Integrand size = 574, antiderivative size = 37 \[ \int \frac {e^{\frac {16+128 x^2+16 e^8 x^2+64 x^4+e^4 \left (-32 x-64 x^3\right )+\left (-48 x^2-8 e^8 x^2-32 x^4+e^4 \left (8 x+32 x^3\right )\right ) \log (3)+\left (4 x^2+e^8 x^2-4 e^4 x^3+4 x^4\right ) \log ^2(3)}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}} \left (32 x^2-16 x^2 \log (3)+2 x^2 \log ^2(3)\right )+e^{\frac {2 \left (16+128 x^2+16 e^8 x^2+64 x^4+e^4 \left (-32 x-64 x^3\right )+\left (-48 x^2-8 e^8 x^2-32 x^4+e^4 \left (8 x+32 x^3\right )\right ) \log (3)+\left (4 x^2+e^8 x^2-4 e^4 x^3+4 x^4\right ) \log ^2(3)\right )}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}} \left (-64+256 x^4+e^4 \left (64 x-128 x^3\right )+\left (-128 x^4+e^4 \left (-16 x+64 x^3\right )\right ) \log (3)+\left (-8 e^4 x^3+16 x^4\right ) \log ^2(3)\right )+\left (32 x^2-16 x^2 \log (3)+2 x^2 \log ^2(3)+e^{\frac {16+128 x^2+16 e^8 x^2+64 x^4+e^4 \left (-32 x-64 x^3\right )+\left (-48 x^2-8 e^8 x^2-32 x^4+e^4 \left (8 x+32 x^3\right )\right ) \log (3)+\left (4 x^2+e^8 x^2-4 e^4 x^3+4 x^4\right ) \log ^2(3)}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}} \left (-64+256 x^4+e^4 \left (64 x-128 x^3\right )+\left (-128 x^4+e^4 \left (-16 x+64 x^3\right )\right ) \log (3)+\left (-8 e^4 x^3+16 x^4\right ) \log ^2(3)\right )\right ) \log (x)}{144 x^3-72 x^3 \log (3)+9 x^3 \log ^2(3)} \, dx=\frac {1}{9} \left (e^{4+\left (-e^4+2 x+\frac {4}{x (4-\log (3))}\right )^2}+\log (x)\right )^2 \]
1/3*(ln(x)+exp((2*x-exp(4)+4/(-ln(3)+4)/x)^2+4))*(1/3*ln(x)+1/3*exp((2*x-e xp(4)+4/(-ln(3)+4)/x)^2+4))
\[ \int \frac {e^{\frac {16+128 x^2+16 e^8 x^2+64 x^4+e^4 \left (-32 x-64 x^3\right )+\left (-48 x^2-8 e^8 x^2-32 x^4+e^4 \left (8 x+32 x^3\right )\right ) \log (3)+\left (4 x^2+e^8 x^2-4 e^4 x^3+4 x^4\right ) \log ^2(3)}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}} \left (32 x^2-16 x^2 \log (3)+2 x^2 \log ^2(3)\right )+e^{\frac {2 \left (16+128 x^2+16 e^8 x^2+64 x^4+e^4 \left (-32 x-64 x^3\right )+\left (-48 x^2-8 e^8 x^2-32 x^4+e^4 \left (8 x+32 x^3\right )\right ) \log (3)+\left (4 x^2+e^8 x^2-4 e^4 x^3+4 x^4\right ) \log ^2(3)\right )}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}} \left (-64+256 x^4+e^4 \left (64 x-128 x^3\right )+\left (-128 x^4+e^4 \left (-16 x+64 x^3\right )\right ) \log (3)+\left (-8 e^4 x^3+16 x^4\right ) \log ^2(3)\right )+\left (32 x^2-16 x^2 \log (3)+2 x^2 \log ^2(3)+e^{\frac {16+128 x^2+16 e^8 x^2+64 x^4+e^4 \left (-32 x-64 x^3\right )+\left (-48 x^2-8 e^8 x^2-32 x^4+e^4 \left (8 x+32 x^3\right )\right ) \log (3)+\left (4 x^2+e^8 x^2-4 e^4 x^3+4 x^4\right ) \log ^2(3)}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}} \left (-64+256 x^4+e^4 \left (64 x-128 x^3\right )+\left (-128 x^4+e^4 \left (-16 x+64 x^3\right )\right ) \log (3)+\left (-8 e^4 x^3+16 x^4\right ) \log ^2(3)\right )\right ) \log (x)}{144 x^3-72 x^3 \log (3)+9 x^3 \log ^2(3)} \, dx=\int \frac {e^{\frac {16+128 x^2+16 e^8 x^2+64 x^4+e^4 \left (-32 x-64 x^3\right )+\left (-48 x^2-8 e^8 x^2-32 x^4+e^4 \left (8 x+32 x^3\right )\right ) \log (3)+\left (4 x^2+e^8 x^2-4 e^4 x^3+4 x^4\right ) \log ^2(3)}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}} \left (32 x^2-16 x^2 \log (3)+2 x^2 \log ^2(3)\right )+e^{\frac {2 \left (16+128 x^2+16 e^8 x^2+64 x^4+e^4 \left (-32 x-64 x^3\right )+\left (-48 x^2-8 e^8 x^2-32 x^4+e^4 \left (8 x+32 x^3\right )\right ) \log (3)+\left (4 x^2+e^8 x^2-4 e^4 x^3+4 x^4\right ) \log ^2(3)\right )}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}} \left (-64+256 x^4+e^4 \left (64 x-128 x^3\right )+\left (-128 x^4+e^4 \left (-16 x+64 x^3\right )\right ) \log (3)+\left (-8 e^4 x^3+16 x^4\right ) \log ^2(3)\right )+\left (32 x^2-16 x^2 \log (3)+2 x^2 \log ^2(3)+e^{\frac {16+128 x^2+16 e^8 x^2+64 x^4+e^4 \left (-32 x-64 x^3\right )+\left (-48 x^2-8 e^8 x^2-32 x^4+e^4 \left (8 x+32 x^3\right )\right ) \log (3)+\left (4 x^2+e^8 x^2-4 e^4 x^3+4 x^4\right ) \log ^2(3)}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}} \left (-64+256 x^4+e^4 \left (64 x-128 x^3\right )+\left (-128 x^4+e^4 \left (-16 x+64 x^3\right )\right ) \log (3)+\left (-8 e^4 x^3+16 x^4\right ) \log ^2(3)\right )\right ) \log (x)}{144 x^3-72 x^3 \log (3)+9 x^3 \log ^2(3)} \, dx \]
Integrate[(E^((16 + 128*x^2 + 16*E^8*x^2 + 64*x^4 + E^4*(-32*x - 64*x^3) + (-48*x^2 - 8*E^8*x^2 - 32*x^4 + E^4*(8*x + 32*x^3))*Log[3] + (4*x^2 + E^8 *x^2 - 4*E^4*x^3 + 4*x^4)*Log[3]^2)/(16*x^2 - 8*x^2*Log[3] + x^2*Log[3]^2) )*(32*x^2 - 16*x^2*Log[3] + 2*x^2*Log[3]^2) + E^((2*(16 + 128*x^2 + 16*E^8 *x^2 + 64*x^4 + E^4*(-32*x - 64*x^3) + (-48*x^2 - 8*E^8*x^2 - 32*x^4 + E^4 *(8*x + 32*x^3))*Log[3] + (4*x^2 + E^8*x^2 - 4*E^4*x^3 + 4*x^4)*Log[3]^2)) /(16*x^2 - 8*x^2*Log[3] + x^2*Log[3]^2))*(-64 + 256*x^4 + E^4*(64*x - 128* x^3) + (-128*x^4 + E^4*(-16*x + 64*x^3))*Log[3] + (-8*E^4*x^3 + 16*x^4)*Lo g[3]^2) + (32*x^2 - 16*x^2*Log[3] + 2*x^2*Log[3]^2 + E^((16 + 128*x^2 + 16 *E^8*x^2 + 64*x^4 + E^4*(-32*x - 64*x^3) + (-48*x^2 - 8*E^8*x^2 - 32*x^4 + E^4*(8*x + 32*x^3))*Log[3] + (4*x^2 + E^8*x^2 - 4*E^4*x^3 + 4*x^4)*Log[3] ^2)/(16*x^2 - 8*x^2*Log[3] + x^2*Log[3]^2))*(-64 + 256*x^4 + E^4*(64*x - 1 28*x^3) + (-128*x^4 + E^4*(-16*x + 64*x^3))*Log[3] + (-8*E^4*x^3 + 16*x^4) *Log[3]^2))*Log[x])/(144*x^3 - 72*x^3*Log[3] + 9*x^3*Log[3]^2),x]
Integrate[(E^((16 + 128*x^2 + 16*E^8*x^2 + 64*x^4 + E^4*(-32*x - 64*x^3) + (-48*x^2 - 8*E^8*x^2 - 32*x^4 + E^4*(8*x + 32*x^3))*Log[3] + (4*x^2 + E^8 *x^2 - 4*E^4*x^3 + 4*x^4)*Log[3]^2)/(16*x^2 - 8*x^2*Log[3] + x^2*Log[3]^2) )*(32*x^2 - 16*x^2*Log[3] + 2*x^2*Log[3]^2) + E^((2*(16 + 128*x^2 + 16*E^8 *x^2 + 64*x^4 + E^4*(-32*x - 64*x^3) + (-48*x^2 - 8*E^8*x^2 - 32*x^4 + E^4 *(8*x + 32*x^3))*Log[3] + (4*x^2 + E^8*x^2 - 4*E^4*x^3 + 4*x^4)*Log[3]^2)) /(16*x^2 - 8*x^2*Log[3] + x^2*Log[3]^2))*(-64 + 256*x^4 + E^4*(64*x - 128* x^3) + (-128*x^4 + E^4*(-16*x + 64*x^3))*Log[3] + (-8*E^4*x^3 + 16*x^4)*Lo g[3]^2) + (32*x^2 - 16*x^2*Log[3] + 2*x^2*Log[3]^2 + E^((16 + 128*x^2 + 16 *E^8*x^2 + 64*x^4 + E^4*(-32*x - 64*x^3) + (-48*x^2 - 8*E^8*x^2 - 32*x^4 + E^4*(8*x + 32*x^3))*Log[3] + (4*x^2 + E^8*x^2 - 4*E^4*x^3 + 4*x^4)*Log[3] ^2)/(16*x^2 - 8*x^2*Log[3] + x^2*Log[3]^2))*(-64 + 256*x^4 + E^4*(64*x - 1 28*x^3) + (-128*x^4 + E^4*(-16*x + 64*x^3))*Log[3] + (-8*E^4*x^3 + 16*x^4) *Log[3]^2))*Log[x])/(144*x^3 - 72*x^3*Log[3] + 9*x^3*Log[3]^2), x]
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {\left (32 x^2+2 x^2 \log ^2(3)-16 x^2 \log (3)\right ) \exp \left (\frac {64 x^4+e^4 \left (-64 x^3-32 x\right )+16 e^8 x^2+128 x^2+\left (4 x^4-4 e^4 x^3+e^8 x^2+4 x^2\right ) \log ^2(3)+\left (-32 x^4+e^4 \left (32 x^3+8 x\right )-8 e^8 x^2-48 x^2\right ) \log (3)+16}{16 x^2+x^2 \log ^2(3)-8 x^2 \log (3)}\right )+\left (256 x^4+e^4 \left (64 x-128 x^3\right )+\left (16 x^4-8 e^4 x^3\right ) \log ^2(3)+\left (e^4 \left (64 x^3-16 x\right )-128 x^4\right ) \log (3)-64\right ) \exp \left (\frac {2 \left (64 x^4+e^4 \left (-64 x^3-32 x\right )+16 e^8 x^2+128 x^2+\left (4 x^4-4 e^4 x^3+e^8 x^2+4 x^2\right ) \log ^2(3)+\left (-32 x^4+e^4 \left (32 x^3+8 x\right )-8 e^8 x^2-48 x^2\right ) \log (3)+16\right )}{16 x^2+x^2 \log ^2(3)-8 x^2 \log (3)}\right )+\log (x) \left (\left (256 x^4+e^4 \left (64 x-128 x^3\right )+\left (16 x^4-8 e^4 x^3\right ) \log ^2(3)+\left (e^4 \left (64 x^3-16 x\right )-128 x^4\right ) \log (3)-64\right ) \exp \left (\frac {64 x^4+e^4 \left (-64 x^3-32 x\right )+16 e^8 x^2+128 x^2+\left (4 x^4-4 e^4 x^3+e^8 x^2+4 x^2\right ) \log ^2(3)+\left (-32 x^4+e^4 \left (32 x^3+8 x\right )-8 e^8 x^2-48 x^2\right ) \log (3)+16}{16 x^2+x^2 \log ^2(3)-8 x^2 \log (3)}\right )+32 x^2+2 x^2 \log ^2(3)-16 x^2 \log (3)\right )}{144 x^3+9 x^3 \log ^2(3)-72 x^3 \log (3)} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {\left (32 x^2+2 x^2 \log ^2(3)-16 x^2 \log (3)\right ) \exp \left (\frac {64 x^4+e^4 \left (-64 x^3-32 x\right )+16 e^8 x^2+128 x^2+\left (4 x^4-4 e^4 x^3+e^8 x^2+4 x^2\right ) \log ^2(3)+\left (-32 x^4+e^4 \left (32 x^3+8 x\right )-8 e^8 x^2-48 x^2\right ) \log (3)+16}{16 x^2+x^2 \log ^2(3)-8 x^2 \log (3)}\right )+\left (256 x^4+e^4 \left (64 x-128 x^3\right )+\left (16 x^4-8 e^4 x^3\right ) \log ^2(3)+\left (e^4 \left (64 x^3-16 x\right )-128 x^4\right ) \log (3)-64\right ) \exp \left (\frac {2 \left (64 x^4+e^4 \left (-64 x^3-32 x\right )+16 e^8 x^2+128 x^2+\left (4 x^4-4 e^4 x^3+e^8 x^2+4 x^2\right ) \log ^2(3)+\left (-32 x^4+e^4 \left (32 x^3+8 x\right )-8 e^8 x^2-48 x^2\right ) \log (3)+16\right )}{16 x^2+x^2 \log ^2(3)-8 x^2 \log (3)}\right )+\log (x) \left (\left (256 x^4+e^4 \left (64 x-128 x^3\right )+\left (16 x^4-8 e^4 x^3\right ) \log ^2(3)+\left (e^4 \left (64 x^3-16 x\right )-128 x^4\right ) \log (3)-64\right ) \exp \left (\frac {64 x^4+e^4 \left (-64 x^3-32 x\right )+16 e^8 x^2+128 x^2+\left (4 x^4-4 e^4 x^3+e^8 x^2+4 x^2\right ) \log ^2(3)+\left (-32 x^4+e^4 \left (32 x^3+8 x\right )-8 e^8 x^2-48 x^2\right ) \log (3)+16}{16 x^2+x^2 \log ^2(3)-8 x^2 \log (3)}\right )+32 x^2+2 x^2 \log ^2(3)-16 x^2 \log (3)\right )}{9 x^3 \log ^2(3)+x^3 (144-72 \log (3))}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {\left (32 x^2+2 x^2 \log ^2(3)-16 x^2 \log (3)\right ) \exp \left (\frac {64 x^4+e^4 \left (-64 x^3-32 x\right )+16 e^8 x^2+128 x^2+\left (4 x^4-4 e^4 x^3+e^8 x^2+4 x^2\right ) \log ^2(3)+\left (-32 x^4+e^4 \left (32 x^3+8 x\right )-8 e^8 x^2-48 x^2\right ) \log (3)+16}{16 x^2+x^2 \log ^2(3)-8 x^2 \log (3)}\right )+\left (256 x^4+e^4 \left (64 x-128 x^3\right )+\left (16 x^4-8 e^4 x^3\right ) \log ^2(3)+\left (e^4 \left (64 x^3-16 x\right )-128 x^4\right ) \log (3)-64\right ) \exp \left (\frac {2 \left (64 x^4+e^4 \left (-64 x^3-32 x\right )+16 e^8 x^2+128 x^2+\left (4 x^4-4 e^4 x^3+e^8 x^2+4 x^2\right ) \log ^2(3)+\left (-32 x^4+e^4 \left (32 x^3+8 x\right )-8 e^8 x^2-48 x^2\right ) \log (3)+16\right )}{16 x^2+x^2 \log ^2(3)-8 x^2 \log (3)}\right )+\log (x) \left (\left (256 x^4+e^4 \left (64 x-128 x^3\right )+\left (16 x^4-8 e^4 x^3\right ) \log ^2(3)+\left (e^4 \left (64 x^3-16 x\right )-128 x^4\right ) \log (3)-64\right ) \exp \left (\frac {64 x^4+e^4 \left (-64 x^3-32 x\right )+16 e^8 x^2+128 x^2+\left (4 x^4-4 e^4 x^3+e^8 x^2+4 x^2\right ) \log ^2(3)+\left (-32 x^4+e^4 \left (32 x^3+8 x\right )-8 e^8 x^2-48 x^2\right ) \log (3)+16}{16 x^2+x^2 \log ^2(3)-8 x^2 \log (3)}\right )+32 x^2+2 x^2 \log ^2(3)-16 x^2 \log (3)\right )}{x^3 \left (144+9 \log ^2(3)-72 \log (3)\right )}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {\int \frac {2 \left (3^{-\frac {32 x^4+8 e^8 x^2+48 x^2-e^4 \left (32 x^3+8 x\right )}{\log ^2(3) x^2-8 \log (3) x^2+16 x^2}} \exp \left (\frac {64 x^4+16 e^8 x^2+128 x^2-32 e^4 \left (2 x^3+x\right )+\left (4 x^4-4 e^4 x^3+e^8 x^2+4 x^2\right ) \log ^2(3)+16}{\log ^2(3) x^2-8 \log (3) x^2+16 x^2}\right ) \left (\log ^2(3) x^2-8 \log (3) x^2+16 x^2\right )-4\ 3^{-\frac {2 \left (32 x^4+8 e^8 x^2+48 x^2-e^4 \left (32 x^3+8 x\right )\right )}{\log ^2(3) x^2-8 \log (3) x^2+16 x^2}} \exp \left (\frac {2 \left (64 x^4+16 e^8 x^2+128 x^2-32 e^4 \left (2 x^3+x\right )+\left (4 x^4-4 e^4 x^3+e^8 x^2+4 x^2\right ) \log ^2(3)+16\right )}{\log ^2(3) x^2-8 \log (3) x^2+16 x^2}\right ) \left (-32 x^4-8 e^4 \left (x-2 x^3\right )+\left (e^4 x^3-2 x^4\right ) \log ^2(3)+2 \left (8 x^4+e^4 \left (x-4 x^3\right )\right ) \log (3)+8\right )+\left (\log ^2(3) x^2-8 \log (3) x^2+16 x^2-4\ 3^{-\frac {32 x^4+8 e^8 x^2+48 x^2-e^4 \left (32 x^3+8 x\right )}{\log ^2(3) x^2-8 \log (3) x^2+16 x^2}} \exp \left (\frac {64 x^4+16 e^8 x^2+128 x^2-32 e^4 \left (2 x^3+x\right )+\left (4 x^4-4 e^4 x^3+e^8 x^2+4 x^2\right ) \log ^2(3)+16}{\log ^2(3) x^2-8 \log (3) x^2+16 x^2}\right ) \left (-32 x^4-8 e^4 \left (x-2 x^3\right )+\left (e^4 x^3-2 x^4\right ) \log ^2(3)+2 \left (8 x^4+e^4 \left (x-4 x^3\right )\right ) \log (3)+8\right )\right ) \log (x)\right )}{x^3}dx}{9 (4-\log (3))^2}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2 \int \frac {3^{-\frac {8 \left (4 x^4+e^8 x^2+6 x^2-e^4 \left (4 x^3+x\right )\right )}{\log ^2(3) x^2-8 \log (3) x^2+16 x^2}} \exp \left (\frac {64 x^4+16 e^8 x^2+128 x^2-32 e^4 \left (2 x^3+x\right )+\left (4 x^4-4 e^4 x^3+e^8 x^2+4 x^2\right ) \log ^2(3)+16}{\log ^2(3) x^2-8 \log (3) x^2+16 x^2}\right ) \left (\log ^2(3) x^2-8 \log (3) x^2+16 x^2\right )-4\ 3^{-\frac {16 \left (4 x^4+e^8 x^2+6 x^2-e^4 \left (4 x^3+x\right )\right )}{\log ^2(3) x^2-8 \log (3) x^2+16 x^2}} \exp \left (\frac {2 \left (64 x^4+16 e^8 x^2+128 x^2-32 e^4 \left (2 x^3+x\right )+\left (4 x^4-4 e^4 x^3+e^8 x^2+4 x^2\right ) \log ^2(3)+16\right )}{\log ^2(3) x^2-8 \log (3) x^2+16 x^2}\right ) \left (-32 x^4-8 e^4 \left (x-2 x^3\right )+\left (e^4 x^3-2 x^4\right ) \log ^2(3)+2 \left (8 x^4+e^4 \left (x-4 x^3\right )\right ) \log (3)+8\right )+\left (\log ^2(3) x^2-8 \log (3) x^2+16 x^2-4\ 3^{-\frac {8 \left (4 x^4+e^8 x^2+6 x^2-e^4 \left (4 x^3+x\right )\right )}{\log ^2(3) x^2-8 \log (3) x^2+16 x^2}} \exp \left (\frac {64 x^4+16 e^8 x^2+128 x^2-32 e^4 \left (2 x^3+x\right )+\left (4 x^4-4 e^4 x^3+e^8 x^2+4 x^2\right ) \log ^2(3)+16}{\log ^2(3) x^2-8 \log (3) x^2+16 x^2}\right ) \left (-32 x^4-8 e^4 \left (x-2 x^3\right )+\left (e^4 x^3-2 x^4\right ) \log ^2(3)+2 \left (8 x^4+e^4 \left (x-4 x^3\right )\right ) \log (3)+8\right )\right ) \log (x)}{x^3}dx}{9 (4-\log (3))^2}\) |
| \(\Big \downarrow \) 2010 |
| \(\displaystyle \frac {2 \int \left (\frac {4\ 3^{-\frac {16 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {2 \left (4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16\right )}{x^2 (-4+\log (3))^2}\right ) \left (2-x^2 (4-\log (3))\right ) \left (-\left ((8-\log (9)) x^2\right )+e^4 (4-\log (3)) x-4\right )}{x^3}+\frac {(-4+\log (3))^2 \log (x)}{x}+\frac {3^{-\frac {8 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16}{x^2 (-4+\log (3))^2}\right ) \left (128 \left (1+\frac {1}{32} \log (3) (-16+\log (9))\right ) \log (x) x^4-64 e^4 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^3+16 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) x^2+32 e^4 \left (1-\frac {\log (3)}{4}\right ) \log (x) x-32 \log (x)\right )}{x^3}\right )dx}{9 (4-\log (3))^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2 \int \left (\frac {4\ 3^{-\frac {16 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {2 \left (4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16\right )}{x^2 (-4+\log (3))^2}\right ) \left (2-x^2 (4-\log (3))\right ) \left (-\left ((8-\log (9)) x^2\right )+e^4 (4-\log (3)) x-4\right )}{x^3}+\frac {(-4+\log (3))^2 \log (x)}{x}+\frac {3^{-\frac {8 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16}{x^2 (-4+\log (3))^2}\right ) \left (128 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^4-64 e^4 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^3+16 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) x^2+32 e^4 \left (1-\frac {\log (3)}{4}\right ) \log (x) x-32 \log (x)\right )}{x^3}\right )dx}{9 (4-\log (3))^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2 \int \left (\frac {4\ 3^{-\frac {16 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {2 \left (4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16\right )}{x^2 (-4+\log (3))^2}\right ) \left (2-x^2 (4-\log (3))\right ) \left (-\left ((8-\log (9)) x^2\right )+e^4 (4-\log (3)) x-4\right )}{x^3}+\frac {(-4+\log (3))^2 \log (x)}{x}+\frac {3^{-\frac {8 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16}{x^2 (-4+\log (3))^2}\right ) \left (128 \left (1+\frac {1}{32} \log (3) (-16+\log (9))\right ) \log (x) x^4-64 e^4 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^3+16 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) x^2+32 e^4 \left (1-\frac {\log (3)}{4}\right ) \log (x) x-32 \log (x)\right )}{x^3}\right )dx}{9 (4-\log (3))^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2 \int \left (\frac {4\ 3^{-\frac {16 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {2 \left (4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16\right )}{x^2 (-4+\log (3))^2}\right ) \left (2-x^2 (4-\log (3))\right ) \left (-\left ((8-\log (9)) x^2\right )+e^4 (4-\log (3)) x-4\right )}{x^3}+\frac {(-4+\log (3))^2 \log (x)}{x}+\frac {3^{-\frac {8 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16}{x^2 (-4+\log (3))^2}\right ) \left (128 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^4-64 e^4 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^3+16 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) x^2+32 e^4 \left (1-\frac {\log (3)}{4}\right ) \log (x) x-32 \log (x)\right )}{x^3}\right )dx}{9 (4-\log (3))^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2 \int \left (\frac {4\ 3^{-\frac {16 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {2 \left (4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16\right )}{x^2 (-4+\log (3))^2}\right ) \left (2-x^2 (4-\log (3))\right ) \left (-\left ((8-\log (9)) x^2\right )+e^4 (4-\log (3)) x-4\right )}{x^3}+\frac {(-4+\log (3))^2 \log (x)}{x}+\frac {3^{-\frac {8 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16}{x^2 (-4+\log (3))^2}\right ) \left (128 \left (1+\frac {1}{32} \log (3) (-16+\log (9))\right ) \log (x) x^4-64 e^4 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^3+16 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) x^2+32 e^4 \left (1-\frac {\log (3)}{4}\right ) \log (x) x-32 \log (x)\right )}{x^3}\right )dx}{9 (4-\log (3))^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2 \int \left (\frac {4\ 3^{-\frac {16 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {2 \left (4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16\right )}{x^2 (-4+\log (3))^2}\right ) \left (2-x^2 (4-\log (3))\right ) \left (-\left ((8-\log (9)) x^2\right )+e^4 (4-\log (3)) x-4\right )}{x^3}+\frac {(-4+\log (3))^2 \log (x)}{x}+\frac {3^{-\frac {8 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16}{x^2 (-4+\log (3))^2}\right ) \left (128 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^4-64 e^4 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^3+16 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) x^2+32 