Integrand size = 286, antiderivative size = 32 \[ \int \frac {e^{\frac {-16 x-4 x^2+8 x^3+2 x^4+e^x \left (32 x+8 x^2\right )+\left (-64-16 x+32 x^2+8 x^3\right ) \log (4)+\left (-64-16 x+32 x^2+8 x^3\right ) \log (x)}{x^2+4 x \log (4)+4 x \log (x)}} \left (16 x^2+8 x^4+4 x^5+\left (128 x+64 x^3+32 x^4\right ) \log (4)+\left (256+128 x^2+64 x^3\right ) \log ^2(4)+e^x \left (-128 x-64 x^2+32 x^3+8 x^4+\left (160 x^2+32 x^3\right ) \log (4)\right )+\left (128 x+64 x^3+32 x^4+e^x \left (160 x^2+32 x^3\right )+\left (512+256 x^2+128 x^3\right ) \log (4)\right ) \log (x)+\left (256+128 x^2+64 x^3\right ) \log ^2(x)\right )}{x^4+8 x^3 \log (4)+16 x^2 \log ^2(4)+\left (8 x^3+32 x^2 \log (4)\right ) \log (x)+16 x^2 \log ^2(x)} \, dx=-5+e^{2 (4+x) \left (-\frac {2}{x}+x+\frac {e^x}{\frac {x}{4}+\log (4)+\log (x)}\right )} \]
\[ \int \frac {e^{\frac {-16 x-4 x^2+8 x^3+2 x^4+e^x \left (32 x+8 x^2\right )+\left (-64-16 x+32 x^2+8 x^3\right ) \log (4)+\left (-64-16 x+32 x^2+8 x^3\right ) \log (x)}{x^2+4 x \log (4)+4 x \log (x)}} \left (16 x^2+8 x^4+4 x^5+\left (128 x+64 x^3+32 x^4\right ) \log (4)+\left (256+128 x^2+64 x^3\right ) \log ^2(4)+e^x \left (-128 x-64 x^2+32 x^3+8 x^4+\left (160 x^2+32 x^3\right ) \log (4)\right )+\left (128 x+64 x^3+32 x^4+e^x \left (160 x^2+32 x^3\right )+\left (512+256 x^2+128 x^3\right ) \log (4)\right ) \log (x)+\left (256+128 x^2+64 x^3\right ) \log ^2(x)\right )}{x^4+8 x^3 \log (4)+16 x^2 \log ^2(4)+\left (8 x^3+32 x^2 \log (4)\right ) \log (x)+16 x^2 \log ^2(x)} \, dx=\int \frac {e^{\frac {-16 x-4 x^2+8 x^3+2 x^4+e^x \left (32 x+8 x^2\right )+\left (-64-16 x+32 x^2+8 x^3\right ) \log (4)+\left (-64-16 x+32 x^2+8 x^3\right ) \log (x)}{x^2+4 x \log (4)+4 x \log (x)}} \left (16 x^2+8 x^4+4 x^5+\left (128 x+64 x^3+32 x^4\right ) \log (4)+\left (256+128 x^2+64 x^3\right ) \log ^2(4)+e^x \left (-128 x-64 x^2+32 x^3+8 x^4+\left (160 x^2+32 x^3\right ) \log (4)\right )+\left (128 x+64 x^3+32 x^4+e^x \left (160 x^2+32 x^3\right )+\left (512+256 x^2+128 x^3\right ) \log (4)\right ) \log (x)+\left (256+128 x^2+64 x^3\right ) \log ^2(x)\right )}{x^4+8 x^3 \log (4)+16 x^2 \log ^2(4)+\left (8 x^3+32 x^2 \log (4)\right ) \log (x)+16 x^2 \log ^2(x)} \, dx \]
Integrate[(E^((-16*x - 4*x^2 + 8*x^3 + 2*x^4 + E^x*(32*x + 8*x^2) + (-64 - 16*x + 32*x^2 + 8*x^3)*Log[4] + (-64 - 16*x + 32*x^2 + 8*x^3)*Log[x])/(x^ 2 + 4*x*Log[4] + 4*x*Log[x]))*(16*x^2 + 8*x^4 + 4*x^5 + (128*x + 64*x^3 + 32*x^4)*Log[4] + (256 + 128*x^2 + 64*x^3)*Log[4]^2 + E^x*(-128*x - 64*x^2 + 32*x^3 + 8*x^4 + (160*x^2 + 32*x^3)*Log[4]) + (128*x + 64*x^3 + 32*x^4 + E^x*(160*x^2 + 32*x^3) + (512 + 256*x^2 + 128*x^3)*Log[4])*Log[x] + (256 + 128*x^2 + 64*x^3)*Log[x]^2))/(x^4 + 8*x^3*Log[4] + 16*x^2*Log[4]^2 + (8* x^3 + 32*x^2*Log[4])*Log[x] + 16*x^2*Log[x]^2),x]
Integrate[(E^((-16*x - 4*x^2 + 8*x^3 + 2*x^4 + E^x*(32*x + 8*x^2) + (-64 - 16*x + 32*x^2 + 8*x^3)*Log[4] + (-64 - 16*x + 32*x^2 + 8*x^3)*Log[x])/(x^ 2 + 4*x*Log[4] + 4*x*Log[x]))*(16*x^2 + 8*x^4 + 4*x^5 + (128*x + 64*x^3 + 32*x^4)*Log[4] + (256 + 128*x^2 + 64*x^3)*Log[4]^2 + E^x*(-128*x - 64*x^2 + 32*x^3 + 8*x^4 + (160*x^2 + 32*x^3)*Log[4]) + (128*x + 64*x^3 + 32*x^4 + E^x*(160*x^2 + 32*x^3) + (512 + 256*x^2 + 128*x^3)*Log[4])*Log[x] + (256 + 128*x^2 + 64*x^3)*Log[x]^2))/(x^4 + 8*x^3*Log[4] + 16*x^2*Log[4]^2 + (8* x^3 + 32*x^2*Log[4])*Log[x] + 16*x^2*Log[x]^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.
