8QqtESGZL6uY+uOjc9lk0Yf6i\nto4fW6E9VtVzbHXAyxvYG/jPXcdaDZTLx/4K+H4s74My+gGVfkCFgwpX2Z4MAbPTbmW868a5fy96\n37xaUe2Q634HE6C+Ydf4wObUHDZJxGaPRsakNnvWtHaGwrws8YkZTO2mPxfzgQqUYC/UDW4AlDb6\nlCe5A5gyTGpjNfTIqTBWEGlHqa1VYfejtBsUGzjc66ef/PBRAJcOfQ2LRo9JGsoS/0684mTRfT5N\n/g0xGDdeSZrjFVolwiteFvMEX1OH0Zu1cSGUwWwgK5P5EC5PJJ+/1GqYx+hvKcZV5m/l2ZD7D6iw\nQWtN8oUImO7vhuNz6J6gBb1Sz+p1sY2s7Sx7NATsEjZcKkbEpj9lTJ6mIXcr5M3LKz7pdz3/p6Sx\nI3QQaJPURaYD8EPGjnoQpgyXGm0FI+PDTIWRdoSEtRrs/2Or4eYdKT4K4NJYu4kYTPxN01QhZiN5\ntWgv5STNJbBL3rRd0Xh8rHzjxitJM6FGeJWk4VKnr94UAeNfw/UylaAH78jVVgdce2UvWgfBrYbu\n1iXqE3X092eshvaK1+1u/hjbONLzG3/8gEo/oMI31hyVeSsC2P3RjC82q7ZD5dyc1WAc8DXM5FcQ\nkwoXzlYQMfakjElt2+fa9pn4EtPtcRnrxjGiDOFnc3913Utu/ktrF2Ai371cmTK2s0eJrT1wqToI\nu8WuhrTDpHjZ9/b/sdWAvhh7+SiAi7A3UG3aa/dfMHPiNFXB1ofEr+K9lDPcQiiEEYGzi7lhdHFY\nRZNrvOI0pKb7mxEhThNJHb96W4SKokiMQM4wbAe/KML7gKgOcqsB5j1vrVxxuJ6R1fCVR39xbS6p\nYfj9Gn2pSpOlcvnKYlGhfweBqHryH9j9GQ8CPMTpa9uhcgpuNSBJT1FlgRh7UsbEebSZ1RB83Jzz\n+nvujGZWw8QePI/Xk3oJPAzNXk5Jo4zt7FF1Yw/U12cJFpCxGhJLZ6nVgLzM9bLekDDQd8+FP2ma\nh7dwTKkEdjiBYsUTuPhHeXbxmwIgSbe9SLsUWy+CBBfuN/A5pjdxPpHU8attIjD/hGg1gN1E1gI5\nmC6y1QA194oRMfxi3719HFkNnHK3+wWmy4a8khpMHMZFTG/2/Ps7Ku2syfpS6cP4Ys8SUl7nQ8B3\nUucTLUgU+RqgOo83SORWg/U1+HaYiLE/pU4c2ubaziAzq2HO14ALH+pydszXkgGA8rMZCvI9B7XY\nnVv+yKPbBF8DqG6sgid219AtgyykHfGSrQYCw89QeAupvqP5wAf6xGn0N0mDsSNEk7zC1chhc2Qi\nSv4maRi70Rvua7BcRl1KkibyGyQZ+59JGi518gqTBHeHZTAnQuSfCFBhYiqO593NDtVkPTgPWBIN\naTJ8XJvpZvlwqyE3uwbitUPbthvPXMsYrCN8DQo7//c7KuU02Voyq0ul+4quZOf684+yy1SOc6Fh\nXO13Y/2aNQ9pV0mNLA8FMCN+3HaLiE1/ypmY0fYorgGGdbCJzQvb/PJ6fcDijbromu7V1Oi0fkGk\nRHm9V13X1K/XE30A8BrWM7iHkLqBBtSbFs42QTjdJAT1GAnCN9sD9+HTY8owqY0WxgCBpf2w0Q5p\nR+zGVgPyoYGDj4akaXtw3duUcbdG3KK/E2lGr9Ct40GIuPgfozRehNEbiAlJOsxRl5KkifwGPsvk\nJkmDb0nq8avVIkT+iTga0s1TdW15x4WMZpNH/MOsTG562ldg2z1NhaOf0FcXzyKg/J//+KiVQLLj\nHX4Suasy1She15SjHT3vqXpGb0ZFHL3d58fvqJTVZHPJrCyVJduj7FNoyuXvEeD7xPy9NLIETzMe\nNj2H6SX5sgCbwvkasA2uTfdsvQrYphJxyqQ0k/yFdTmYl/b4BhimYkQirnV73B+w5gGCI+Ag0xJG\nz5AXruEocfrjCjKZGLcrNKaw2NY+hBd8CT04zr0Z0GHDWqd+ZlK4s6POa+gErkyZoLq1fRCPdqig\n9yHtiI+zGoxFZJS64KGb1Cz7BYBXO8/+8Ml9l02Mxn8n0oxeAewZ88jzHaXxIozedOEEaZd81KUk\nabjfwOeY3iRp8DVJPXq1XgRk5/0TaEJALXImmi0PLIzKrJQJ01LkDDNLiZFDfJWRuyFxqBzsa5gc\nX9glva2v7LHYc78SY8iSj4p4jsv697+jUl6T7SWzqlQ+f0zv+uLWFPshsPVT30+CGU4lHrSEQ3/c\nTQH78if8ToZVzmpoIODQ+UnrBnwAtSeugAkG4hMTyLMu2hfs1wAnO9BLkwYHf+BLwI7KzkZjD4Td\ntjkDHdfWwy5NYChAC4kGgjm+DHbNsw8xUTRMZOdGdBigmdO1NmEP3L6/MmVIaiMo2C9Gt+76ClC4\nWW7UsrTqEGyXxi70xJxdx9zAaYlNAWdXBRvGd9k5ASfSCK9gGJxjZJ8LafLCse7XcU26FIFb8Btk\nBJHSOKmlV8ECWC5C8E/YtRI32l2hLorGVuG6GO7+yCooIFrQElWijAaJQ+Vgq8Et95BlsXvUzBW6\nnBY+GbKmOEFSxPzVXve/o1Jek+0ls6pU8gLsVVgb+LDQH73dEwEoi1MW+Mo6YrftH0dJrmTjyFvY\nLRfNA2sAgFll9lRkVgPQ0XuIJny9YE7Pv42tBru+c4EYZkkEd/HupUyUN3Y04jVrNQipJtJs8VdO\nsLOeHCbCki6F/AYs2cztpNTGmcQYzIsQ/BO1iwDpgyspcOLPXjSvI5xDEVK4u8ShMrYacoU94pR9\nECaGeuO+yhHaiRY0hKpXl5tizyW2jr30bTjMk715X6PLD6nkVZkonDdKRtpaTCwVmGKbGSSwIvzc\n7SsZWn4u538gp4dk6X+Z3nbb/r06Wlyd8OwezmoA/4UJVDB2Ac5QRAYCRcdHD4NLIYqNnAIVN3aO\nZov2UibKNNsvTnXZEQf2I59m0XbOjJO5zbAzA3YWVWpoM40XZ7l+4JuVeqsI3j9Bp1fNevB9dRmd\nQ8FVY/cUiAGPRlaDy8129+CWalrwcEz0uwJJj5E75nJbrtLP+K89Z6NC2wj82rD36bLL+9WXprAa\nCXKO88tq/aUqSUp7VfKFs6FkVpcKgG9tk3Ep/OmTSTv3TyX7hcwlm/LL9LIO3RsE/u1wmXNMbxDc\nYN0GfugE48AavckmwMH4GkykA5oIr/AQzIcqGLmsVZ+RDBZfRk36TsokuUZZsHeZLptRjG/jrYvY\n+2XbObME5jbHDv0jrzsfkacppd9Z+0giNs8mpN4mgouAATPTdaPmTNxs/vjCb7/BZijq6y1cfnjp\n2DCHSmo1wH7qePU2hAUgxF+TW58KJH4Oi5wgyGR0mbFuaeoWlNPCOU+2cMdM7424jh44jZaoMqH1\nl6okFM6FVMkXzuqSWV8qUEyvM3bQ9T69wagW6gODwIR/61sQwhbxYSb195D41XRdee3gPAf8LB84\nI4Q1EBZWdMXwgsUUDTRctx7fw+O2xQkKegi/+WFbfEvpadHgPAhWzfdTJs61znzf660GOIRxQNNJ\nuBZt55yky7OrAF/qL5JE+Z9Zv0E+yYTUG0Tg/gky1YILKiNFqC3MasjQmsfcoZJYDZUdmNetsxrs\nDuQQ5ZLwY78FEmp6H1MC9dcrLLx0K4eqNlPFKN+QYah0ONkyezmNIMrFsphQZUrrb1IpYCUq7VTJ\nF87ykgk5rSwVLDbhaLXZ0pwgqNqWPpkJqrlXryV1ao6JeV/OfriL2Hw/Uc89laf0L63CeKpNW8Vo\nTGyGUBCOOH6z6Ild1LCE9EZnVy8h3kyT+QJyA/3N+fxtwgm/wacEC/6JsF/0XN7+oOzMGoo0feRQ\nGYb/8vduuUVnps7ghfNKdH6TDUfM+niJxIXazJkCPOeZKc+QYeifMLZ49vILSCQ5MXXgPKn1F6kU\nNJLLz6qyuHAmSibktLJUAHcTET5bfMsJQBYz27U8hUQZNJLerngmjLT2sWtWyLCA9ECZPGs+ensu\n+WYXyP13JAdaDTbYICyOW6mkdSwuSdTtVs2X5BbR5Af6Edn3/JjwG3xKiQ3+CbNK1sq3qELHDpXE\n12CtA5gss74GM+0GvH3kBOEQap1IYo9gvSy2mtH7ZHYtJf6jvyHD0D8t6vfI3hHlxGw852mtv0gl\nrxEEU9nJqbj8rCrLCme6ZEJOK0sFcB9ZoqMyX/cAJvTI1l2XkFOXuwVo8hh1lwOgtYNdw8V9//5A\nmTxrmmtFac1WAlZs7oJ4X5GlHNLZ2qXpPN2iRtZTr7vpccWn7IpfwKgOe1svoFaSfxoBcwyrQWBJ\nhU4cKrHVYJb9gJEAfbhh+HATFY2JsWCngbHugpH40QUsKsbLnDVr7qb/w+i7eBXRiJ5lSHYAb4FG\n9PTAaYRThvZRXhVR629UiWHFlPaawJ5yCMWiwpkpGZbTqlLB/NmUrA+lxOdvXO/7PiGafXTVTVAz\nfmnfvIzqVRPtmUUOPR6PmrFrOEngLz8N76FGi6HK8lOeLkq4RqbNrCmuG6SgdQCmkYH/aMu5ed7L\nSScpfTBwBMmKH0sa2RXs9iRlJtmebJXX7yHQhWoc7vJqJg6V2Gp4mPYRJ0dsd9MaawGi3aFHrVoW\nXBraUU4CT+1gyvK54F5mi65X2/mZBDlByDCMam1zLdPTUycJtE9zqshaf6NKASuutNcEeg1EZ1nh\nTJdMyGldqWD+3thloZT4fPtVC+P7ldyCQiwhGZzskbs1b6xf+VY/OjS33eVXq8fxqKJdE5MQB/kp\nvcW/MoX8lKdLEi6XaStruybHikAz6mbagm05N8d7OekMJQUDR4is+LGkkV3BblfSdDfkXZkrsx9C\n4B665g0VOrEacBRqFm1Yq8HNQvaWsd1uqsFjTc2B1CZjTuIHLm6vn5sXbfNuMSBPkmHon8TmLilZ\nvy6ZywnxGmZ1Deec0Tqr0jsaHacS1wiQ4Ep7Tdz+WO8UzrulAulp8gTLKxQp/tp61cwXtpGHD52N\n0ucnPsIbe+csU1gH5V0vURCubNdEJD5n+al/DTcyhfwUPqOQNCJZIVOULrCbZ80WXLrwIos02lbu\nxMI53vOkpOAMJcU1M/lX3W5oZFfxf4c4PoPgHU6a9qcR4F6pDRU6thqMq9hMrsGh8QCbnSir3Vnp\ntEklvAhjspjE7pdOe4jEe3rDLmhwiQcj+TGa+BaThQxDF7PkG/HO71jOsSpZrfMqycJ6XS4TCh+q\nUsAqVtpp4konKhxRFa+J+PYdFSAtP942FCky3XjVRV17iTfyaMVZ72AbpGzNmxon6M1wOoSPhA2s\neBBuxq7hJCEH+Wl4nwtVzqULtSKKkV0j02bWbNWWOwPJuhbZlnNzvOdJScE5yjc9UhsaWV5ox94v\nmnY8VgTlfn4ESr6UaUOFjtdQ0HaUsJEIdvE2zL2kkcK4qx2RuIGLCwN2Q12L4ssmFw9G8jFo4ltM\nT02CO8fFsOxodGEzEP8njRaogjtlCFrnVZKF9