e^4 \left (1-\frac {\log (3)}{4}\right ) \log (x) x-32 \log (x)\right )}{x^3}\right )dx}{9 (4-\log (3))^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2 \int \left (\frac {4\ 3^{-\frac {16 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {2 \left (4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16\right )}{x^2 (-4+\log (3))^2}\right ) \left (2-x^2 (4-\log (3))\right ) \left (-\left ((8-\log (9)) x^2\right )+e^4 (4-\log (3)) x-4\right )}{x^3}+\frac {(-4+\log (3))^2 \log (x)}{x}+\frac {3^{-\frac {8 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16}{x^2 (-4+\log (3))^2}\right ) \left (128 \left (1+\frac {1}{32} \log (3) (-16+\log (9))\right ) \log (x) x^4-64 e^4 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^3+16 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) x^2+32 e^4 \left (1-\frac {\log (3)}{4}\right ) \log (x) x-32 \log (x)\right )}{x^3}\right )dx}{9 (4-\log (3))^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2 \int \left (\frac {4\ 3^{-\frac {16 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {2 \left (4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16\right )}{x^2 (-4+\log (3))^2}\right ) \left (2-x^2 (4-\log (3))\right ) \left (-\left ((8-\log (9)) x^2\right )+e^4 (4-\log (3)) x-4\right )}{x^3}+\frac {(-4+\log (3))^2 \log (x)}{x}+\frac {3^{-\frac {8 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16}{x^2 (-4+\log (3))^2}\right ) \left (128 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^4-64 e^4 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^3+16 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) x^2+32 e^4 \left (1-\frac {\log (3)}{4}\right ) \log (x) x-32 \log (x)\right )}{x^3}\right )dx}{9 (4-\log (3))^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2 \int \left (\frac {4\ 3^{-\frac {16 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {2 \left (4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16\right )}{x^2 (-4+\log (3))^2}\right ) \left (2-x^2 (4-\log (3))\right ) \left (-\left ((8-\log (9)) x^2\right )+e^4 (4-\log (3)) x-4\right )}{x^3}+\frac {(-4+\log (3))^2 \log (x)}{x}+\frac {3^{-\frac {8 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16}{x^2 (-4+\log (3))^2}\right ) \left (128 \left (1+\frac {1}{32} \log (3) (-16+\log (9))\right ) \log (x) x^4-64 e^4 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^3+16 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) x^2+32 e^4 \left (1-\frac {\log (3)}{4}\right ) \log (x) x-32 \log (x)\right )}{x^3}\right )dx}{9 (4-\log (3))^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2 \int \left (\frac {4\ 3^{-\frac {16 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {2 \left (4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16\right )}{x^2 (-4+\log (3))^2}\right ) \left (2-x^2 (4-\log (3))\right ) \left (-\left ((8-\log (9)) x^2\right )+e^4 (4-\log (3)) x-4\right )}{x^3}+\frac {(-4+\log (3))^2 \log (x)}{x}+\frac {3^{-\frac {8 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16}{x^2 (-4+\log (3))^2}\right ) \left (128 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^4-64 e^4 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^3+16 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) x^2+32 e^4 \left (1-\frac {\log (3)}{4}\right ) \log (x) x-32 \log (x)\right )}{x^3}\right )dx}{9 (4-\log (3))^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2 \int \left (\frac {4\ 3^{-\frac {16 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {2 \left (4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16\right )}{x^2 (-4+\log (3))^2}\right ) \left (2-x^2 (4-\log (3))\right ) \left (-\left ((8-\log (9)) x^2\right )+e^4 (4-\log (3)) x-4\right )}{x^3}+\frac {(-4+\log (3))^2 \log (x)}{x}+\frac {3^{-\frac {8 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16}{x^2 (-4+\log (3))^2}\right ) \left (128 \left (1+\frac {1}{32} \log (3) (-16+\log (9))\right ) \log (x) x^4-64 e^4 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^3+16 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) x^2+32 e^4 \left (1-\frac {\log (3)}{4}\right ) \log (x) x-32 \log (x)\right )}{x^3}\right )dx}{9 (4-\log (3))^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2 \int \left (\frac {4\ 3^{-\frac {16 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {2 \left (4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16\right )}{x^2 (-4+\log (3))^2}\right ) \left (2-x^2 (4-\log (3))\right ) \left (-\left ((8-\log (9)) x^2\right )+e^4 (4-\log (3)) x-4\right )}{x^3}+\frac {(-4+\log (3))^2 \log (x)}{x}+\frac {3^{-\frac {8 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16}{x^2 (-4+\log (3))^2}\right ) \left (128 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^4-64 e^4 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^3+16 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) x^2+32 e^4 \left (1-\frac {\log (3)}{4}\right ) \log (x) x-32 \log (x)\right )}{x^3}\right )dx}{9 (4-\log (3))^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2 \int \left (\frac {4\ 3^{-\frac {16 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {2 \left (4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16\right )}{x^2 (-4+\log (3))^2}\right ) \left (2-x^2 (4-\log (3))\right ) \left (-\left ((8-\log (9)) x^2\right )+e^4 (4-\log (3)) x-4\right )}{x^3}+\frac {(-4+\log (3))^2 \log (x)}{x}+\frac {3^{-\frac {8 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16}{x^2 (-4+\log (3))^2}\right ) \left (128 \left (1+\frac {1}{32} \log (3) (-16+\log (9))\right ) \log (x) x^4-64 e^4 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^3+16 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) x^2+32 e^4 \left (1-\frac {\log (3)}{4}\right ) \log (x) x-32 \log (x)\right )}{x^3}\right )dx}{9 (4-\log (3))^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2 \int \left (\frac {4\ 3^{-\frac {16 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {2 \left (4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16\right )}{x^2 (-4+\log (3))^2}\right ) \left (2-x^2 (4-\log (3))\right ) \left (-\left ((8-\log (9)) x^2\right )+e^4 (4-\log (3)) x-4\right )}{x^3}+\frac {(-4+\log (3))^2 \log (x)}{x}+\frac {3^{-\frac {8 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16}{x^2 (-4+\log (3))^2}\right ) \left (128 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^4-64 e^4 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^3+16 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) x^2+32 e^4 \left (1-\frac {\log (3)}{4}\right ) \log (x) x-32 \log (x)\right )}{x^3}\right )dx}{9 (4-\log (3))^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2 \int \left (\frac {4\ 3^{-\frac {16 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {2 \left (4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16\right )}{x^2 (-4+\log (3))^2}\right ) \left (2-x^2 (4-\log (3))\right ) \left (-\left ((8-\log (9)) x^2\right )+e^4 (4-\log (3)) x-4\right )}{x^3}+\frac {(-4+\log (3))^2 \log (x)}{x}+\frac {3^{-\frac {8 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16}{x^2 (-4+\log (3))^2}\right ) \left (128 \left (1+\frac {1}{32} \log (3) (-16+\log (9))\right ) \log (x) x^4-64 e^4 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^3+16 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) x^2+32 e^4 \left (1-\frac {\log (3)}{4}\right ) \log (x) x-32 \log (x)\right )}{x^3}\right )dx}{9 (4-\log (3))^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2 \int \left (\frac {4\ 3^{-\frac {16 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {2 \left (4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16\right )}{x^2 (-4+\log (3))^2}\right ) \left (2-x^2 (4-\log (3))\right ) \left (-\left ((8-\log (9)) x^2\right )+e^4 (4-\log (3)) x-4\right )}{x^3}+\frac {(-4+\log (3))^2 \log (x)}{x}+\frac {3^{-\frac {8 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16}{x^2 (-4+\log (3))^2}\right ) \left (128 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^4-64 e^4 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^3+16 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) x^2+32 e^4 \left (1-\frac {\log (3)}{4}\right ) \log (x) x-32 \log (x)\right )}{x^3}\right )dx}{9 (4-\log (3))^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2 \int \left (\frac {4\ 3^{-\frac {16 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {2 \left (4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16\right )}{x^2 (-4+\log (3))^2}\right ) \left (2-x^2 (4-\log (3))\right ) \left (-\left ((8-\log (9)) x^2\right )+e^4 (4-\log (3)) x-4\right )}{x^3}+\frac {(-4+\log (3))^2 \log (x)}{x}+\frac {3^{-\frac {8 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16}{x^2 (-4+\log (3))^2}\right ) \left (128 \left (1+\frac {1}{32} \log (3) (-16+\log (9))\right ) \log (x) x^4-64 e^4 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^3+16 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) x^2+32 e^4 \left (1-\frac {\log (3)}{4}\right ) \log (x) x-32 \log (x)\right )}{x^3}\right )dx}{9 (4-\log (3))^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2 \int \left (\frac {4\ 3^{-\frac {16 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {2 \left (4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16\right )}{x^2 (-4+\log (3))^2}\right ) \left (2-x^2 (4-\log (3))\right ) \left (-\left ((8-\log (9)) x^2\right )+e^4 (4-\log (3)) x-4\right )}{x^3}+\frac {(-4+\log (3))^2 \log (x)}{x}+\frac {3^{-\frac {8 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16}{x^2 (-4+\log (3))^2}\right ) \left (128 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^4-64 e^4 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^3+16 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) x^2+32 e^4 \left (1-\frac {\log (3)}{4}\right ) \log (x) x-32 \log (x)\right )}{x^3}\right )dx}{9 (4-\log (3))^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2 \int \left (\frac {4\ 3^{-\frac {16 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {2 \left (4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16\right )}{x^2 (-4+\log (3))^2}\right ) \left (2-x^2 (4-\log (3))\right ) \left (-\left ((8-\log (9)) x^2\right )+e^4 (4-\log (3)) x-4\right )}{x^3}+\frac {(-4+\log (3))^2 \log (x)}{x}+\frac {3^{-\frac {8 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16}{x^2 (-4+\log (3))^2}\right ) \left (128 \left (1+\frac {1}{32} \log (3) (-16+\log (9))\right ) \log (x) x^4-64 e^4 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^3+16 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) x^2+32 e^4 \left (1-\frac {\log (3)}{4}\right ) \log (x) x-32 \log (x)\right )}{x^3}\right )dx}{9 (4-\log (3))^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2 \int \left (\frac {4\ 3^{-\frac {16 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {2 \left (4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16\right )}{x^2 (-4+\log (3))^2}\right ) \left (2-x^2 (4-\log (3))\right ) \left (-\left ((8-\log (9)) x^2\right )+e^4 (4-\log (3)) x-4\right )}{x^3}+\frac {(-4+\log (3))^2 \log (x)}{x}+\frac {3^{-\frac {8 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16}{x^2 (-4+\log (3))^2}\right ) \left (128 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^4-64 e^4 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^3+16 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) x^2+32 e^4 \left (1-\frac {\log (3)}{4}\right ) \log (x) x-32 \log (x)\right )}{x^3}\right )dx}{9 (4-\log (3))^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2 \int \left (\frac {4\ 3^{-\frac {16 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {2 \left (4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16\right )}{x^2 (-4+\log (3))^2}\right ) \left (2-x^2 (4-\log (3))\right ) \left (-\left ((8-\log (9)) x^2\right )+e^4 (4-\log (3)) x-4\right )}{x^3}+\frac {(-4+\log (3))^2 \log (x)}{x}+\frac {3^{-\frac {8 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16}{x^2 (-4+\log (3))^2}\right ) \left (128 \left (1+\frac {1}{32} \log (3) (-16+\log (9))\right ) \log (x) x^4-64 e^4 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^3+16 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) x^2+32 e^4 \left (1-\frac {\log (3)}{4}\right ) \log (x) x-32 \log (x)\right )}{x^3}\right )dx}{9 (4-\log (3))^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2 \int \left (\frac {4\ 3^{-\frac {16 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {2 \left (4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16\right )}{x^2 (-4+\log (3))^2}\right ) \left (2-x^2 (4-\log (3))\right ) \left (-\left ((8-\log (9)) x^2\right )+e^4 (4-\log (3)) x-4\right )}{x^3}+\frac {(-4+\log (3))^2 \log (x)}{x}+\frac {3^{-\frac {8 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16}{x^2 (-4+\log (3))^2}\right ) \left (128 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^4-64 e^4 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^3+16 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) x^2+32 e^4 \left (1-\frac {\log (3)}{4}\right ) \log (x) x-32 \log (x)\right )}{x^3}\right )dx}{9 (4-\log (3))^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2 \int \left (\frac {4\ 3^{-\frac {16 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {2 \left (4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16\right )}{x^2 (-4+\log (3))^2}\right ) \left (2-x^2 (4-\log (3))\right ) \left (-\left ((8-\log (9)) x^2\right )+e^4 (4-\log (3)) x-4\right )}{x^3}+\frac {(-4+\log (3))^2 \log (x)}{x}+\frac {3^{-\frac {8 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16}{x^2 (-4+\log (3))^2}\right ) \left (128 \left (1+\frac {1}{32} \log (3) (-16+\log (9))\right ) \log (x) x^4-64 e^4 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^3+16 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) x^2+32 e^4 \left (1-\frac {\log (3)}{4}\right ) \log (x) x-32 \log (x)\right )}{x^3}\right )dx}{9 (4-\log (3))^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2 \int \left (\frac {4\ 3^{-\frac {16 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {2 \left (4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16\right )}{x^2 (-4+\log (3))^2}\right ) \left (2-x^2 (4-\log (3))\right ) \left (-\left ((8-\log (9)) x^2\right )+e^4 (4-\log (3)) x-4\right )}{x^3}+\frac {(-4+\log (3))^2 \log (x)}{x}+\frac {3^{-\frac {8 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16}{x^2 (-4+\log (3))^2}\right ) \left (128 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^4-64 e^4 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^3+16 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) x^2+32 e^4 \left (1-\frac {\log (3)}{4}\right ) \log (x) x-32 \log (x)\right )}{x^3}\right )dx}{9 (4-\log (3))^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2 \int \left (\frac {4\ 3^{-\frac {16 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {2 \left (4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16\right )}{x^2 (-4+\log (3))^2}\right ) \left (2-x^2 (4-\log (3))\right ) \left (-\left ((8-\log (9)) x^2\right )+e^4 (4-\log (3)) x-4\right )}{x^3}+\frac {(-4+\log (3))^2 \log (x)}{x}+\frac {3^{-\frac {8 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16}{x^2 (-4+\log (3))^2}\right ) \left (128 \left (1+\frac {1}{32} \log (3) (-16+\log (9))\right ) \log (x) x^4-64 e^4 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^3+16 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) x^2+32 e^4 \left (1-\frac {\log (3)}{4}\right ) \log (x) x-32 \log (x)\right )}{x^3}\right )dx}{9 (4-\log (3))^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2 \int \left (\frac {4\ 3^{-\frac {16 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {2 \left (4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16\right )}{x^2 (-4+\log (3))^2}\right ) \left (2-x^2 (4-\log (3))\right ) \left (-\left ((8-\log (9)) x^2\right )+e^4 (4-\log (3)) x-4\right )}{x^3}+\frac {(-4+\log (3))^2 \log (x)}{x}+\frac {3^{-\frac {8 \left (4 x^3-4 e^4 x^2+\left (6+e^8\right ) x-e^4\right )}{x (-4+\log (3))^2}} \exp \left (\frac {4 \left (16+\log ^2(3)\right ) x^4-4 e^4 \left (16+\log ^2(3)\right ) x^3+\left (e^8 \left (16+\log ^2(3)\right )+4 \left (32+\log ^2(3)\right )\right ) x^2-32 e^4 x+16}{x^2 (-4+\log (3))^2}\right ) \left (128 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^4-64 e^4 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) \log (x) x^3+16 \left (1+\frac {1}{16} (-8+\log (3)) \log (3)\right ) x^2+32 e^4 \left (1-\frac {\log (3)}{4}\right ) \log (x) x-32 \log (x)\right )}{x^3}\right )dx}{9 (4-\log (3))^2}\) |
Int[(E^((16 + 128*x^2 + 16*E^8*x^2 + 64*x^4 + E^4*(-32*x - 64*x^3) + (-48* x^2 - 8*E^8*x^2 - 32*x^4 + E^4*(8*x + 32*x^3))*Log[3] + (4*x^2 + E^8*x^2 - 4*E^4*x^3 + 4*x^4)*Log[3]^2)/(16*x^2 - 8*x^2*Log[3] + x^2*Log[3]^2))*(32* x^2 - 16*x^2*Log[3] + 2*x^2*Log[3]^2) + E^((2*(16 + 128*x^2 + 16*E^8*x^2 + 64*x^4 + E^4*(-32*x - 64*x^3) + (-48*x^2 - 8*E^8*x^2 - 32*x^4 + E^4*(8*x + 32*x^3))*Log[3] + (4*x^2 + E^8*x^2 - 4*E^4*x^3 + 4*x^4)*Log[3]^2))/(16*x ^2 - 8*x^2*Log[3] + x^2*Log[3]^2))*(-64 + 256*x^4 + E^4*(64*x - 128*x^3) + (-128*x^4 + E^4*(-16*x + 64*x^3))*Log[3] + (-8*E^4*x^3 + 16*x^4)*Log[3]^2 ) + (32*x^2 - 16*x^2*Log[3] + 2*x^2*Log[3]^2 + E^((16 + 128*x^2 + 16*E^8*x ^2 + 64*x^4 + E^4*(-32*x - 64*x^3) + (-48*x^2 - 8*E^8*x^2 - 32*x^4 + E^4*( 8*x + 32*x^3))*Log[3] + (4*x^2 + E^8*x^2 - 4*E^4*x^3 + 4*x^4)*Log[3]^2)/(1 6*x^2 - 8*x^2*Log[3] + x^2*Log[3]^2))*(-64 + 256*x^4 + E^4*(64*x - 128*x^3 ) + (-128*x^4 + E^4*(-16*x + 64*x^3))*Log[3] + (-8*E^4*x^3 + 16*x^4)*Log[3 ]^2))*Log[x])/(144*x^3 - 72*x^3*Log[3] + 9*x^3*Log[3]^2),x]
3.11.26.3.1 Defintions of rubi rules used
Int[(u_.)*((v_.) + (a_.)*(Fx_) + (b_.)*(Fx_))^(p_.), x_Symbol] :> Int[u*(v + (a + b)*Fx)^p, x] /; FreeQ[{a, b}, x] && !FreeQ[Fx, x]
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x] , x] /; FreeQ[{c, m}, x] && SumQ[u] && !LinearQ[u, x] && !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]
Leaf count of result is larger than twice the leaf count of optimal. \(279\) vs. \(2(64)=128\).