| \(\displaystyle \int \frac {\left (4 x^5+8 x^4+16 x^2+\left (32 x^4+64 x^3+128 x\right ) \log (4)+\left (64 x^3+128 x^2+256\right ) \log ^2(x)+\left (64 x^3+128 x^2+256\right ) \log ^2(4)+e^x \left (8 x^4+32 x^3-64 x^2+\left (32 x^3+160 x^2\right ) \log (4)-128 x\right )+\left (32 x^4+64 x^3+e^x \left (32 x^3+160 x^2\right )+\left (128 x^3+256 x^2+512\right ) \log (4)+128 x\right ) \log (x)\right ) \exp \left (\frac {2 x^4+8 x^3-4 x^2+e^x \left (8 x^2+32 x\right )+\left (8 x^3+32 x^2-16 x-64\right ) \log (x)+\left (8 x^3+32 x^2-16 x-64\right ) \log (4)-16 x}{x^2+4 x \log (x)+4 x \log (4)}\right )}{x^4+8 x^3 \log (4)+16 x^2 \log ^2(x)+16 x^2 \log ^2(4)+\left (8 x^3+32 x^2 \log (4)\right ) \log (x)} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (4 x^5+8 x^4+16 x^2+\left (32 x^4+64 x^3+128 x\right ) \log (4)+\left (64 x^3+128 x^2+256\right ) \log ^2(x)+\left (64 x^3+128 x^2+256\right ) \log ^2(4)+e^x \left (8 x^4+32 x^3-64 x^2+\left (32 x^3+160 x^2\right ) \log (4)-128 x\right )+\left (32 x^4+64 x^3+e^x \left (32 x^3+160 x^2\right )+\left (128 x^3+256 x^2+512\right ) \log (4)+128 x\right ) \log (x)\right ) \exp \left (\frac {2 (x+4) \left (x^3+4 x^2 \log (x)+4 x^2 \log (4)+4 e^x x-2 x-8 \log (x)-8 \log (4)\right )}{x^2+4 x \log (x)+4 x \log (4)}\right )}{x^2 (x+4 \log (x)+\log (256))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {4 e^{\frac {2 (x+4) \left (x^3+4 \log (x) x^2+4 \log (4) x^2+4 e^x x-2 x-8 \log (x)-8 \log (4)\right )}{x^2+4 \log (x) x+4 \log (4) x}} x^3}{(x+4 \log (x)+\log (256))^2}+\frac {8 e^{\frac {2 (x+4) \left (x^3+4 \log (x) x^2+4 \log (4) x^2+4 e^x x-2 x-8 \log (x)-8 \log (4)\right )}{x^2+4 \log (x) x+4 \log (4) x}} x^2}{(x+4 \log (x)+\log (256))^2}+\frac {32 e^{\frac {2 (x+4) \left (x^3+4 \log (x) x^2+4 \log (4) x^2+4 e^x x-2 x-8 \log (x)-8 \log (4)\right )}{x^2+4 \log (x) x+4 \log (4) x}} \log (x) x^2}{(x+4 \log (x)+\log (256))^2}+\frac {64 e^{\frac {2 (x+4) \left (x^3+4 \log (x) x^2+4 \log (4) x^2+4 e^x x-2 x-8 \log (x)-8 \log (4)\right )}{x^2+4 \log (x) x+4 \log (4) x}} \log (x) x}{(x+4 \log (x)+\log (256))^2}+\frac {16 e^{\frac {2 (x+4) \left (x^3+4 \log (x) x^2+4 \log (4) x^2+4 e^x x-2 x-8 \log (x)-8 \log (4)\right )}{x^2+4 \log (x) x+4 \log (4) x}}}{(x+4 \log (x)+\log (256))^2}+\frac {8 e^{x+\frac {2 (x+4) \left (x^3+4 \log (x) x^2+4 \log (4) x^2+4 e^x x-2 x-8 \log (x)-8 \log (4)\right )}{x^2+4 \log (x) x+4 \log (4) x}} \left (x^3+4 \log (x) x^2+4 (1+\log (4)) x^2+20 \log (x) x-8 (1-\log (32)) x-16\right )}{(x+4 \log (x)+\log (256))^2 x}+\frac {128 e^{\frac {2 (x+4) \left (x^3+4 \log (x) x^2+4 \log (4) x^2+4 e^x x-2 x-8 \log (x)-8 \log (4)\right )}{x^2+4 \log (x) x+4 \log (4) x}} \log (x)}{(x+4 \log (x)+\log (256))^2 x}+\frac {32 e^{\frac {2 (x+4) \left (x^3+4 \log (x) x^2+4 \log (4) x^2+4 e^x x-2 x-8 \log (x)-8 \log (4)\right )}{x^2+4 \log (x) x+4 \log (4) x}} \left (x^3+2 x^2+4\right ) \log (4)}{(x+4 \log (x)+\log (256))^2 x}+\frac {64 e^{\frac {2 (x+4) \left (x^3+4 \log (x) x^2+4 \log (4) x^2+4 e^x x-2 x-8 \log (x)-8 \log (4)\right )}{x^2+4 \log (x) x+4 \log (4) x}} \left (x^3+2 x^2+4\right ) \log ^2(x)}{(x+4 \log (x)+\log (256))^2 x^2}+\frac {128 e^{\frac {2 (x+4) \left (x^3+4 \log (x) x^2+4 \log (4) x^2+4 e^x x-2 x-8 \log (x)-8 \log (4)\right )}{x^2+4 \log (x) x+4 \log (4) x}} \left (x^3+2 x^2+4\right ) \log (4) \log (x)}{(x+4 \log (x)+\log (256))^2 x^2}+\frac {64 e^{\frac {2 (x+4) \left (x^3+4 \log (x) x^2+4 \log (4) x^2+4 e^x x-2 x-8 \log (x)-8 \log (4)\right )}{x^2+4 \log (x) x+4 \log (4) x}} \left (x^3+2 x^2+4\right ) \log ^2(4)}{(x+4 \log (x)+\log (256))^2 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {4 \left (16 \left (x^3+2 x^2+4\right ) \log ^2(x)+\left (x^3+2 x^2+4\right ) (x+\log (256))^2+2 e^x x \left (x^3+4 x^2 (1+\log (4))+8 x (\log (32)-1)-16\right )+8 \left (x^4+x^3 \left (e^x+2+\log (256)\right )+x^2 \left (5 e^x+8 \log (4)\right )+4 x+16 \log (4)\right ) \log (x)\right ) \exp \left (\frac {2 (x+4) \left (x^3+4 x^2 \log (4)+4 \left (x^2-2\right ) \log (x)+\left (4 e^x-2\right ) x-8 \log (4)\right )}{x (x+4 \log (x)+\log (256))}\right )}{x^2 (x+4 \log (x)+\log (256))^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 4 \int -\frac {4^{\frac {8 x (x+4)}{x+4 \log (x)+\log (256)}-\frac {16 (x+4)}{x (x+4 \log (x)+\log (256))}} \exp \left (-\frac {2 (x+4) \left (2 \left (1-2 e^x\right ) x-x^3\right )}{x (x+4 \log (x)+\log (256))}\right ) x^{-\frac {8 (x+4) \left (2-x^2\right )}{x (x+4 \log (x)+\log (256))}-2} \left (-\left (\left (x^3+2 x^2+4\right ) (x+\log (256))^2\right )-16 \left (x^3+2 x^2+4\right ) \log ^2(x)+2 e^x x \left (-x^3-4 (1+\log (4)) x^2+8 (1-\log (32)) x+16\right )-8 \left (x^4+\left (2+e^x+\log (256)\right ) x^3+\left (5 e^x+8 \log (4)\right ) x^2+4 x+16 \log (4)\right ) \log (x)\right )}{(x+4 \log (x)+\log (256))^2}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -4 \int \frac {4^{\frac {8 x (x+4)}{x+4 \log (x)+\log (256)}-\frac {16 (x+4)}{x (x+4 \log (x)+\log (256))}} \exp \left (-\frac {2 (x+4) \left (2 \left (1-2 e^x\right ) x-x^3\right )}{x (x+4 \log (x)+\log (256))}\right ) x^{-\frac {8 (x+4) \left (2-x^2\right )}{x (x+4 \log (x)+\log (256))}-2} \left (-\left (\left (x^3+2 x^2+4\right ) (x+\log (256))^2\right )-16 \left (x^3+2 x^2+4\right ) \log ^2(x)+2 e^x x \left (-x^3-4 (1+\log (4)) x^2+8 (1-\log (32)) x+16\right )-8 \left (x^4+\left (2+e^x+\log (256)\right ) x^3+\left (5 e^x+8 \log (4)\right ) x^2+4 x+16 \log (4)\right ) \log (x)\right )}{(x+4 \log (x)+\log (256))^2}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle -4 \int \frac {4^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}} \exp \left (-\frac {2 (x+4) \left (2 \left (1-2 e^x\right ) x-x^3\right )}{x (x+4 \log (x)+\log (256))}\right ) x^{-\frac {8 (x+4) \left (2-x^2\right )}{x (x+4 \log (x)+\log (256))}-2} \left (-\left (\left (x^3+2 x^2+4\right ) (x+\log (256))^2\right )-16 \left (x^3+2 x^2+4\right ) \log ^2(x)+2 e^x x \left (-x^3-4 (1+\log (4)) x^2+8 (1-\log (32)) x+16\right )-8 \left (x^4+\left (2+e^x+\log (256)\right ) x^3+\left (5 e^x+8 \log (4)\right ) x^2+4 x+16 \log (4)\right ) \log (x)\right )}{(x+4 \log (x)+\log (256))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-\frac {4^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+3} e^{-\frac {2 (x+4) \left (2 \left (1-2 e^x\right ) x-x^3\right )}{x (x+4 \log (x)+\log (256))}} \log (4) \log (x) x^{-\frac {8 (x+4) \left (2-x^2\right )}{x (x+4 \log (x)+\log (256))}}}{(x+4 \log (x)+\log (256))^2}-\frac {4^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}} e^{-\frac {2 (x+4) \left (2 \left (1-2 e^x\right ) x-x^3\right )}{x (x+4 \log (x)+\log (256))}} \left (x^3+2 x^2+4\right ) (x+\log (256))^2 x^{-\frac {8 (x+4) \left (2-x^2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}-\frac {4^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+2} e^{-\frac {2 (x+4) \left (2 \left (1-2 e^x\right ) x-x^3\right )}{x (x+4 \log (x)+\log (256))}} \left (x^3+2 x^2+4\right ) \log ^2(x) x^{-\frac {8 (x+4) \left (2-x^2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+7} e^{-\frac {2 (x+4) \left (2 \left (1-2 e^x\right ) x-x^3\right )}{x (x+4 \log (x)+\log (256))}} \log (4) \log (x) x^{-\frac {8 (x+4) \left (2-x^2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}+\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+1} e^{x-\frac {2 (x+4) \left (2 \left (1-2 e^x\right ) x-x^3\right )}{x (x+4 \log (x)+\log (256))}} \left (-x^3-4 \log (x) x^2-4 (1+\log (4)) x^2-20 \log (x) x+8 (1-\log (32)) x+16\right ) x^{-\frac {8 (x+4) \left (2-x^2\right )}{x (x+4 \log (x)+\log (256))}-1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+5} e^{-\frac {2 (x+4) \left (2 \left (1-2 e^x\right ) x-x^3\right )}{x (x+4 \log (x)+\log (256))}} \log (x) x^{-\frac {8 (x+4) \left (2-x^2\right )}{x (x+4 \log (x)+\log (256))}-1}}{(x+4 \log (x)+\log (256))^2}-\frac {4^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+2} e^{-\frac {2 (x+4) \left (2 \left (1-2 e^x\right ) x-x^3\right )}{x (x+4 \log (x)+\log (256))}} (1+\log (16)) \log (x) x^{1-\frac {8 (x+4) \left (2-x^2\right )}{x (x+4 \log (x)+\log (256))}}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+3} e^{-\frac {2 (x+4) \left (2 \left (1-2 e^x\right ) x-x^3\right )}{x (x+4 \log (x)+\log (256))}} \log (x) x^{2-\frac {8 (x+4) \left (2-x^2\right )}{x (x+4 \log (x)+\log (256))}}}{(x+4 \log (x)+\log (256))^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}} \exp \left (\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}\right ) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2} \left (-\left (\left (x^3+2 x^2+4\right ) (x+\log (256))^2\right )-16 \left (x^3+2 x^2+4\right ) \log ^2(x)-2 e^x x \left (x^3+4 (1+\log (4)) x^2+8 (-1+\log (32)) x-16\right )-8 \left (x^4+\left (2+e^x+\log (256)\right ) x^3+\left (5 e^x+8 \log (4)\right ) x^2+4 x+16 \log (4)\right ) \log (x)\right )}{(x+4 \log (x)+\log (256))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+6} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (4) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (x^3+2 x^2+4\right ) (x+\log (256))^2 x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+4} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (x^3+2 x^2+4\right ) \log ^2(x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+7} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (4) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}+\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+1} e^{x+\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (-x^3-4 \log (x) x^2-4 (1+\log (4)) x^2-20 \log (x) x+8 (1-\log (32)) x+16\right ) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+5} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+4} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} (1+\log (16)) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+3} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+2}}{(x+4 \log (x)+\log (256))^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}} \exp \left (\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}\right ) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2} \left (-\left (\left (x^3+2 x^2+4\right ) (x+\log (256))^2\right )-16 \left (x^3+2 x^2+4\right ) \log ^2(x)-2 e^x x \left (x^3+4 (1+\log (4)) x^2+8 (-1+\log (32)) x-16\right )-8 \left (x^4+\left (2+e^x+\log (256)\right ) x^3+\left (5 e^x+8 \log (4)\right ) x^2+4 x+16 \log (4)\right ) \log (x)\right )}{(x+4 \log (x)+\log (256))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+6} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (4) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (x^3+2 x^2+4\right ) (x+\log (256))^2 x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+4} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (x^3+2 x^2+4\right ) \log ^2(x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+7} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (4) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}+\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+1} e^{x+\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (-x^3-4 \log (x) x^2-4 (1+\log (4)) x^2-20 \log (x) x+8 (1-\log (32)) x+16\right ) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+5} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+4} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} (1+\log (16)) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+3} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+2}}{(x+4 \log (x)+\log (256))^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}} \exp \left (\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}\right ) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2} \left (-\left (\left (x^3+2 x^2+4\right ) (x+\log (256))^2\right )-16 \left (x^3+2 x^2+4\right ) \log ^2(x)-2 e^x x \left (x^3+4 (1+\log (4)) x^2+8 (-1+\log (32)) x-16\right )-8 \left (x^4+\left (2+e^x+\log (256)\right ) x^3+\left (5 e^x+8 \log (4)\right ) x^2+4 x+16 \log (4)\right ) \log (x)\right )}{(x+4 \log (x)+\log (256))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+6} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (4) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (x^3+2 x^2+4\right ) (x+\log (256))^2 x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+4} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (x^3+2 x^2+4\right ) \log ^2(x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+7} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (4) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}+\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+1} e^{x+\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (-x^3-4 \log (x) x^2-4 (1+\log (4)) x^2-20 \log (x) x+8 (1-\log (32)) x+16\right ) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+5} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+4} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} (1+\log (16)) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+3} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+2}}{(x+4 \log (x)+\log (256))^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}} \exp \left (\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}\right ) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2} \left (-\left (\left (x^3+2 x^2+4\right ) (x+\log (256))^2\right )-16 \left (x^3+2 x^2+4\right ) \log ^2(x)-2 e^x x \left (x^3+4 (1+\log (4)) x^2+8 (-1+\log (32)) x-16\right )-8 \left (x^4+\left (2+e^x+\log (256)\right ) x^3+\left (5 e^x+8 \log (4)\right ) x^2+4 x+16 \log (4)\right ) \log (x)\right )}{(x+4 \log (x)+\log (256))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+6} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (4) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (x^3+2 x^2+4\right ) (x+\log (256))^2 x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+4} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (x^3+2 x^2+4\right ) \log ^2(x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+7} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (4) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}+\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+1} e^{x+\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (-x^3-4 \log (x) x^2-4 (1+\log (4)) x^2-20 \log (x) x+8 (1-\log (32)) x+16\right ) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+5} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+4} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} (1+\log (16)) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+3} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+2}}{(x+4 \log (x)+\log (256))^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}} \exp \left (\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}\right ) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2} \left (-\left (\left (x^3+2 x^2+4\right ) (x+\log (256))^2\right )-16 \left (x^3+2 x^2+4\right ) \log ^2(x)-2 e^x x \left (x^3+4 (1+\log (4)) x^2+8 (-1+\log (32)) x-16\right )-8 \left (x^4+\left (2+e^x+\log (256)\right ) x^3+\left (5 e^x+8 \log (4)\right ) x^2+4 x+16 \log (4)\right ) \log (x)\right )}{(x+4 \log (x)+\log (256))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+6} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (4) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (x^3+2 x^2+4\right ) (x+\log (256))^2 x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+4} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (x^3+2 x^2+4\right ) \log ^2(x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+7} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (4) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}+\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+1} e^{x+\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (-x^3-4 \log (x) x^2-4 (1+\log (4)) x^2-20 \log (x) x+8 (1-\log (32)) x+16\right ) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+5} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+4} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} (1+\log (16)) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+3} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+2}}{(x+4 \log (x)+\log (256))^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}} \exp \left (\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}\right ) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2} \left (-\left (\left (x^3+2 x^2+4\right ) (x+\log (256))^2\right )-16 \left (x^3+2 x^2+4\right ) \log ^2(x)-2 e^x x \left (x^3+4 (1+\log (4)) x^2+8 (-1+\log (32)) x-16\right )-8 \left (x^4+\left (2+e^x+\log (256)\right ) x^3+\left (5 e^x+8 \log (4)\right ) x^2+4 x+16 \log (4)\right ) \log (x)\right )}{(x+4 \log (x)+\log (256))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+6} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (4) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (x^3+2 x^2+4\right ) (x+\log (256))^2 x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+4} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (x^3+2 x^2+4\right ) \log ^2(x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+7} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (4) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}+\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+1} e^{x+\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (-x^3-4 \log (x) x^2-4 (1+\log (4)) x^2-20 \log (x) x+8 (1-\log (32)) x+16\right ) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+5} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+4} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} (1+\log (16)) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+3} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+2}}{(x+4 \log (x)+\log (256))^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}} \exp \left (\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}\right ) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2} \left (-\left (\left (x^3+2 x^2+4\right ) (x+\log (256))^2\right )-16 \left (x^3+2 x^2+4\right ) \log ^2(x)-2 e^x x \left (x^3+4 (1+\log (4)) x^2+8 (-1+\log (32)) x-16\right )-8 \left (x^4+\left (2+e^x+\log (256)\right ) x^3+\left (5 e^x+8 \log (4)\right ) x^2+4 x+16 \log (4)\right ) \log (x)\right )}{(x+4 \log (x)+\log (256))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+6} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (4) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (x^3+2 x^2+4\right ) (x+\log (256))^2 x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+4} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (x^3+2 x^2+4\right ) \log ^2(x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+7} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (4) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}+\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+1} e^{x+\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (-x^3-4 \log (x) x^2-4 (1+\log (4)) x^2-20 \log (x) x+8 (1-\log (32)) x+16\right ) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+5} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+4} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} (1+\log (16)) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+3} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+2}}{(x+4 \log (x)+\log (256))^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}} \exp \left (\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}\right ) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2} \left (-\left (\left (x^3+2 x^2+4\right ) (x+\log (256))^2\right )-16 \left (x^3+2 x^2+4\right ) \log ^2(x)-2 e^x x \left (x^3+4 (1+\log (4)) x^2+8 (-1+\log (32)) x-16\right )-8 \left (x^4+\left (2+e^x+\log (256)\right ) x^3+\left (5 e^x+8 \log (4)\right ) x^2+4 x+16 \log (4)\right ) \log (x)\right )}{(x+4 \log (x)+\log (256))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+6} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (4) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (x^3+2 x^2+4\right ) (x+\log (256))^2 x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+4} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (x^3+2 x^2+4\right ) \log ^2(x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+7} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (4) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}+\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+1} e^{x+\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (-x^3-4 \log (x) x^2-4 (1+\log (4)) x^2-20 \log (x) x+8 (1-\log (32)) x+16\right ) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+5} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+4} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} (1+\log (16)) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+3} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+2}}{(x+4 \log (x)+\log (256))^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}} \exp \left (\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}\right ) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2} \left (-\left (\left (x^3+2 x^2+4\right ) (x+\log (256))^2\right )-16 \left (x^3+2 x^2+4\right ) \log ^2(x)-2 e^x x \left (x^3+4 (1+\log (4)) x^2+8 (-1+\log (32)) x-16\right )-8 \left (x^4+\left (2+e^x+\log (256)\right ) x^3+\left (5 e^x+8 \log (4)\right ) x^2+4 x+16 \log (4)\right ) \log (x)\right )}{(x+4 \log (x)+\log (256))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+6} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (4) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (x^3+2 x^2+4\right ) (x+\log (256))^2 x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+4} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (x^3+2 x^2+4\right ) \log ^2(x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+7} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (4) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}+\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+1} e^{x+\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (-x^3-4 \log (x) x^2-4 (1+\log (4)) x^2-20 \log (x) x+8 (1-\log (32)) x+16\right ) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+5} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+4} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} (1+\log (16)) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+3} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+2}}{(x+4 \log (x)+\log (256))^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}} \exp \left (\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}\right ) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2} \left (-\left (\left (x^3+2 x^2+4\right ) (x+\log (256))^2\right )-16 \left (x^3+2 x^2+4\right ) \log ^2(x)-2 e^x x \left (x^3+4 (1+\log (4)) x^2+8 (-1+\log (32)) x-16\right )-8 \left (x^4+\left (2+e^x+\log (256)\right ) x^3+\left (5 e^x+8 \log (4)\right ) x^2+4 x+16 \log (4)\right ) \log (x)\right )}{(x+4 \log (x)+\log (256))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+6} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (4) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (x^3+2 x^2+4\right ) (x+\log (256))^2 x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+4} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (x^3+2 x^2+4\right ) \log ^2(x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+7} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (4) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}+\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+1} e^{x+\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (-x^3-4 \log (x) x^2-4 (1+\log (4)) x^2-20 \log (x) x+8 (1-\log (32)) x+16\right ) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+5} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+4} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} (1+\log (16)) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+3} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+2}}{(x+4 \log (x)+\log (256))^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}} \exp \left (\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}\right ) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2} \left (-\left (\left (x^3+2 x^2+4\right ) (x+\log (256))^2\right )-16 \left (x^3+2 x^2+4\right ) \log ^2(x)-2 e^x x \left (x^3+4 (1+\log (4)) x^2+8 (-1+\log (32)) x-16\right )-8 \left (x^4+\left (2+e^x+\log (256)\right ) x^3+\left (5 e^x+8 \log (4)\right ) x^2+4 x+16 \log (4)\right ) \log (x)\right )}{(x+4 \log (x)+\log (256))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+6} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (4) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (x^3+2 x^2+4\right ) (x+\log (256))^2 x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+4} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (x^3+2 x^2+4\right ) \log ^2(x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+7} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (4) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2}}{(x+4 \log (x)+\log (256))^2}+\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+1} e^{x+\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \left (-x^3-4 \log (x) x^2-4 (1+\log (4)) x^2-20 \log (x) x+8 (1-\log (32)) x+16\right ) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+5} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+4} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} (1+\log (16)) \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+1}}{(x+4 \log (x)+\log (256))^2}-\frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+3} e^{\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}} \log (x) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}+2}}{(x+4 \log (x)+\log (256))^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {2^{\frac {16 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}} \exp \left (\frac {2 (x+4) \left (x^2+4 e^x-2\right )}{x+4 \log (x)+\log (256)}\right ) x^{\frac {8 (x+4) \left (x^2-2\right )}{x (x+4 \log (x)+\log (256))}-2} \left (-\left (\left (x^3+2 x^2+4\right ) (x+\log (256))^2\right )-16 \left (x^3+2 x^2+4\right ) \log ^2(x)-2 e^x x \left (x^3+4 (1+\log (4)) x^2+8 (-1+\log (32)) x-16\right )-8 \left (x^4+\left (2+e^x+\log (256)\right ) x^3+\left (5 e^x+8 \log (4)\right ) x^2+4 x+16 \log (4)\right ) \log (x)\right )}{(x+4 \log (x)+\log (256))^2}dx\) |
Int[(E^((-16*x - 4*x^2 + 8*x^3 + 2*x^4 + E^x*(32*x + 8*x^2) + (-64 - 16*x + 32*x^2 + 8*x^3)*Log[4] + (-64 - 16*x + 32*x^2 + 8*x^3)*Log[x])/(x^2 + 4* x*Log[4] + 4*x*Log[x]))*(16*x^2 + 8*x^4 + 4*x^5 + (128*x + 64*x^3 + 32*x^4 )*Log[4] + (256 + 128*x^2 + 64*x^3)*Log[4]^2 + E^x*(-128*x - 64*x^2 + 32*x ^3 + 8*x^4 + (160*x^2 + 32*x^3)*Log[4]) + (128*x + 64*x^3 + 32*x^4 + E^x*( 160*x^2 + 32*x^3) + (512 + 256*x^2 + 128*x^3)*Log[4])*Log[x] + (256 + 128* x^2 + 64*x^3)*Log[x]^2))/(x^4 + 8*x^3*Log[4] + 16*x^2*Log[4]^2 + (8*x^3 + 32*x^2*Log[4])*Log[x] + 16*x^2*Log[x]^2),x]
3.26.94.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Time = 117.57 (sec) , antiderivative size = 56, normalized size of antiderivative = 1.75
| method | result | size |
| risch | \({\mathrm e}^{\frac {2 \left (4+x \right ) \left (4 x^{2} \ln \left (x \right )+8 x^{2} \ln \left (2\right )+x^{3}+4 \,{\mathrm e}^{x} x -8 \ln \left (x \right )-16 \ln \left (2\right )-2 x \right )}{x \left (4 \ln \left (x \right )+8 \ln \left (2\right )+x \right )}}\) | \(56\) |
| parallelrisch | \({\mathrm e}^{\frac {\left (8 x^{3}+32 x^{2}-16 x -64\right ) \ln \left (x \right )+\left (8 x^{2}+32 x \right ) {\mathrm e}^{x}+2 \left (8 x^{3}+32 x^{2}-16 x -64\right ) \ln \left (2\right )+2 x^{4}+8 x^{3}-4 x^{2}-16 x}{x \left (4 \ln \left (x \right )+8 \ln \left (2\right )+x \right )}}\) | \(86\) |
int(((64*x^3+128*x^2+256)*ln(x)^2+((32*x^3+160*x^2)*exp(x)+2*(128*x^3+256* x^2+512)*ln(2)+32*x^4+64*x^3+128*x)*ln(x)+(2*(32*x^3+160*x^2)*ln(2)+8*x^4+ 32*x^3-64*x^2-128*x)*exp(x)+4*(64*x^3+128*x^2+256)*ln(2)^2+2*(32*x^4+64*x^ 3+128*x)*ln(2)+4*x^5+8*x^4+16*x^2)*exp(((8*x^3+32*x^2-16*x-64)*ln(x)+(8*x^ 2+32*x)*exp(x)+2*(8*x^3+32*x^2-16*x-64)*ln(2)+2*x^4+8*x^3-4*x^2-16*x)/(4*x *ln(x)+8*x*ln(2)+x^2))/(16*x^2*ln(x)^2+(64*x^2*ln(2)+8*x^3)*ln(x)+64*x^2*l n(2)^2+16*x^3*ln(2)+x^4),x,method=_RETURNVERBOSE)
exp(2*(4+x)*(4*x^2*ln(x)+8*x^2*ln(2)+x^3+4*exp(x)*x-8*ln(x)-16*ln(2)-2*x)/ x/(4*ln(x)+8*ln(2)+x))
Leaf count of result is larger than twice the leaf count of optimal. 81 vs. \(2 (31) = 62\).