bpMKYyyHqaSZ5woTaNKWzpR4YiqeE3Et++oAGkf\nbLuIXayGG3h//AgfhdtwIXLl9faCnc2wJnR2qz5jG8SHEzre+MYcUFgVQ9uxMwj9iX/kUkGDImPX\ncJIgs/w0vA/emmCr4NtsOl8rIpI1Mm1nzez7p61VoaTs5kQLeNN2/znSoOA0pYtr5lCuud/QyK5h\n/x5tfRPt3veYauofQ6D2x5ijYhsqdOxrcJ572IBngKMI2ttQwNkX/oRMwWpISGjggie/wAVnv/rr\nUdlD1sSDkTyd+BZ5UJPAF+5w9j6f9MYKnchJenLOuO2QoPWESrKwpMukwjzj3VUirBKlSZOLLZ0I\nPVEV0sRt/Szsw0U5rVYh7COGSOxiNSCjN6/KhK9XOPWOLjzc6xytTmM1xIcTuoysrwFn88xdiOj1\nnyXFRGAQbsau4SQwkWA8cmhV2TwwYQhk5Qpyikw6vlE7lVXMeoFMPneeYbQH/CxrNpdo90sJMzjO\n8cF5B2VA3cCbnCuc1Ms2T+mxcKHaHMo19xsa2TXs36QtfUDNm4w0+e8i4Mc0RsUNFTqxGrqwQekY\nNMFqiIn8wMXN77LGou4v1mrgByNRC+mPV8VzYOFChyZvD+ARbzwo08jHTg/Tv7JGs6oQmwmVmLC8\nnXN9raDwp1SSsIJ+zXvwbemwwgHxPe5MFW81hLd7qUChfBZm0WrYHDiyKqERwMwxwJ0NlLNh/sPD\n/gWfr7EI4sMJXfXIWg1uTi8OwnWJ0j88ZDWEHPOnUKDCkk1OkUnHN2oPtYInTIVxvzmJzz16uIp1\nWDnh9sv3Qcp0YiHnHZQBaYLYEqmXbZ7SCxzyzig//dh/FdNkf/W2VGfDX0H/LfnW8UKxDRU6sRr4\nR5qAUHVD4W0K9i0zMhq49C4K0ja3hgBGcdZqYAcj2UUZLfgzbvDP8A5veXsAHKQMp3d4ILmElAtU\nodQTKrlzFMzpW259CdNFUPhTKgkagzqkycWVDiscOhKCqcI04W93U8HvWY5AW6vh8aTLDbepDA7/\nS6f3WOBsF3d/2ah+WCBqkIoPJ3QizVsNPB6VDLJE0ZiE7Fn+FMw8zGl1OsDROIgmYmTJDJzg7XKH\nb9CGjZjY6CWs/eierbckq4EmF2mFKucNddXUgERsidTJtoCSBAYDzFrNh9cqzUAR+FEEUqvh4Zc9\nTCo8uUNL7a0Xv+cz7F7V3THWzC7CciMnaiG9r4G99W2VlUPIUBh+STLPaSRwHrMRVMqo4nSRFP6U\nStMaeVV84fxFqXgPPGIt+hqCt0kMxnSBj9TryVG2tBRymgqqpilxWDqJl+xriA8nNIS2L7dGhbEf\ncIbCfj9+hoLHo0ZjaMcB/nAS6jDTpxTIGlKlFPQtRdz4Ru3BluQkiRlI/DkJPLN+qejhAtZ+dM8L\n2G57TEHKfsu5iLc4gZghDch4BWVKL7BfVkXK6l9FQBFYg0BqNVyiXePXcAq0nRkp4O8oXtFs98AO\nRgotpLcaorehPQis+Z0wz85f+/sdNLpIKkXCUqMNbm6f8VjhM6jkVWGFI6tCmkRv91KBbygdTZZ4\n+HyHJgZjOuGmiagwZqhcfJ2bMDOrOyiuoYRCRIvAkITDCZ2Qia8BfrozCGnmMIlHDbXEa5kJOU4S\nUiBrSLYs3SVsB+471Yh1Ysk6/hEJKG+WHSQPZ1mH0f2FRUPaNRQuSNlvOZfwZjiR2DnSgMwcJQm8\necdmBr7eKgL/MAIjq2FfLMLGUHA0FEwbRwcjhSGF6wLit6E9kGViTYtMcMxTUikWNghDfa2k8LlU\nIk3+pFRKP7/EQyl5kfkObSpUc5qIrIYZqovtyly3Uw0vWESBksDhalBn6waPIYwPJ4QT5uEyb+A/\nmMQAGvCk+TMI3VLDJB41VPigp0ySPPWBrOvSoe/Ew0ydasKaHAmBM6gRh0Hb3OOHS1j70T3fWt6t\nsLTfC205F/Nmw4kwNZkhZciQgjJlENiFanOF9V4RUASWI3Cw1QAHu05cvqulnpbTsvaAP/b3GNT+\nF5eskleFOipJtJOpJGsSurZjS2WIY3IkvJxfIwRjUmQAEAfhrKciEPnpiGmqMOsOPjFcCEjROCx0\nTxRqyUN5ziVAm+cRKlKgCYGs4Vl6J6TD+b6wrIM61TThnCXLwmhD0mWsaXR/uYYQPbclqBykTBkw\nZXJiW1KOzCQlExhMSL0UAUVgOwIHWw2XyS1VfOMQGhWvCW8P/EN2QxsxsEcfuhVV8qpcBF2cYKdT\nSdQkdG2CJjuqsGAFjOvQQoisiwyIQjVHRNB7mJCXGaow644bdUAsCK3o2cNquMgL4EItydTVKE7X\n0/hAVv8kvZHTRduBZzrVOUsWBv7gVQnbK7icF7AOo3v2rdotUYBJRhxkHykzQQekXLZpSi8wGYeY\nk16KgCKwHoFhWBb+uJ6zTVHmv+WocRjx5+3B6CU84MfvSu+PeyaoNK0KiXI6lQRN4iabJPd/d1Rh\n/sRS16GxEFnmuyZfw5jIT0eA1HkqNusOdOA3p52GyyfMOLx9UcB/zGjWaojJd/0lx8jOmYGLRBBZ\ns9E9O73Knx0zF6RMGYu86WX0dxmlDwaO0uoPRUARWIpAOSxxFC/lJtFVtMZKern9WSEMhLdzW5fy\nd1TaW5M1pUKb9WSxpw4tCsb0/a7r2UWiELE5QRVm3UEC2C7g5ZcVZyVa8+I57sSW2ZZrMnmfds4M\nfCMHP7rnJ2XbTZ6Q6x5Byhuk88HAG9JqEkVAEcBt4ny01FFw+AUVu2ZwDNeFIh6T+TFcp1XaOc9V\n7Oj0w5yErkPLRJ06e0AkClP1U1R+1h0EgBj+vFMsJ+Dk8735TWZ27pfcgPLbX51bZJVOEVAEcgi0\ng8YG5bDR58ciUExGymbyTn0NEhmbqndWg0AVZt3Ny3u7t0+sPHbqT1DppI/wCHq6QnAmPdG/ioAi\n8F0I3IY/WonwXTCptAcgsKkH8VZDfoaKJi1Q5CwVm3U3qhVHz9QdAOAXsiy0ufnCUlORFQGGQD8O\njmZv9VYROBKBZvVofFFkwLKpej/rbjV8bDjD5UhsfpN37bcI+U39VCtF4PcRuM3NLf8+BKrhnyFQ\nnqmnXrB7xJ8B9TMZr7cTf0Z1VUQR+A0ECp2f+I2C/FIt7KaPXyq8ir0aATp9YnVCTaAIKALnQKA9\neK+Gc2ipUpwXAbuh43nlU8n2RKD2QSl7clVeioAi8DEEep2e+BjWmpGMwDMbrijT69MvRkAL+4sL\nT0VXBBCB+nZdtb5eUVMEdkcAz3zS659AQIv6nyhmVfK3Eahvdof/XbRsNZxsFxyViSJwBgRog+0z\nyKIyKAKKwFkQKPdbeNlu2bLnLDioHIqAIpAg8ND93xJE9KcioAjAsO9e5wAAE1JJREFUCcF7HNSD\nQHZ776ynpfODCLQ6I3byUuV7ab7UbDh5aal4isAfIFAPcURk3RXmDJ+ya1ed5dOfaeX9H+CoWS5B\nYM3ZVkv4Kc3uCERrI5/qP9wdYGWoCHw9As+BOwnq5vF4QqzDqyjhxOTlytV6Js1ysP5ZymL1VpAf\nhAoOf9VrgJMombdBP+sPVkDNShH4FgReA7QU/jKGQnO3m+882KEznkK+ebKmRqbQp/88AtEw9nRo\nNBrMa8vkyYBQF+Lp6qkKpAj8OQLVwE/tsYPB62CnnxfPUfQuwZ9rowKcGIHrmddYlukcftW2/IDn\nU+B6oEyBdcWRuOkcxSlKXoVQBE6EAAQ2MOPAWg3NzTQcFRt0TEt8U1fDNED6FlzfzzOjYMN5mIQg\nbXVjv89we6BMjPWVfff9sNzheAaEVAZFQBE4HoGBH0XR43CweJjtn+rFpsBLm5bjy+nrcwgHF7Vt\nZ8zTBwTVtEUzNaRfTrqCsngW6VqO2hgIXCAwnGs+eefw5yShSOSn4T3ciSTiwyhZlG5nmXjujHVv\nxgxOCh0QxMWhvxQBReASWQ2Xvi1MoHt7uzZpy5oF63bqUWRWbH3xGQTczISfxYKxrDvs8mVW3lT5\nrcaWky6nbGH03PCOEVFwK4ZigXrJ1xCTEILyU3pr/ook4sMo2SUm2VUmmXXtSwoEefEfsWD6SxFQ\nBP5NBGKrYQsGFY+M2MJA0/wyAm7E/qC1ubizR23X5xR2/U7Dl/EgFPR7nnQ5pWd6A6uhSrxj1tUA\nbjYuUH2VvPMRiS83+al/jTciifgQiEmvNN0OMs2zvrEpipq7IlENvRQBReBfR+B9q6Gg/kCEUmp5\nRcJdH24KvFNRp8tgE6gXNzpuySF1D3E0N2s8dOmYfjnpcsoLkWKfWCaGbuvWhHKBatnZxkkCXPLT\n8B7uRBLxIRCTsEm6PWSaZ93wEMhr6paJlMr9OPRT2lYPc6Lqc0VAEViJwPtWw52NXkaZUwNk2yo+\nkzoixQdtX7uJkTnSacqeDZfEjISHIOo001GaXZQ6XtQVWk2SbpG0LG5XM+dVUE0Y+q6zcQW122Gs\nTc1O6tjmSZdT8o74kiz6IVcDF6gu6ppEZgXPScJj+Wl4D3ciifgQk5FecbpdZJpn7Q08lKRL3DL4\nbHS9Wlek7o0Fbu4TzgR7xNwFJlvqYcxUfykCisAbCLxtNVSDG6jFQtjZ7MYNOnoXWBbPpMYp8Fdj\ndtoxDdsM6QwlbFO1+AqizjBNOO6k1OGirtBqmnSNpB6rq/UtPN2mYeUAXcrDBh+6SmGjDNjQ3nVs\nGdKwSND3rjnKVxe2owy9pR/3k4w2OBPEYgLdoCamPhCg5yRQXcnEZQm5eJRBLiHnVsnCcpIFMoXc\neULOO+DAKTjrjrsXSvnzZppB8AOM/mvDN3xKSDDzCS+ikJhsqoeRxPpDEVAEtiMgWA1l0a04MEAe\njNjZ7MqN1urWNatz87iwN2VVPU1bnCElx8YM5YoT+5ioM0wRZcof2smdlDpc1BVaTZOukDRUSDdW\nvTrbsjaTA+a/1vVOd6glVXsP0beuY8uQwlu/JnKG8nEJCwIcKQrW2uVBD3JIkXXABQoKRHecJMjM\nn3LxWFJO4hPyh7C7kiQsJ2Hs+C0nCblHTxnvgAOn4PxehId5OOlKtMnMKhgsTPYp4ZuZTzhPwb4y\nicmmeogC6aUIKAI7ICBYDdB+Y0O+8Hqm/mWTzs5mN24KsnMhcfLkLiSgpgzHpc4BmZnyXUophrKJ\nKjFR57P3koLvdi+ljhZ1hVYzpMsl9UhXrnrcyCNlrQb85Y45cBsQ3ozV0FzhuuN/QCGTQveEyC+g\nBI7mKNaIFIbA1mjo7s5q6ZwbJBHIOhIeT7qMfJLMsSZOPFgySVc+IeeWEZaTkCNhgjXlHsvkeCc4\nRKyZpyNep/GMbAhfrvymgA3lKzSn2aeE72c+4TwF+8pEJhvqIcqjlyKgCOyBwNhqQAdlFyKOYHF9\nG35d6qJ4Ptnvy536cSYNzWa7BqfqL9bXsGAeF4bwhlGOlOU2SUleZyaVeJuIOpd9aM/2U+pwUdEv\nMglq0GqadE7SUeUwh6HWOFt0