Time = 2.58 (sec) , antiderivative size = 280, normalized size of antiderivative = 7.57
| method | result | size |
| risch | \(\frac {\ln \left (x \right )^{2}}{9}+\frac {2 \left (\frac {1}{6561}\right )^{\frac {{\mathrm e}^{8}}{\left (-4+\ln \left (3\right )\right )^{2}}} 6561^{\frac {{\mathrm e}^{4}}{x \left (-4+\ln \left (3\right )\right )^{2}}} {\mathrm e}^{-\frac {4 \ln \left (3\right )^{2} {\mathrm e}^{4} x^{3}-4 x^{4} \ln \left (3\right )^{2}-\ln \left (3\right )^{2} {\mathrm e}^{8} x^{2}-32 \ln \left (3\right ) {\mathrm e}^{4} x^{3}+32 x^{4} \ln \left (3\right )-4 x^{2} \ln \left (3\right )^{2}+64 x^{3} {\mathrm e}^{4}-64 x^{4}+48 x^{2} \ln \left (3\right )-16 x^{2} {\mathrm e}^{8}+32 x \,{\mathrm e}^{4}-128 x^{2}-16}{x^{2} \left (-4+\ln \left (3\right )\right )^{2}}} \ln \left (x \right )}{9}+\frac {6561^{\frac {2 \,{\mathrm e}^{4}}{x \left (-4+\ln \left (3\right )\right )^{2}}} 6561^{-\frac {2 \,{\mathrm e}^{8}}{\left (-4+\ln \left (3\right )\right )^{2}}} {\mathrm e}^{-\frac {2 \left (4 \ln \left (3\right )^{2} {\mathrm e}^{4} x^{3}-4 x^{4} \ln \left (3\right )^{2}-\ln \left (3\right )^{2} {\mathrm e}^{8} x^{2}-32 \ln \left (3\right ) {\mathrm e}^{4} x^{3}+32 x^{4} \ln \left (3\right )-4 x^{2} \ln \left (3\right )^{2}+64 x^{3} {\mathrm e}^{4}-64 x^{4}+48 x^{2} \ln \left (3\right )-16 x^{2} {\mathrm e}^{8}+32 x \,{\mathrm e}^{4}-128 x^{2}-16\right )}{x^{2} \left (-4+\ln \left (3\right )\right )^{2}}}}{9}\) | \(280\) |
| parts | \(\frac {\left (\frac {2 \ln \left (3\right )}{9}-\frac {8}{9}\right ) {\mathrm e}^{\frac {\left (x^{2} {\mathrm e}^{8}-4 x^{3} {\mathrm e}^{4}+4 x^{4}+4 x^{2}\right ) \ln \left (3\right )^{2}+\left (-8 x^{2} {\mathrm e}^{8}+\left (32 x^{3}+8 x \right ) {\mathrm e}^{4}-32 x^{4}-48 x^{2}\right ) \ln \left (3\right )+16 x^{2} {\mathrm e}^{8}+\left (-64 x^{3}-32 x \right ) {\mathrm e}^{4}+64 x^{4}+128 x^{2}+16}{x^{2} \ln \left (3\right )^{2}-8 x^{2} \ln \left (3\right )+16 x^{2}}} \ln \left (x \right )}{-4+\ln \left (3\right )}+\frac {\ln \left (x \right )^{2}}{9}-\frac {4 \left (-\frac {\ln \left (3\right )^{2}}{4}+2 \ln \left (3\right )-4\right ) {\mathrm e}^{\frac {2 \left (x^{2} {\mathrm e}^{8}-4 x^{3} {\mathrm e}^{4}+4 x^{4}+4 x^{2}\right ) \ln \left (3\right )^{2}+2 \left (-8 x^{2} {\mathrm e}^{8}+\left (32 x^{3}+8 x \right ) {\mathrm e}^{4}-32 x^{4}-48 x^{2}\right ) \ln \left (3\right )+32 x^{2} {\mathrm e}^{8}+2 \left (-64 x^{3}-32 x \right ) {\mathrm e}^{4}+128 x^{4}+256 x^{2}+32}{x^{2} \ln \left (3\right )^{2}-8 x^{2} \ln \left (3\right )+16 x^{2}}}}{9 \left (\ln \left (3\right )^{2}-8 \ln \left (3\right )+16\right )}\) | \(299\) |
| default | \(\frac {\left (2 \ln \left (3\right )-8\right ) {\mathrm e}^{\frac {\left (x^{2} {\mathrm e}^{8}-4 x^{3} {\mathrm e}^{4}+4 x^{4}+4 x^{2}\right ) \ln \left (3\right )^{2}+\left (-8 x^{2} {\mathrm e}^{8}+\left (32 x^{3}+8 x \right ) {\mathrm e}^{4}-32 x^{4}-48 x^{2}\right ) \ln \left (3\right )+16 x^{2} {\mathrm e}^{8}+\left (-64 x^{3}-32 x \right ) {\mathrm e}^{4}+64 x^{4}+128 x^{2}+16}{x^{2} \ln \left (3\right )^{2}-8 x^{2} \ln \left (3\right )+16 x^{2}}} \ln \left (x \right )}{-36+9 \ln \left (3\right )}+\frac {\ln \left (x \right )^{2}}{9}-\frac {4 \left (-\frac {\ln \left (3\right )^{2}}{4}+2 \ln \left (3\right )-4\right ) {\mathrm e}^{\frac {2 \left (x^{2} {\mathrm e}^{8}-4 x^{3} {\mathrm e}^{4}+4 x^{4}+4 x^{2}\right ) \ln \left (3\right )^{2}+2 \left (-8 x^{2} {\mathrm e}^{8}+\left (32 x^{3}+8 x \right ) {\mathrm e}^{4}-32 x^{4}-48 x^{2}\right ) \ln \left (3\right )+32 x^{2} {\mathrm e}^{8}+2 \left (-64 x^{3}-32 x \right ) {\mathrm e}^{4}+128 x^{4}+256 x^{2}+32}{x^{2} \ln \left (3\right )^{2}-8 x^{2} \ln \left (3\right )+16 x^{2}}}}{9 \left (\ln \left (3\right )^{2}-8 \ln \left (3\right )+16\right )}\) | \(300\) |
| parallelrisch | \(\frac {\ln \left (3\right )^{2} \ln \left (x \right )^{2}+2 \ln \left (3\right )^{2} \ln \left (x \right ) {\mathrm e}^{\frac {\left (x^{2} {\mathrm e}^{8}-4 x^{3} {\mathrm e}^{4}+4 x^{4}+4 x^{2}\right ) \ln \left (3\right )^{2}+\left (-8 x^{2} {\mathrm e}^{8}+\left (32 x^{3}+8 x \right ) {\mathrm e}^{4}-32 x^{4}-48 x^{2}\right ) \ln \left (3\right )+16 x^{2} {\mathrm e}^{8}+\left (-64 x^{3}-32 x \right ) {\mathrm e}^{4}+64 x^{4}+128 x^{2}+16}{x^{2} \left (\ln \left (3\right )^{2}-8 \ln \left (3\right )+16\right )}}+\ln \left (3\right )^{2} {\mathrm e}^{\frac {2 \left (x^{2} {\mathrm e}^{8}-4 x^{3} {\mathrm e}^{4}+4 x^{4}+4 x^{2}\right ) \ln \left (3\right )^{2}+2 \left (-8 x^{2} {\mathrm e}^{8}+\left (32 x^{3}+8 x \right ) {\mathrm e}^{4}-32 x^{4}-48 x^{2}\right ) \ln \left (3\right )+32 x^{2} {\mathrm e}^{8}+2 \left (-64 x^{3}-32 x \right ) {\mathrm e}^{4}+128 x^{4}+256 x^{2}+32}{x^{2} \left (\ln \left (3\right )^{2}-8 \ln \left (3\right )+16\right )}}-8 \ln \left (3\right ) \ln \left (x \right )^{2}-16 \ln \left (3\right ) \ln \left (x \right ) {\mathrm e}^{\frac {\left (x^{2} {\mathrm e}^{8}-4 x^{3} {\mathrm e}^{4}+4 x^{4}+4 x^{2}\right ) \ln \left (3\right )^{2}+\left (-8 x^{2} {\mathrm e}^{8}+\left (32 x^{3}+8 x \right ) {\mathrm e}^{4}-32 x^{4}-48 x^{2}\right ) \ln \left (3\right )+16 x^{2} {\mathrm e}^{8}+\left (-64 x^{3}-32 x \right ) {\mathrm e}^{4}+64 x^{4}+128 x^{2}+16}{x^{2} \left (\ln \left (3\right )^{2}-8 \ln \left (3\right )+16\right )}}-8 \ln \left (3\right ) {\mathrm e}^{\frac {2 \left (x^{2} {\mathrm e}^{8}-4 x^{3} {\mathrm e}^{4}+4 x^{4}+4 x^{2}\right ) \ln \left (3\right )^{2}+2 \left (-8 x^{2} {\mathrm e}^{8}+\left (32 x^{3}+8 x \right ) {\mathrm e}^{4}-32 x^{4}-48 x^{2}\right ) \ln \left (3\right )+32 x^{2} {\mathrm e}^{8}+2 \left (-64 x^{3}-32 x \right ) {\mathrm e}^{4}+128 x^{4}+256 x^{2}+32}{x^{2} \left (\ln \left (3\right )^{2}-8 \ln \left (3\right )+16\right )}}+16 \ln \left (x \right )^{2}+32 \ln \left (x \right ) {\mathrm e}^{\frac {\left (x^{2} {\mathrm e}^{8}-4 x^{3} {\mathrm e}^{4}+4 x^{4}+4 x^{2}\right ) \ln \left (3\right )^{2}+\left (-8 x^{2} {\mathrm e}^{8}+\left (32 x^{3}+8 x \right ) {\mathrm e}^{4}-32 x^{4}-48 x^{2}\right ) \ln \left (3\right )+16 x^{2} {\mathrm e}^{8}+\left (-64 x^{3}-32 x \right ) {\mathrm e}^{4}+64 x^{4}+128 x^{2}+16}{x^{2} \left (\ln \left (3\right )^{2}-8 \ln \left (3\right )+16\right )}}+16 \,{\mathrm e}^{\frac {2 \left (x^{2} {\mathrm e}^{8}-4 x^{3} {\mathrm e}^{4}+4 x^{4}+4 x^{2}\right ) \ln \left (3\right )^{2}+2 \left (-8 x^{2} {\mathrm e}^{8}+\left (32 x^{3}+8 x \right ) {\mathrm e}^{4}-32 x^{4}-48 x^{2}\right ) \ln \left (3\right )+32 x^{2} {\mathrm e}^{8}+2 \left (-64 x^{3}-32 x \right ) {\mathrm e}^{4}+128 x^{4}+256 x^{2}+32}{x^{2} \left (\ln \left (3\right )^{2}-8 \ln \left (3\right )+16\right )}}}{9 \ln \left (3\right )^{2}-72 \ln \left (3\right )+144}\) | \(770\) |
int(((((-8*x^3*exp(4)+16*x^4)*ln(3)^2+((64*x^3-16*x)*exp(4)-128*x^4)*ln(3) +(-128*x^3+64*x)*exp(4)+256*x^4-64)*exp(((x^2*exp(4)^2-4*x^3*exp(4)+4*x^4+ 4*x^2)*ln(3)^2+(-8*x^2*exp(4)^2+(32*x^3+8*x)*exp(4)-32*x^4-48*x^2)*ln(3)+1 6*x^2*exp(4)^2+(-64*x^3-32*x)*exp(4)+64*x^4+128*x^2+16)/(x^2*ln(3)^2-8*x^2 *ln(3)+16*x^2))+2*x^2*ln(3)^2-16*x^2*ln(3)+32*x^2)*ln(x)+((-8*x^3*exp(4)+1 6*x^4)*ln(3)^2+((64*x^3-16*x)*exp(4)-128*x^4)*ln(3)+(-128*x^3+64*x)*exp(4) +256*x^4-64)*exp(((x^2*exp(4)^2-4*x^3*exp(4)+4*x^4+4*x^2)*ln(3)^2+(-8*x^2* exp(4)^2+(32*x^3+8*x)*exp(4)-32*x^4-48*x^2)*ln(3)+16*x^2*exp(4)^2+(-64*x^3 -32*x)*exp(4)+64*x^4+128*x^2+16)/(x^2*ln(3)^2-8*x^2*ln(3)+16*x^2))^2+(2*x^ 2*ln(3)^2-16*x^2*ln(3)+32*x^2)*exp(((x^2*exp(4)^2-4*x^3*exp(4)+4*x^4+4*x^2 )*ln(3)^2+(-8*x^2*exp(4)^2+(32*x^3+8*x)*exp(4)-32*x^4-48*x^2)*ln(3)+16*x^2 *exp(4)^2+(-64*x^3-32*x)*exp(4)+64*x^4+128*x^2+16)/(x^2*ln(3)^2-8*x^2*ln(3 )+16*x^2)))/(9*x^3*ln(3)^2-72*x^3*ln(3)+144*x^3),x,method=_RETURNVERBOSE)
1/9*ln(x)^2+2/9*(1/6561)^(1/(-4+ln(3))^2*exp(8))*6561^(1/x/(-4+ln(3))^2*ex p(4))*exp(-(4*ln(3)^2*exp(4)*x^3-4*x^4*ln(3)^2-ln(3)^2*exp(8)*x^2-32*ln(3) *exp(4)*x^3+32*x^4*ln(3)-4*x^2*ln(3)^2+64*x^3*exp(4)-64*x^4+48*x^2*ln(3)-1 6*x^2*exp(8)+32*x*exp(4)-128*x^2-16)/x^2/(-4+ln(3))^2)*ln(x)+1/9*(6561^(1/ x/(-4+ln(3))^2*exp(4)))^2*((1/6561)^(1/(-4+ln(3))^2*exp(8)))^2*exp(-2*(4*l n(3)^2*exp(4)*x^3-4*x^4*ln(3)^2-ln(3)^2*exp(8)*x^2-32*ln(3)*exp(4)*x^3+32* x^4*ln(3)-4*x^2*ln(3)^2+64*x^3*exp(4)-64*x^4+48*x^2*ln(3)-16*x^2*exp(8)+32 *x*exp(4)-128*x^2-16)/x^2/(-4+ln(3))^2)
Leaf count of result is larger than twice the leaf count of optimal. 246 vs. \(2 (31) = 62\).
