\[ \int \frac {e^{-\frac {3025+6065 x+2856 x^2+58 x^3-174 x^4-3 x^5+9 x^6+x^7+\left (660+852 x+144 x^2-60 x^3-12 x^4\right ) \log (4)+\left (-74-106 x-24 x^2+10 x^3+2 x^4\right ) \log ^2(4)+(-12-12 x) \log ^3(4)+(1+x) \log ^4(4)}{3025+1760 x-184 x^2-238 x^3-16 x^4+8 x^5+x^6+\left (660+192 x-48 x^2-12 x^3\right ) \log (4)+\left (-74-32 x+8 x^2+2 x^3\right ) \log ^2(4)-12 \log ^3(4)+\log ^4(4)}} \left (-166375+91575 x+259580 x^2+126599 x^3+21533 x^4+3943 x^5+2515 x^6+625 x^7+17 x^8-11 x^9-x^{10}+\left (-54450+30450 x+50352 x^2+9612 x^3-2076 x^4-282 x^5+126 x^6+18 x^7\right ) \log (4)+\left (3135-863 x-6232 x^2-1926 x^3+238 x^4+47 x^5-21 x^6-3 x^7\right ) \log ^2(4)+\left (1764-1188 x-720 x^2+108 x^3+36 x^4\right ) \log ^3(4)+\left (-57+9 x+60 x^2-9 x^3-3 x^4\right ) \log ^4(4)+(-18+18 x) \log ^5(4)+(1-x) \log ^6(4)\right )}{-166375-145200 x-5940 x^2+26099 x^3+5712 x^4-1320 x^5-485 x^6+12 x^8+x^9+\left (-54450-31680 x+3312 x^2+4284 x^3+288 x^4-144 x^5-18 x^6\right ) \log (4)+\left (3135+3552 x-120 x^2-606 x^3-48 x^4+24 x^5+3 x^6\right ) \log ^2(4)+\left (1764+576 x-144 x^2-36 x^3\right ) \log ^3(4)+\left (-57-48 x+12 x^2+3 x^3\right ) \log ^4(4)-18 \log ^5(4)+\log ^6(4)} \, dx \]
Optimal antiderivative \[ x \,{\mathrm e}^{-\frac {5 x}{\left (x +\frac {\left (2 \ln \left (2\right )-3\right )^{2}}{\left (4+x \right )^{2}}-4\right )^{2}}-x -1} \]
command
integrate((64*(1-x)*ln(2)**6+32*(18*x-18)*ln(2)**5+16*(-3*x**4-9*x**3+60*x**2+9*x-57)*ln(2)**4+8*(36*x**4+108*x**3-720*x**2-1188*x+1764)*ln(2)**3+4*(-3*x**7-21*x**6+47*x**5+238*x**4-1926*x**3-6232*x**2-863*x+3135)*ln(2)**2+2*(18*x**7+126*x**6-282*x**5-2076*x**4+9612*x**3+50352*x**2+30450*x-54450)*ln(2)-x**10-11*x**9+17*x**8+625*x**7+2515*x**6+3943*x**5+21533*x**4+126599*x**3+259580*x**2+91575*x-166375)/(64*ln(2)**6-576*ln(2)**5+16*(3*x**3+12*x**2-48*x-57)*ln(2)**4+8*(-36*x**3-144*x**2+576*x+1764)*ln(2)**3+4*(3*x**6+24*x**5-48*x**4-606*x**3-120*x**2+3552*x+3135)*ln(2)**2+2*(-18*x**6-144*x**5+288*x**4+4284*x**3+3312*x**2-31680*x-54450)*ln(2)+x**9+12*x**8-485*x**6-1320*x**5+5712*x**4+26099*x**3-5940*x**2-145200*x-166375)/exp((16*(1+x)*ln(2)**4+8*(-12*x-12)*ln(2)**3+4*(2*x**4+10*x**3-24*x**2-106*x-74)*ln(2)**2+2*(-12*x**4-60*x**3+144*x**2+852*x+660)*ln(2)+x**7+9*x**6-3*x**5-174*x**4+58*x**3+2856*x**2+6065*x+3025)/(16*ln(2)**4-96*ln(2)**3+4*(2*x**3+8*x**2-32*x-74)*ln(2)**2+2*(-12*x**3-48*x**2+192*x+660)*ln(2)+x**6+8*x**5-16*x**4-238*x**3-184*x**2+1760*x+3025)),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ x e^{- \frac {x^{7} + 9 x^{6} - 3 x^{5} - 174 x^{4} + 58 x^{3} + 2856 x^{2} + 6065 x + \left (- 96 x - 96\right ) \log {\left (2 \right )}^{3} + \left (16 x + 16\right ) \log {\left (2 \right )}^{4} + \left (- 24 x^{4} - 120 x^{3} + 288 x^{2} + 1704 x + 1320\right ) \log {\left (2 \right )} + \left (8 x^{4} + 40 x^{3} - 96 x^{2} - 424 x - 296\right ) \log {\left (2 \right )}^{2} + 3025}{x^{6} + 8 x^{5} - 16 x^{4} - 238 x^{3} - 184 x^{2} + 1760 x + \left (- 24 x^{3} - 96 x^{2} + 384 x + 1320\right ) \log {\left (2 \right )} + \left (8 x^{3} + 32 x^{2} - 128 x - 296\right ) \log {\left (2 \right )}^{2} - 96 \log {\left (2 \right )}^{3} + 16 \log {\left (2 \right )}^{4} + 3025}} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________