pa7ZOB2sPYA2yoUOO7BWgxGTyjhHShGWwdrMUFZsip6YXh6AxaO6\nlHVnpIDOzWQK/9kNz6xA3h9AL+1fTgIpjUEQJwS6uNudSBhxE4WNZAIVvJeFiRVx8blHTxlvj0PM\nmnkj4rMuyaPGMkxv69uAe8qPPqVM3EqQIPeRs/ookiT1sHreF28uk8o+97tqrstHUOWdbOM5tvpe\nEfhiBIbhfxLp40MlcFq6xtVq9jLOwdY1t/iols/aNrPZpWuP4bOzVgOfSQ2zwsAlNCQ0V8xJaYyF\n+c1Q+iFTH6YSMNnEFYkqZS9LKirFJT2PqF6BHKhLRZ0BdVQ5APWiu5hW1w1socOGEjSu+MpsBVDS\nVoTUA0MaKuMcaVh/OEd5eTh/QmBaXfu+N5Ng9WCSv8ieyQvka49MkjwN4vl0sNYTDYxE2eShIGyc\nLjgSAmNcRhqxdrknTwNvgixO57wRhm986v0rPhWX5+zvX7fBNBHxp8Rrm6+CkMZLEEWJZD4dzsSH\nZ4zqoTWRQjPlJXvnxk5g1QumaCiXCoN29FIEfh2Bsa/hTq0oqm4DmmgGFDoBM7q6h1mJSl7QbWaz\nsdVHHmBzWKuB+ORmsoG4dG0KJ4VHfowVmhyR0g+ZXN5GAPyv51r5p3jDRRWzj4adlL+sFJeUtY5/\nK+o8qEtFTUFNUB1VDkC3aqzfqvCjwb5okbC9DUVRNDYNEApWAxzAKJGy9YdUGjIlFrlfAkCkdxNw\nC2+gMpuXlPGEQIYa/pNJkqdMPEonJ4zTicLGJMBu7MZISFzu8VPOm3CIKSCwhF5cQlGh/JkP3KsG\nNzAN1N8xLiX6lC78E+bfkM8oooCn/iNn9ZEz8aEfaT18GMOJopO5aG/c0+a4z8Xjjzcy06SKwBch\nMLYaoqBp+8mElWp34z5ofFsMi9iMnznR2M5mP8z3Zrb0sVYDn0mlfiKZbHWRatEcsxtjLaAMQ6bo\nEB6QLms1cFGhAXSd25ykGaVoNHgmUUF5SastoqagJqiOKgerFePujr3EW+q84TZ0KwmN+cnXH05S\n1mDbUliFyLREP9krNzxkAkli4DOJhIuXSycknBXW8JLcGFEmYu4R7yxk3i3jJ5NslqIzkYdWmIWr\n9a13YNuvHtIK31DyXXCKTH3kJP7rTutha1qlAljseLnwl4taDTuCqqx+AoGR1RDvgDOYjv/hTQN7\nHmYTvJayAxOcnDCbbc9GhgFjWwwFzvhFc6286QxNGTVZMWkYY81Q+iGTb7tcKWWtBi5qmH6Ps2e9\ng8s/q1SQlHV+olKfEhUAEPPnA9eFqKagJlbDqHKwL4RCR9kjflt1QzhAKkjDSeieLxKcpoRtBCge\nV7QaYKFvzWsh5WD/skKPX9CvSGZ6eOHi+YfxjZhwVljgIbkxYtZy7py3DBn3RoQhgeFtm4A4m+iX\n9aR1/SX+lLJfe5Ag/srETycioU8mrYdXY+vve0BnT9bSCquhrHjEVwSS/lAEfgeBkdXwCBaBj1p4\nJNMQN+MRNCDECy/rFrbwgQkJO5tNu+eAi9wkSOZaWbMcGhIXT5SQhjHWHCVN4KZDyJHVIIsqZy9K\nKisVJGVWg8z1c6LK+a8XNQU1sRrsV2ErB8HrvxS+T7F/KN/4KBr5NXu6nPIikcI8dO9nThhbc8sK\nPX11+G9JWPga5Z2n1kkjsubeiDBPYBnb6A+XyahY8blZ0gBLTuKvPvmEA5z+E04opPqYkLhPhtXD\nsmi7CkyLR/GEkEw0ft67UMEWIhpexXArjCH7bMquayznsni1sAfN43rv+vZaYjxH398GiM1phvur\nhOPYIPeq619mzwtH/Z5AmloROB0CI6shOsHSbJ8zmtt8sKCfNhgQEOmG8UgluHzdbDa1FC/4nHp5\nctcC4huSi+1ckklXNsaapgxDpoIW4zvEU6shI6qYPR+PhvxFpZikzGqQuH5SVCn/aOAatJJIvagp\nqJLVYCuHh9dX+DjGzj/+2xtY5Alub+kS/QES4QefyY6EXQRg3gizWJUxpQWq+GhcrPi0hp4bDwWL\nvvrkE2bfEFW2hEL6dGISoR4+8Oizp2mDdglrqExEpdmSjI77fD7BTVrakA1s0B4YwXEv+hqmcs0x\nHXZfEbtpBVgNdr8rmDN5eGoESS9F4GcQ+O9/k8FHZAaYmV+0GqLJ35uZtrAQFMxqqPGMgTpsx3cB\nr+XERTYFkFBDIlPzMdYkJRsypXOcidWwTtRNkk4r9ZWipqBKVoOpHCN4oWDZNk5yMf/BU++G/oO8\nz5olq+xGRButYm6lYh2rIX/1ga38CfOPXP50wifj62FtvGg2oGGXsAY7y1Ghv9VbDSb020R72W1s\nMFz86paHmX1NzSoL00LibIaxKi5AE6jHGOkTReCLERj5GhobuGhVcusq4xmKKMaakzf3V9e9+OBN\nbiAM72gwN0EHxHyMNU3ph0x9WDjd4p5B15vZOuhK9s4aUTdKKjd9vqp8oagMVAh/F1AF5WzlGMML\nOzdElqfH4W9vzAjxb0U4We5+zyuS6xYWTEnFSmTsr/CN8m9IeA2J+Uee+XTokwn10I5ZbFe/R1gD\nznXghaMkbzUYGwXnaCuIzoKrgbaFGpIH+CD6DppMu9GoiYGA3Ss69LwEasNT/1MEfgWBkdVAVrRV\n0IZCRQslumgmmFsN47ipR+i8JwFL/B0TtMsoadVUYJT4GjaLuix/k+8y0u8RdSzp2NfgKscYXkBE\nd/QL1fG0dyEWiURkVoNYrEQX/s589Qu+i0kSVg/NFnN2hsD+H4TYdNe7nWgwlsNbDcbKQauBNYM2\n/hLyAIdCewEfqzWJjdVQt9cBQikZ9SZZNJEicFYERlZDvNfj03wyLzYNYcLHSv9Z8xmKeB7DaNx7\nwo8C0HGHhxUEvnp2qagMjIW3Y1BHVgNVDgHesGvEwuyU7C8QoPPmQt4354yHJ2KxBkp/d+xXH+ph\nbQSyAQ1mO6jRZ+9FWnbjfQ0wMkKrARsN2wRaX4NvRPyGkcUNFmHDXhfBaihRiNfwWLDRxTKhlEoR\nOBkCI6uBFhxZOdNdnmA3GHyBHjh7tWydlvMR+k+LaM7wN/E1qKi7FEqCqq8cMrzmrIJd8lUmByHA\ngpIoBxYNKRcrEX7+b20mFCC2AMwU3A6qf3vho92aukKXA05CoFs1WA2Xm5mswL1avNVQDWBngYFg\nG0QT12DaP5jGCNSfR0ZzVAQORCC1GkxUMMsPNm+BowLga6wH/GTKWwu7LzRh+NGxhZpmuVF9znNs\nk/5NRWVlvP02RjVUjgy87w4FtwuqKZchIJQQ21E5U6zLWB9BhYsdXhB/C0MZOGDTbL32XjYVNnXW\nJsDoysRqsK4I3M6Upi/gDptFayBYC8NGQ0LATKB+TyZNrQicDIHUaihdPBCJieuX7VY5JjgeZuzw\nClYDuOKIFFwQGC0Ufp7pLu7fVNR9yiZGlVWOE9eEfTT/d7hw5+PZirVuuq4qmw7aoPK5S9MD+z+0\nboFx08By0qoZhqbqn4Mxnuqm6NoazlIZhqdbH2ZO0rLHaRna+tG+4MA/bBUd9b9TVVTTfwSBYfhv\npKlZdBQ9mf5B8UPTVH//Nu7f/l6eCQlU1Alw9NWHEbCxAx/OVLNTBBSB8yKQ+hrsQTDL5a2iYyuW\np/s0ZS34Xj8tw8L8VNSFQCnZBxDQoL4PgKxZKALfhEBqNbz4dg1LFOEOzCX0SqMIKALfg4AuIPye\nslJJFYGPIJBaDXQy7eLMKRBocQIlVAQUga9BgC+S+hqhVVBFQBE4DgFuNTwgwMdswb4mu2Ktc2IN\nc6VVBBSBP0WAb+P2p4Jo5oqAInAOBLjVcH1exlvDzYnJd4Cao9X3ioAi8F0IxLu+fZfsKq0ioAgc\ngAC3GqrWHHO9LhfaTm1dKqVWBBSBL0CgxE0R9VIEFAFFwCPArQb/cNUN2wVmVTolVgQUgbMj0LG9\nX88uq8qnCCgCn0DgfatBAxs+UU6ahyLwFwg8w4Zuf5G95qkIKAKnQyC2Grp2/XnGD7475On0U4EU\nAUVgOwI6QbEdO02pCPwmAje+38IL9nPv4dCWdVfYk31dOqVWBBSBcyPQsdNuzy2pSqcIKAIfQuCJ\nR8nTdcPd01e3E7qKgvDTv4rAbyGgQUu/VZ6qjSKwAwKvIey3UJvzK+/uWJblzO/2cPnlCZRSEVAE\nvgCBXmMhv6CUVERF4MMI3MNBEpVpI26rT63sV7snPqyjZqcIKAIbELjiUdF6KQKKgCLAEejCsdeV\n6f1v6xdoa+PCEdV7ReA3EOjv33Pm228grlooAl+BQOPDpK2v4b7eaijv1VeoqkIqAorAYgTqO8Y5\n6aUIKAKKQILAleYobFzDloWUva7qTkDVn4rAtyPQ6PzEtxehyq8IHIRAO7hwxm1rKFCqYvV6zYN0\nUbaKgCKwCwIvtrpqF4bKRBFQBH4GgYezGjoYXKzfr8HA0Kyf1/gZ+FQRReD3EHhcf08n1UgRUAT2\nRqBr261eyULnQPcuDeWnCPwZAnWjkZB/Br5mrAicE4H/BzrSmNNzCwoKAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\begin{cases} \\frac{0.2}{\\left(4 D_{1} + D_{2}\\right) \\left(\\frac{D_{3}}{4 D_{1} + D_{2}} + 1\\right)} + \\frac{0.2}{\\left(D_{1} + 4 D_{2}\\right) \\left(\\frac{D_{3}}{D_{1} + 4 D_{2}} + 1\\right)} + \\frac{0.2}{\\left(D_{1} + D_{2}\\right) \\left(\\frac{D_{3}}{D_{1} + D_{2}} + 1\\right)} + \\frac{0.4}{\\left(1 - \\frac{2}{2 D_{1} + 2 D_{2} + 2 D_{3}} \\sqrt{\\operatorname{polar\\_lift}{\\left (D_{1}^{2} - D_{1} D_{2} - D_{1} D_{3} + D_{2}^{2} - D_{2} D_{3} + D_{3}^{2} \\right )}}\\right) \\left(2 D_{1} + 2 D_{2} + 2 D_{3}\\right)} & \\text{for}\\: \\left|{\\operatorname{periodic_{argument}}{\\left (e^{i \\pi} \\sqrt{\\operatorname{polar\\_lift}{\\left (D_{1}^{2} - D_{1} D_{2} - D_{1} D_{3} + D_{2}^{2} - D_{2} D_{3} + D_{3}^{2} \\right )}},\\infty \\right )}}\\right| \\leq \\frac{\\pi}{2} \\\\\\int_{0}^{\\infty} 0.2 \\left(e^{t \\left(4 D_{1} + 7 D_{2} + 7 D_{3}\\right)} + e^{t \\left(7 D_{1} + 4 D_{2} + 7 D_{3}\\right)} + e^{t \\left(7 D_{1} + 7 D_{2} + 7 D_{3}\\right)} + 2 e^{t \\left(6 D_{1} + 6 D_{2} + 6 D_{3} + 2 \\sqrt{D_{1}^{2} - D_{1} D_{2} - D_{1} D_{3} + D_{2}^{2} - D_{2} D_{3} + D_{3}^{2}}\\right)}\\right) e^{- 8 t \\left(D_{1} + D_{2} + D_{3}\\right)}\\, dt & \\text{otherwise} \\end{cases}$$"