Time = 0.28 (sec) , antiderivative size = 246, normalized size of antiderivative = 6.65 \[ \int \frac {e^{\frac {16+128 x^2+16 e^8 x^2+64 x^4+e^4 \left (-32 x-64 x^3\right )+\left (-48 x^2-8 e^8 x^2-32 x^4+e^4 \left (8 x+32 x^3\right )\right ) \log (3)+\left (4 x^2+e^8 x^2-4 e^4 x^3+4 x^4\right ) \log ^2(3)}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}} \left (32 x^2-16 x^2 \log (3)+2 x^2 \log ^2(3)\right )+e^{\frac {2 \left (16+128 x^2+16 e^8 x^2+64 x^4+e^4 \left (-32 x-64 x^3\right )+\left (-48 x^2-8 e^8 x^2-32 x^4+e^4 \left (8 x+32 x^3\right )\right ) \log (3)+\left (4 x^2+e^8 x^2-4 e^4 x^3+4 x^4\right ) \log ^2(3)\right )}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}} \left (-64+256 x^4+e^4 \left (64 x-128 x^3\right )+\left (-128 x^4+e^4 \left (-16 x+64 x^3\right )\right ) \log (3)+\left (-8 e^4 x^3+16 x^4\right ) \log ^2(3)\right )+\left (32 x^2-16 x^2 \log (3)+2 x^2 \log ^2(3)+e^{\frac {16+128 x^2+16 e^8 x^2+64 x^4+e^4 \left (-32 x-64 x^3\right )+\left (-48 x^2-8 e^8 x^2-32 x^4+e^4 \left (8 x+32 x^3\right )\right ) \log (3)+\left (4 x^2+e^8 x^2-4 e^4 x^3+4 x^4\right ) \log ^2(3)}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}} \left (-64+256 x^4+e^4 \left (64 x-128 x^3\right )+\left (-128 x^4+e^4 \left (-16 x+64 x^3\right )\right ) \log (3)+\left (-8 e^4 x^3+16 x^4\right ) \log ^2(3)\right )\right ) \log (x)}{144 x^3-72 x^3 \log (3)+9 x^3 \log ^2(3)} \, dx=\frac {2}{9} \, e^{\left (\frac {64 \, x^{4} + 16 \, x^{2} e^{8} + {\left (4 \, x^{4} - 4 \, x^{3} e^{4} + x^{2} e^{8} + 4 \, x^{2}\right )} \log \left (3\right )^{2} + 128 \, x^{2} - 32 \, {\left (2 \, x^{3} + x\right )} e^{4} - 8 \, {\left (4 \, x^{4} + x^{2} e^{8} + 6 \, x^{2} - {\left (4 \, x^{3} + x\right )} e^{4}\right )} \log \left (3\right ) + 16}{x^{2} \log \left (3\right )^{2} - 8 \, x^{2} \log \left (3\right ) + 16 \, x^{2}}\right )} \log \left (x\right ) + \frac {1}{9} \, \log \left (x\right )^{2} + \frac {1}{9} \, e^{\left (\frac {2 \, {\left (64 \, x^{4} + 16 \, x^{2} e^{8} + {\left (4 \, x^{4} - 4 \, x^{3} e^{4} + x^{2} e^{8} + 4 \, x^{2}\right )} \log \left (3\right )^{2} + 128 \, x^{2} - 32 \, {\left (2 \, x^{3} + x\right )} e^{4} - 8 \, {\left (4 \, x^{4} + x^{2} e^{8} + 6 \, x^{2} - {\left (4 \, x^{3} + x\right )} e^{4}\right )} \log \left (3\right ) + 16\right )}}{x^{2} \log \left (3\right )^{2} - 8 \, x^{2} \log \left (3\right ) + 16 \, x^{2}}\right )} \]
integrate(((((-8*x^3*exp(4)+16*x^4)*log(3)^2+((64*x^3-16*x)*exp(4)-128*x^4 )*log(3)+(-128*x^3+64*x)*exp(4)+256*x^4-64)*exp(((x^2*exp(4)^2-4*x^3*exp(4 )+4*x^4+4*x^2)*log(3)^2+(-8*x^2*exp(4)^2+(32*x^3+8*x)*exp(4)-32*x^4-48*x^2 )*log(3)+16*x^2*exp(4)^2+(-64*x^3-32*x)*exp(4)+64*x^4+128*x^2+16)/(x^2*log (3)^2-8*x^2*log(3)+16*x^2))+2*x^2*log(3)^2-16*x^2*log(3)+32*x^2)*log(x)+(( -8*x^3*exp(4)+16*x^4)*log(3)^2+((64*x^3-16*x)*exp(4)-128*x^4)*log(3)+(-128 *x^3+64*x)*exp(4)+256*x^4-64)*exp(((x^2*exp(4)^2-4*x^3*exp(4)+4*x^4+4*x^2) *log(3)^2+(-8*x^2*exp(4)^2+(32*x^3+8*x)*exp(4)-32*x^4-48*x^2)*log(3)+16*x^ 2*exp(4)^2+(-64*x^3-32*x)*exp(4)+64*x^4+128*x^2+16)/(x^2*log(3)^2-8*x^2*lo g(3)+16*x^2))^2+(2*x^2*log(3)^2-16*x^2*log(3)+32*x^2)*exp(((x^2*exp(4)^2-4 *x^3*exp(4)+4*x^4+4*x^2)*log(3)^2+(-8*x^2*exp(4)^2+(32*x^3+8*x)*exp(4)-32* x^4-48*x^2)*log(3)+16*x^2*exp(4)^2+(-64*x^3-32*x)*exp(4)+64*x^4+128*x^2+16 )/(x^2*log(3)^2-8*x^2*log(3)+16*x^2)))/(9*x^3*log(3)^2-72*x^3*log(3)+144*x ^3),x, algorithm=\
2/9*e^((64*x^4 + 16*x^2*e^8 + (4*x^4 - 4*x^3*e^4 + x^2*e^8 + 4*x^2)*log(3) ^2 + 128*x^2 - 32*(2*x^3 + x)*e^4 - 8*(4*x^4 + x^2*e^8 + 6*x^2 - (4*x^3 + x)*e^4)*log(3) + 16)/(x^2*log(3)^2 - 8*x^2*log(3) + 16*x^2))*log(x) + 1/9* log(x)^2 + 1/9*e^(2*(64*x^4 + 16*x^2*e^8 + (4*x^4 - 4*x^3*e^4 + x^2*e^8 + 4*x^2)*log(3)^2 + 128*x^2 - 32*(2*x^3 + x)*e^4 - 8*(4*x^4 + x^2*e^8 + 6*x^ 2 - (4*x^3 + x)*e^4)*log(3) + 16)/(x^2*log(3)^2 - 8*x^2*log(3) + 16*x^2))
Leaf count of result is larger than twice the leaf count of optimal. 264 vs. \(2 (27) = 54\).
Time = 1.06 (sec) , antiderivative size = 264, normalized size of antiderivative = 7.14 \[ \int \frac {e^{\frac {16+128 x^2+16 e^8 x^2+64 x^4+e^4 \left (-32 x-64 x^3\right )+\left (-48 x^2-8 e^8 x^2-32 x^4+e^4 \left (8 x+32 x^3\right )\right ) \log (3)+\left (4 x^2+e^8 x^2-4 e^4 x^3+4 x^4\right ) \log ^2(3)}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}} \left (32 x^2-16 x^2 \log (3)+2 x^2 \log ^2(3)\right )+e^{\frac {2 \left (16+128 x^2+16 e^8 x^2+64 x^4+e^4 \left (-32 x-64 x^3\right )+\left (-48 x^2-8 e^8 x^2-32 x^4+e^4 \left (8 x+32 x^3\right )\right ) \log (3)+\left (4 x^2+e^8 x^2-4 e^4 x^3+4 x^4\right ) \log ^2(3)\right )}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}} \left (-64+256 x^4+e^4 \left (64 x-128 x^3\right )+\left (-128 x^4+e^4 \left (-16 x+64 x^3\right )\right ) \log (3)+\left (-8 e^4 x^3+16 x^4\right ) \log ^2(3)\right )+\left (32 x^2-16 x^2 \log (3)+2 x^2 \log ^2(3)+e^{\frac {16+128 x^2+16 e^8 x^2+64 x^4+e^4 \left (-32 x-64 x^3\right )+\left (-48 x^2-8 e^8 x^2-32 x^4+e^4 \left (8 x+32 x^3\right )\right ) \log (3)+\left (4 x^2+e^8 x^2-4 e^4 x^3+4 x^4\right ) \log ^2(3)}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}} \left (-64+256 x^4+e^4 \left (64 x-128 x^3\right )+\left (-128 x^4+e^4 \left (-16 x+64 x^3\right )\right ) \log (3)+\left (-8 e^4 x^3+16 x^4\right ) \log ^2(3)\right )\right ) \log (x)}{144 x^3-72 x^3 \log (3)+9 x^3 \log ^2(3)} \, dx=\frac {e^{\frac {2 \cdot \left (64 x^{4} + 128 x^{2} + 16 x^{2} e^{8} + \left (- 64 x^{3} - 32 x\right ) e^{4} + \left (- 32 x^{4} - 8 x^{2} e^{8} - 48 x^{2} + \left (32 x^{3} + 8 x\right ) e^{4}\right ) \log {\left (3 \right )} + \left (4 x^{4} - 4 x^{3} e^{4} + 4 x^{2} + x^{2} e^{8}\right ) \log {\left (3 \right )}^{2} + 16\right )}{- 8 x^{2} \log {\left (3 \right )} + x^{2} \log {\left (3 \right )}^{2} + 16 x^{2}}}}{9} + \frac {2 e^{\frac {64 x^{4} + 128 x^{2} + 16 x^{2} e^{8} + \left (- 64 x^{3} - 32 x\right ) e^{4} + \left (- 32 x^{4} - 8 x^{2} e^{8} - 48 x^{2} + \left (32 x^{3} + 8 x\right ) e^{4}\right ) \log {\left (3 \right )} + \left (4 x^{4} - 4 x^{3} e^{4} + 4 x^{2} + x^{2} e^{8}\right ) \log {\left (3 \right )}^{2} + 16}{- 8 x^{2} \log {\left (3 \right )} + x^{2} \log {\left (3 \right )}^{2} + 16 x^{2}}} \log {\left (x \right )}}{9} + \frac {\log {\left (x \right )}^{2}}{9} \]
integrate(((((-8*x**3*exp(4)+16*x**4)*ln(3)**2+((64*x**3-16*x)*exp(4)-128* x**4)*ln(3)+(-128*x**3+64*x)*exp(4)+256*x**4-64)*exp(((x**2*exp(4)**2-4*x* *3*exp(4)+4*x**4+4*x**2)*ln(3)**2+(-8*x**2*exp(4)**2+(32*x**3+8*x)*exp(4)- 32*x**4-48*x**2)*ln(3)+16*x**2*exp(4)**2+(-64*x**3-32*x)*exp(4)+64*x**4+12 8*x**2+16)/(x**2*ln(3)**2-8*x**2*ln(3)+16*x**2))+2*x**2*ln(3)**2-16*x**2*l n(3)+32*x**2)*ln(x)+((-8*x**3*exp(4)+16*x**4)*ln(3)**2+((64*x**3-16*x)*exp (4)-128*x**4)*ln(3)+(-128*x**3+64*x)*exp(4)+256*x**4-64)*exp(((x**2*exp(4) **2-4*x**3*exp(4)+4*x**4+4*x**2)*ln(3)**2+(-8*x**2*exp(4)**2+(32*x**3+8*x) *exp(4)-32*x**4-48*x**2)*ln(3)+16*x**2*exp(4)**2+(-64*x**3-32*x)*exp(4)+64 *x**4+128*x**2+16)/(x**2*ln(3)**2-8*x**2*ln(3)+16*x**2))**2+(2*x**2*ln(3)* *2-16*x**2*ln(3)+32*x**2)*exp(((x**2*exp(4)**2-4*x**3*exp(4)+4*x**4+4*x**2 )*ln(3)**2+(-8*x**2*exp(4)**2+(32*x**3+8*x)*exp(4)-32*x**4-48*x**2)*ln(3)+ 16*x**2*exp(4)**2+(-64*x**3-32*x)*exp(4)+64*x**4+128*x**2+16)/(x**2*ln(3)* *2-8*x**2*ln(3)+16*x**2)))/(9*x**3*ln(3)**2-72*x**3*ln(3)+144*x**3),x)
exp(2*(64*x**4 + 128*x**2 + 16*x**2*exp(8) + (-64*x**3 - 32*x)*exp(4) + (- 32*x**4 - 8*x**2*exp(8) - 48*x**2 + (32*x**3 + 8*x)*exp(4))*log(3) + (4*x* *4 - 4*x**3*exp(4) + 4*x**2 + x**2*exp(8))*log(3)**2 + 16)/(-8*x**2*log(3) + x**2*log(3)**2 + 16*x**2))/9 + 2*exp((64*x**4 + 128*x**2 + 16*x**2*exp( 8) + (-64*x**3 - 32*x)*exp(4) + (-32*x**4 - 8*x**2*exp(8) - 48*x**2 + (32* x**3 + 8*x)*exp(4))*log(3) + (4*x**4 - 4*x**3*exp(4) + 4*x**2 + x**2*exp(8 ))*log(3)**2 + 16)/(-8*x**2*log(3) + x**2*log(3)**2 + 16*x**2))*log(x)/9 + log(x)**2/9
Leaf count of result is larger than twice the leaf count of optimal. 652 vs. \(2 (31) = 62\).