      ],
      "text/plain": [
       "⎧                                                                             \n",
       "⎪                  0.2                           0.2                         0\n",
       "⎪      ─────────────────────────── + ─────────────────────────── + ───────────\n",
       "⎪                  ⎛    D₃       ⎞               ⎛    D₃       ⎞             ⎛\n",
       "⎪      (4⋅D₁ + D₂)⋅⎜───────── + 1⎟   (D₁ + 4⋅D₂)⋅⎜───────── + 1⎟   (D₁ + D₂)⋅⎜\n",
       "⎪                  ⎝4⋅D₁ + D₂    ⎠               ⎝D₁ + 4⋅D₂    ⎠             ⎝\n",
       "⎪                                                                             \n",
       "⎪                                                                             \n",
       "⎨                                                                             \n",
       "⎪∞                                                                            \n",
       "⎪⌠                                                                            \n",
       "⎪⎮     ⎛                                                                      \n",
       "⎪⎮     ⎜                                                                      \n",
       "⎪⎮     ⎜ t⋅(4⋅D₁ + 7⋅D₂ + 7⋅D₃)    t⋅(7⋅D₁ + 4⋅D₂ + 7⋅D₃)    t⋅(7⋅D₁ + 7⋅D₂ + \n",
       "⎪⎮ 0.2⋅⎝ℯ                       + ℯ                       + ℯ                 \n",
       "⎪⌡                                                                            \n",
       "⎩0                                                                            \n",
       "\n",
       "                                                                              \n",
       ".2                                                      0.4                   \n",
       "──────────── + ───────────────────────────────────────────────────────────────\n",
       "   D₃      ⎞   ⎛         _____________________________________________________\n",
       "─────── + 1⎟   ⎜        ╱           ⎛  2                     2             2⎞ \n",
       "D₁ + D₂    ⎠   ⎜    2⋅╲╱  polar_lift⎝D₁  - D₁⋅D₂ - D₁⋅D₃ + D₂  - D₂⋅D₃ + D₃ ⎠ \n",
       "               ⎜1 - ──────────────────────────────────────────────────────────\n",
       "               ⎝                        2⋅D₁ + 2⋅D₂ + 2⋅D₃                    \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "             ⎛                          ______________________________________\n",
       "             ⎜                         ╱   2                     2            \n",
       "7⋅D₃)      t⋅⎝6⋅D₁ + 6⋅D₂ + 6⋅D₃ + 2⋅╲╱  D₁  - D₁⋅D₂ - D₁⋅D₃ + D₂  - D₂⋅D₃ + D\n",
       "      + 2⋅ℯ                                                                   \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                   │                 ⎛        ________________\n",
       "                                   │                 ⎜ ⅈ⋅π   ╱           ⎛  2 \n",
       "──────────────────────         for │periodic_argument⎝ℯ   ⋅╲╱  polar_lift⎝D₁  \n",
       "⎞                                                                             \n",
       "⎟                                                                             \n",
       "⎟                                                                             \n",
       "⎟⋅(2⋅D₁ + 2⋅D₂ + 2⋅D₃)                                                        \n",
       "⎠                                                                             \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "___⎞⎞                                                                         \n",
       " 2 ⎟⎟                                                                         \n",
       "₃  ⎠⎟  -8⋅t⋅(D₁ + D₂ + D₃)                                                    \n",
       "    ⎠⋅ℯ                    dt                                            other\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "_____________________________________   ⎞│    \n",
       "                    2             2⎞    ⎟│   π\n",
       "- D₁⋅D₂ - D₁⋅D₃ + D₂  - D₂⋅D₃ + D₃ ⎠ , ∞⎠│ ≤ ─\n",
       "                                             2\n",
       "                                              \n",
       "                                              \n",
       "                                              \n",
       "                                              \n",
       "                                              \n",
       "                                              \n",
       "                                              \n",
       "                                              \n",
       "                                              \n",
       "                                              \n",
       "wise                                          \n",
       "                                              \n",
       "                                              "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "with assume.assuming(Q.is_true(d1 > d2), Q.is_true(d2 > d3)):\n",
    "    res = integrate(C2, (t, 0, oo))\n",
    "res"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  },
  "toc": {
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": "block",
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}