Time = 0.72 (sec) , antiderivative size = 652, normalized size of antiderivative = 17.62 \[ \int \frac {e^{\frac {16+128 x^2+16 e^8 x^2+64 x^4+e^4 \left (-32 x-64 x^3\right )+\left (-48 x^2-8 e^8 x^2-32 x^4+e^4 \left (8 x+32 x^3\right )\right ) \log (3)+\left (4 x^2+e^8 x^2-4 e^4 x^3+4 x^4\right ) \log ^2(3)}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}} \left (32 x^2-16 x^2 \log (3)+2 x^2 \log ^2(3)\right )+e^{\frac {2 \left (16+128 x^2+16 e^8 x^2+64 x^4+e^4 \left (-32 x-64 x^3\right )+\left (-48 x^2-8 e^8 x^2-32 x^4+e^4 \left (8 x+32 x^3\right )\right ) \log (3)+\left (4 x^2+e^8 x^2-4 e^4 x^3+4 x^4\right ) \log ^2(3)\right )}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}} \left (-64+256 x^4+e^4 \left (64 x-128 x^3\right )+\left (-128 x^4+e^4 \left (-16 x+64 x^3\right )\right ) \log (3)+\left (-8 e^4 x^3+16 x^4\right ) \log ^2(3)\right )+\left (32 x^2-16 x^2 \log (3)+2 x^2 \log ^2(3)+e^{\frac {16+128 x^2+16 e^8 x^2+64 x^4+e^4 \left (-32 x-64 x^3\right )+\left (-48 x^2-8 e^8 x^2-32 x^4+e^4 \left (8 x+32 x^3\right )\right ) \log (3)+\left (4 x^2+e^8 x^2-4 e^4 x^3+4 x^4\right ) \log ^2(3)}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}} \left (-64+256 x^4+e^4 \left (64 x-128 x^3\right )+\left (-128 x^4+e^4 \left (-16 x+64 x^3\right )\right ) \log (3)+\left (-8 e^4 x^3+16 x^4\right ) \log ^2(3)\right )\right ) \log (x)}{144 x^3-72 x^3 \log (3)+9 x^3 \log ^2(3)} \, dx=\text {Too large to display} \]
integrate(((((-8*x^3*exp(4)+16*x^4)*log(3)^2+((64*x^3-16*x)*exp(4)-128*x^4 )*log(3)+(-128*x^3+64*x)*exp(4)+256*x^4-64)*exp(((x^2*exp(4)^2-4*x^3*exp(4 )+4*x^4+4*x^2)*log(3)^2+(-8*x^2*exp(4)^2+(32*x^3+8*x)*exp(4)-32*x^4-48*x^2 )*log(3)+16*x^2*exp(4)^2+(-64*x^3-32*x)*exp(4)+64*x^4+128*x^2+16)/(x^2*log (3)^2-8*x^2*log(3)+16*x^2))+2*x^2*log(3)^2-16*x^2*log(3)+32*x^2)*log(x)+(( -8*x^3*exp(4)+16*x^4)*log(3)^2+((64*x^3-16*x)*exp(4)-128*x^4)*log(3)+(-128 *x^3+64*x)*exp(4)+256*x^4-64)*exp(((x^2*exp(4)^2-4*x^3*exp(4)+4*x^4+4*x^2) *log(3)^2+(-8*x^2*exp(4)^2+(32*x^3+8*x)*exp(4)-32*x^4-48*x^2)*log(3)+16*x^ 2*exp(4)^2+(-64*x^3-32*x)*exp(4)+64*x^4+128*x^2+16)/(x^2*log(3)^2-8*x^2*lo g(3)+16*x^2))^2+(2*x^2*log(3)^2-16*x^2*log(3)+32*x^2)*exp(((x^2*exp(4)^2-4 *x^3*exp(4)+4*x^4+4*x^2)*log(3)^2+(-8*x^2*exp(4)^2+(32*x^3+8*x)*exp(4)-32* x^4-48*x^2)*log(3)+16*x^2*exp(4)^2+(-64*x^3-32*x)*exp(4)+64*x^4+128*x^2+16 )/(x^2*log(3)^2-8*x^2*log(3)+16*x^2)))/(9*x^3*log(3)^2-72*x^3*log(3)+144*x ^3),x, algorithm=\
(2*3^(8*e^8/(log(3)^2 - 8*log(3) + 16))*3^(48/(log(3)^2 - 8*log(3) + 16))* e^(4*x^2*log(3)^2/(log(3)^2 - 8*log(3) + 16) - 4*x*e^4*log(3)^2/(log(3)^2 - 8*log(3) + 16) + 32*x^2*log(3)/(log(3)^2 - 8*log(3) + 16) + 32*x*e^4*log (3)/(log(3)^2 - 8*log(3) + 16) + e^8*log(3)^2/(log(3)^2 - 8*log(3) + 16) + 64*x^2/(log(3)^2 - 8*log(3) + 16) + 64*x*e^4/(log(3)^2 - 8*log(3) + 16) + 4*log(3)^2/(log(3)^2 - 8*log(3) + 16) + 16*e^8/(log(3)^2 - 8*log(3) + 16) + 8*e^4*log(3)/((log(3)^2 - 8*log(3) + 16)*x) + 128/(log(3)^2 - 8*log(3) + 16) + 32*e^4/((log(3)^2 - 8*log(3) + 16)*x) + 16/((log(3)^2 - 8*log(3) + 16)*x^2))*log(x) + 3^(16*e^8/(log(3)^2 - 8*log(3) + 16) + 96/(log(3)^2 - 8*log(3) + 16))*e^(64*x^2*log(3)/(log(3)^2 - 8*log(3) + 16) + 128*x*e^4/(l og(3)^2 - 8*log(3) + 16) + 64*e^4/((log(3)^2 - 8*log(3) + 16)*x))*log(x)^2 + e^(8*x^2*log(3)^2/(log(3)^2 - 8*log(3) + 16) - 8*x*e^4*log(3)^2/(log(3) ^2 - 8*log(3) + 16) + 64*x*e^4*log(3)/(log(3)^2 - 8*log(3) + 16) + 2*e^8*l og(3)^2/(log(3)^2 - 8*log(3) + 16) + 128*x^2/(log(3)^2 - 8*log(3) + 16) + 8*log(3)^2/(log(3)^2 - 8*log(3) + 16) + 32*e^8/(log(3)^2 - 8*log(3) + 16) + 16*e^4*log(3)/((log(3)^2 - 8*log(3) + 16)*x) + 256/(log(3)^2 - 8*log(3) + 16) + 32/((log(3)^2 - 8*log(3) + 16)*x^2)))*3^(-16*e^8/(log(3)^2 - 8*log (3) + 16) - 96/(log(3)^2 - 8*log(3) + 16) - 2)*e^(-64*x^2*log(3)/(log(3)^2 - 8*log(3) + 16) - 128*x*e^4/(log(3)^2 - 8*log(3) + 16) - 64*e^4/((log(3) ^2 - 8*log(3) + 16)*x))
Leaf count of result is larger than twice the leaf count of optimal. 282 vs. \(2 (31) = 62\).
Time = 5.25 (sec) , antiderivative size = 282, normalized size of antiderivative = 7.62 \[ \int \frac {e^{\frac {16+128 x^2+16 e^8 x^2+64 x^4+e^4 \left (-32 x-64 x^3\right )+\left (-48 x^2-8 e^8 x^2-32 x^4+e^4 \left (8 x+32 x^3\right )\right ) \log (3)+\left (4 x^2+e^8 x^2-4 e^4 x^3+4 x^4\right ) \log ^2(3)}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}} \left (32 x^2-16 x^2 \log (3)+2 x^2 \log ^2(3)\right )+e^{\frac {2 \left (16+128 x^2+16 e^8 x^2+64 x^4+e^4 \left (-32 x-64 x^3\right )+\left (-48 x^2-8 e^8 x^2-32 x^4+e^4 \left (8 x+32 x^3\right )\right ) \log (3)+\left (4 x^2+e^8 x^2-4 e^4 x^3+4 x^4\right ) \log ^2(3)\right )}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}} \left (-64+256 x^4+e^4 \left (64 x-128 x^3\right )+\left (-128 x^4+e^4 \left (-16 x+64 x^3\right )\right ) \log (3)+\left (-8 e^4 x^3+16 x^4\right ) \log ^2(3)\right )+\left (32 x^2-16 x^2 \log (3)+2 x^2 \log ^2(3)+e^{\frac {16+128 x^2+16 e^8 x^2+64 x^4+e^4 \left (-32 x-64 x^3\right )+\left (-48 x^2-8 e^8 x^2-32 x^4+e^4 \left (8 x+32 x^3\right )\right ) \log (3)+\left (4 x^2+e^8 x^2-4 e^4 x^3+4 x^4\right ) \log ^2(3)}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}} \left (-64+256 x^4+e^4 \left (64 x-128 x^3\right )+\left (-128 x^4+e^4 \left (-16 x+64 x^3\right )\right ) \log (3)+\left (-8 e^4 x^3+16 x^4\right ) \log ^2(3)\right )\right ) \log (x)}{144 x^3-72 x^3 \log (3)+9 x^3 \log ^2(3)} \, dx=\frac {2}{9} \, e^{\left (\frac {4 \, x^{4} \log \left (3\right )^{2} - 4 \, x^{3} e^{4} \log \left (3\right )^{2} - 32 \, x^{4} \log \left (3\right ) + 32 \, x^{3} e^{4} \log \left (3\right ) + x^{2} e^{8} \log \left (3\right )^{2} + 64 \, x^{4} - 64 \, x^{3} e^{4} - 8 \, x^{2} e^{8} \log \left (3\right ) + 4 \, x^{2} \log \left (3\right )^{2} + 16 \, x^{2} e^{8} - 48 \, x^{2} \log \left (3\right ) + 8 \, x e^{4} \log \left (3\right ) + 128 \, x^{2} - 32 \, x e^{4} + 16}{x^{2} \log \left (3\right )^{2} - 8 \, x^{2} \log \left (3\right ) + 16 \, x^{2}}\right )} \log \left (x\right ) + \frac {1}{9} \, \log \left (x\right )^{2} + \frac {1}{9} \, e^{\left (\frac {2 \, {\left (4 \, x^{4} \log \left (3\right )^{2} - 4 \, x^{3} e^{4} \log \left (3\right )^{2} - 32 \, x^{4} \log \left (3\right ) + 32 \, x^{3} e^{4} \log \left (3\right ) + x^{2} e^{8} \log \left (3\right )^{2} + 64 \, x^{4} - 64 \, x^{3} e^{4} - 8 \, x^{2} e^{8} \log \left (3\right ) + 4 \, x^{2} \log \left (3\right )^{2} + 16 \, x^{2} e^{8} - 48 \, x^{2} \log \left (3\right ) + 8 \, x e^{4} \log \left (3\right ) + 128 \, x^{2} - 32 \, x e^{4} + 16\right )}}{x^{2} \log \left (3\right )^{2} - 8 \, x^{2} \log \left (3\right ) + 16 \, x^{2}}\right )} \]
integrate(((((-8*x^3*exp(4)+16*x^4)*log(3)^2+((64*x^3-16*x)*exp(4)-128*x^4 )*log(3)+(-128*x^3+64*x)*exp(4)+256*x^4-64)*exp(((x^2*exp(4)^2-4*x^3*exp(4 )+4*x^4+4*x^2)*log(3)^2+(-8*x^2*exp(4)^2+(32*x^3+8*x)*exp(4)-32*x^4-48*x^2 )*log(3)+16*x^2*exp(4)^2+(-64*x^3-32*x)*exp(4)+64*x^4+128*x^2+16)/(x^2*log (3)^2-8*x^2*log(3)+16*x^2))+2*x^2*log(3)^2-16*x^2*log(3)+32*x^2)*log(x)+(( -8*x^3*exp(4)+16*x^4)*log(3)^2+((64*x^3-16*x)*exp(4)-128*x^4)*log(3)+(-128 *x^3+64*x)*exp(4)+256*x^4-64)*exp(((x^2*exp(4)^2-4*x^3*exp(4)+4*x^4+4*x^2) *log(3)^2+(-8*x^2*exp(4)^2+(32*x^3+8*x)*exp(4)-32*x^4-48*x^2)*log(3)+16*x^ 2*exp(4)^2+(-64*x^3-32*x)*exp(4)+64*x^4+128*x^2+16)/(x^2*log(3)^2-8*x^2*lo g(3)+16*x^2))^2+(2*x^2*log(3)^2-16*x^2*log(3)+32*x^2)*exp(((x^2*exp(4)^2-4 *x^3*exp(4)+4*x^4+4*x^2)*log(3)^2+(-8*x^2*exp(4)^2+(32*x^3+8*x)*exp(4)-32* x^4-48*x^2)*log(3)+16*x^2*exp(4)^2+(-64*x^3-32*x)*exp(4)+64*x^4+128*x^2+16 )/(x^2*log(3)^2-8*x^2*log(3)+16*x^2)))/(9*x^3*log(3)^2-72*x^3*log(3)+144*x ^3),x, algorithm=\
2/9*e^((4*x^4*log(3)^2 - 4*x^3*e^4*log(3)^2 - 32*x^4*log(3) + 32*x^3*e^4*l og(3) + x^2*e^8*log(3)^2 + 64*x^4 - 64*x^3*e^4 - 8*x^2*e^8*log(3) + 4*x^2* log(3)^2 + 16*x^2*e^8 - 48*x^2*log(3) + 8*x*e^4*log(3) + 128*x^2 - 32*x*e^ 4 + 16)/(x^2*log(3)^2 - 8*x^2*log(3) + 16*x^2))*log(x) + 1/9*log(x)^2 + 1/ 9*e^(2*(4*x^4*log(3)^2 - 4*x^3*e^4*log(3)^2 - 32*x^4*log(3) + 32*x^3*e^4*l og(3) + x^2*e^8*log(3)^2 + 64*x^4 - 64*x^3*e^4 - 8*x^2*e^8*log(3) + 4*x^2* log(3)^2 + 16*x^2*e^8 - 48*x^2*log(3) + 8*x*e^4*log(3) + 128*x^2 - 32*x*e^ 4 + 16)/(x^2*log(3)^2 - 8*x^2*log(3) + 16*x^2))
Timed out. \[ \int \frac {e^{\frac {16+128 x^2+16 e^8 x^2+64 x^4+e^4 \left (-32 x-64 x^3\right )+\left (-48 x^2-8 e^8 x^2-32 x^4+e^4 \left (8 x+32 x^3\right )\right ) \log (3)+\left (4 x^2+e^8 x^2-4 e^4 x^3+4 x^4\right ) \log ^2(3)}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}} \left (32 x^2-16 x^2 \log (3)+2 x^2 \log ^2(3)\right )+e^{\frac {2 \left (16+128 x^2+16 e^8 x^2+64 x^4+e^4 \left (-32 x-64 x^3\right )+\left (-48 x^2-8 e^8 x^2-32 x^4+e^4 \left (8 x+32 x^3\right )\right ) \log (3)+\left (4 x^2+e^8 x^2-4 e^4 x^3+4 x^4\right ) \log ^2(3)\right )}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}} \left (-64+256 x^4+e^4 \left (64 x-128 x^3\right )+\left (-128 x^4+e^4 \left (-16 x+64 x^3\right )\right ) \log (3)+\left (-8 e^4 x^3+16 x^4\right ) \log ^2(3)\right )+\left (32 x^2-16 x^2 \log (3)+2 x^2 \log ^2(3)+e^{\frac {16+128 x^2+16 e^8 x^2+64 x^4+e^4 \left (-32 x-64 x^3\right )+\left (-48 x^2-8 e^8 x^2-32 x^4+e^4 \left (8 x+32 x^3\right )\right ) \log (3)+\left (4 x^2+e^8 x^2-4 e^4 x^3+4 x^4\right ) \log ^2(3)}{16 x^2-8 x^2 \log (3)+x^2 \log ^2(3)}} \left (-64+256 x^4+e^4 \left (64 x-128 x^3\right )+\left (-128 x^4+e^4 \left (-16 x+64 x^3\right )\right ) \log (3)+\left (-8 e^4 x^3+16 x^4\right ) \log ^2(3)\right )\right ) \log (x)}{144 x^3-72 x^3 \log (3)+9 x^3 \log ^2(3)} \, dx=-\int -\frac {\ln \left (x\right )\,\left (2\,x^2\,{\ln \left (3\right )}^2-16\,x^2\,\ln \left (3\right )-{\mathrm {e}}^{\frac {{\ln \left (3\right )}^2\,\left (x^2\,{\mathrm {e}}^8-4\,x^3\,{\mathrm {e}}^4+4\,x^2+4\,x^4\right )-{\mathrm {e}}^4\,\left (64\,x^3+32\,x\right )-\ln \left (3\right )\,\left (8\,x^2\,{\mathrm {e}}^8-{\mathrm {e}}^4\,\left (32\,x^3+8\,x\right )+48\,x^2+32\,x^4\right )+16\,x^2\,{\mathrm {e}}^8+128\,x^2+64\,x^4+16}{x^2\,{\ln \left (3\right )}^2-8\,x^2\,\ln \left (3\right )+16\,x^2}}\,\left ({\ln \left (3\right )}^2\,\left (8\,x^3\,{\mathrm {e}}^4-16\,x^4\right )-{\mathrm {e}}^4\,\left (64\,x-128\,x^3\right )+\ln \left (3\right )\,\left ({\mathrm {e}}^4\,\left (16\,x-64\,x^3\right )+128\,x^4\right )-256\,x^4+64\right )+32\,x^2\right )+{\mathrm {e}}^{\frac {{\ln \left (3\right )}^2\,\left (x^2\,{\mathrm {e}}^8-4\,x^3\,{\mathrm {e}}^4+4\,x^2+4\,x^4\right )-{\mathrm {e}}^4\,\left (64\,x^3+32\,x\right )-\ln \left (3\right )\,\left (8\,x^2\,{\mathrm {e}}^8-{\mathrm {e}}^4\,\left (32\,x^3+8\,x\right )+48\,x^2+32\,x^4\right )+16\,x^2\,{\mathrm {e}}^8+128\,x^2+64\,x^4+16}{x^2\,{\ln \left (3\right )}^2-8\,x^2\,\ln \left (3\right )+16\,x^2}}\,\left (2\,x^2\,{\ln \left (3\right )}^2-16\,x^2\,\ln \left (3\right )+32\,x^2\right )-{\mathrm {e}}^{\frac {2\,\left ({\ln \left (3\right )}^2\,\left (x^2\,{\mathrm {e}}^8-4\,x^3\,{\mathrm {e}}^4+4\,x^2+4\,x^4\right )-{\mathrm {e}}^4\,\left (64\,x^3+32\,x\right )-\ln \left (3\right )\,\left (8\,x^2\,{\mathrm {e}}^8-{\mathrm {e}}^4\,\left (32\,x^3+8\,x\right )+48\,x^2+32\,x^4\right )+16\,x^2\,{\mathrm {e}}^8+128\,x^2+64\,x^4+16\right )}{x^2\,{\ln \left (3\right )}^2-8\,x^2\,\ln \left (3\right )+16\,x^2}}\,\left ({\ln \left (3\right )}^2\,\left (8\,x^3\,{\mathrm {e}}^4-16\,x^4\right )-{\mathrm {e}}^4\,\left (64\,x-128\,x^3\right )+\ln \left (3\right )\,\left ({\mathrm {e}}^4\,\left (16\,x-64\,x^3\right )+128\,x^4\right )-256\,x^4+64\right )}{9\,x^3\,{\ln \left (3\right )}^2-72\,x^3\,\ln \left (3\right )+144\,x^3} \,d x \]
int((log(x)*(2*x^2*log(3)^2 - 16*x^2*log(3) - exp((log(3)^2*(x^2*exp(8) - 4*x^3*exp(4) + 4*x^2 + 4*x^4) - exp(4)*(32*x + 64*x^3) - log(3)*(8*x^2*exp (8) - exp(4)*(8*x + 32*x^3) + 48*x^2 + 32*x^4) + 16*x^2*exp(8) + 128*x^2 + 64*x^4 + 16)/(x^2*log(3)^2 - 8*x^2*log(3) + 16*x^2))*(log(3)^2*(8*x^3*exp (4) - 16*x^4) - exp(4)*(64*x - 128*x^3) + log(3)*(exp(4)*(16*x - 64*x^3) + 128*x^4) - 256*x^4 + 64) + 32*x^2) + exp((log(3)^2*(x^2*exp(8) - 4*x^3*ex p(4) + 4*x^2 + 4*x^4) - exp(4)*(32*x + 64*x^3) - log(3)*(8*x^2*exp(8) - ex p(4)*(8*x + 32*x^3) + 48*x^2 + 32*x^4) + 16*x^2*exp(8) + 128*x^2 + 64*x^4 + 16)/(x^2*log(3)^2 - 8*x^2*log(3) + 16*x^2))*(2*x^2*log(3)^2 - 16*x^2*log (3) + 32*x^2) - exp((2*(log(3)^2*(x^2*exp(8) - 4*x^3*exp(4) + 4*x^2 + 4*x^ 4) - exp(4)*(32*x + 64*x^3) - log(3)*(8*x^2*exp(8) - exp(4)*(8*x + 32*x^3) + 48*x^2 + 32*x^4) + 16*x^2*exp(8) + 128*x^2 + 64*x^4 + 16))/(x^2*log(3)^ 2 - 8*x^2*log(3) + 16*x^2))*(log(3)^2*(8*x^3*exp(4) - 16*x^4) - exp(4)*(64 *x - 128*x^3) + log(3)*(exp(4)*(16*x - 64*x^3) + 128*x^4) - 256*x^4 + 64)) /(9*x^3*log(3)^2 - 72*x^3*log(3) + 144*x^3),x)
-int(-(log(x)*(2*x^2*log(3)^2 - 16*x^2*log(3) - exp((log(3)^2*(x^2*exp(8) - 4*x^3*exp(4) + 4*x^2 + 4*x^4) - exp(4)*(32*x + 64*x^3) - log(3)*(8*x^2*e xp(8) - exp(4)*(8*x + 32*x^3) + 48*x^2 + 32*x^4) + 16*x^2*exp(8) + 128*x^2 + 64*x^4 + 16)/(x^2*log(3)^2 - 8*x^2*log(3) + 16*x^2))*(log(3)^2*(8*x^3*e xp(4) - 16*x^4) - exp(4)*(64*x - 128*x^3) + log(3)*(exp(4)*(16*x - 64*x^3) + 128*x^4) - 256*x^4 + 64) + 32*x^2) + exp((log(3)^2*(x^2*exp(8) - 4*x^3* exp(4) + 4*x^2 + 4*x^4) - exp(4)*(32*x + 64*x^3) - log(3)*(8*x^2*exp(8) - exp(4)*(8*x + 32*x^3) + 48*x^2 + 32*x^4) + 16*x^2*exp(8) + 128*x^2 + 64*x^ 4 + 16)/(x^2*log(3)^2 - 8*x^2*log(3) + 16*x^2))*(2*x^2*log(3)^2 - 16*x^2*l og(3) + 32*x^2) - exp((2*(log(3)^2*(x^2*exp(8) - 4*x^3*exp(4) + 4*x^2 + 4* x^4) - exp(4)*(32*x + 64*x^3) - log(3)*(8*x^2*exp(8) - exp(4)*(8*x + 32*x^ 3) + 48*x^2 + 32*x^4) + 16*x^2*exp(8) + 128*x^2 + 64*x^4 + 16))/(x^2*log(3 )^2 - 8*x^2*log(3) + 16*x^2))*(log(3)^2*(8*x^3*exp(4) - 16*x^4) - exp(4)*( 64*x - 128*x^3) + log(3)*(exp(4)*(16*x - 64*x^3) + 128*x^4) - 256*x^4 + 64 ))/(9*x^3*log(3)^2 - 72*x^3*log(3) + 144*x^3), x)