Time = 0.28 (sec) , antiderivative size = 81, normalized size of antiderivative = 2.53 \[ \int \frac {e^{\frac {-16 x-4 x^2+8 x^3+2 x^4+e^x \left (32 x+8 x^2\right )+\left (-64-16 x+32 x^2+8 x^3\right ) \log (4)+\left (-64-16 x+32 x^2+8 x^3\right ) \log (x)}{x^2+4 x \log (4)+4 x \log (x)}} \left (16 x^2+8 x^4+4 x^5+\left (128 x+64 x^3+32 x^4\right ) \log (4)+\left (256+128 x^2+64 x^3\right ) \log ^2(4)+e^x \left (-128 x-64 x^2+32 x^3+8 x^4+\left (160 x^2+32 x^3\right ) \log (4)\right )+\left (128 x+64 x^3+32 x^4+e^x \left (160 x^2+32 x^3\right )+\left (512+256 x^2+128 x^3\right ) \log (4)\right ) \log (x)+\left (256+128 x^2+64 x^3\right ) \log ^2(x)\right )}{x^4+8 x^3 \log (4)+16 x^2 \log ^2(4)+\left (8 x^3+32 x^2 \log (4)\right ) \log (x)+16 x^2 \log ^2(x)} \, dx=e^{\left (\frac {2 \, {\left (x^{4} + 4 \, x^{3} - 2 \, x^{2} + 4 \, {\left (x^{2} + 4 \, x\right )} e^{x} + 8 \, {\left (x^{3} + 4 \, x^{2} - 2 \, x - 8\right )} \log \left (2\right ) + 4 \, {\left (x^{3} + 4 \, x^{2} - 2 \, x - 8\right )} \log \left (x\right ) - 8 \, x\right )}}{x^{2} + 8 \, x \log \left (2\right ) + 4 \, x \log \left (x\right )}\right )} \]
integrate(((64*x^3+128*x^2+256)*log(x)^2+((32*x^3+160*x^2)*exp(x)+2*(128*x ^3+256*x^2+512)*log(2)+32*x^4+64*x^3+128*x)*log(x)+(2*(32*x^3+160*x^2)*log (2)+8*x^4+32*x^3-64*x^2-128*x)*exp(x)+4*(64*x^3+128*x^2+256)*log(2)^2+2*(3 2*x^4+64*x^3+128*x)*log(2)+4*x^5+8*x^4+16*x^2)*exp(((8*x^3+32*x^2-16*x-64) *log(x)+(8*x^2+32*x)*exp(x)+2*(8*x^3+32*x^2-16*x-64)*log(2)+2*x^4+8*x^3-4* x^2-16*x)/(4*x*log(x)+8*x*log(2)+x^2))/(16*x^2*log(x)^2+(64*x^2*log(2)+8*x ^3)*log(x)+64*x^2*log(2)^2+16*x^3*log(2)+x^4),x, algorithm=\
e^(2*(x^4 + 4*x^3 - 2*x^2 + 4*(x^2 + 4*x)*e^x + 8*(x^3 + 4*x^2 - 2*x - 8)* log(2) + 4*(x^3 + 4*x^2 - 2*x - 8)*log(x) - 8*x)/(x^2 + 8*x*log(2) + 4*x*l og(x)))
Leaf count of result is larger than twice the leaf count of optimal. 85 vs. \(2 (29) = 58\).
Time = 1.26 (sec) , antiderivative size = 85, normalized size of antiderivative = 2.66 \[ \int \frac {e^{\frac {-16 x-4 x^2+8 x^3+2 x^4+e^x \left (32 x+8 x^2\right )+\left (-64-16 x+32 x^2+8 x^3\right ) \log (4)+\left (-64-16 x+32 x^2+8 x^3\right ) \log (x)}{x^2+4 x \log (4)+4 x \log (x)}} \left (16 x^2+8 x^4+4 x^5+\left (128 x+64 x^3+32 x^4\right ) \log (4)+\left (256+128 x^2+64 x^3\right ) \log ^2(4)+e^x \left (-128 x-64 x^2+32 x^3+8 x^4+\left (160 x^2+32 x^3\right ) \log (4)\right )+\left (128 x+64 x^3+32 x^4+e^x \left (160 x^2+32 x^3\right )+\left (512+256 x^2+128 x^3\right ) \log (4)\right ) \log (x)+\left (256+128 x^2+64 x^3\right ) \log ^2(x)\right )}{x^4+8 x^3 \log (4)+16 x^2 \log ^2(4)+\left (8 x^3+32 x^2 \log (4)\right ) \log (x)+16 x^2 \log ^2(x)} \, dx=e^{\frac {2 x^{4} + 8 x^{3} - 4 x^{2} - 16 x + \left (8 x^{2} + 32 x\right ) e^{x} + \left (8 x^{3} + 32 x^{2} - 16 x - 64\right ) \log {\left (x \right )} + \left (16 x^{3} + 64 x^{2} - 32 x - 128\right ) \log {\left (2 \right )}}{x^{2} + 4 x \log {\left (x \right )} + 8 x \log {\left (2 \right )}}} \]
integrate(((64*x**3+128*x**2+256)*ln(x)**2+((32*x**3+160*x**2)*exp(x)+2*(1 28*x**3+256*x**2+512)*ln(2)+32*x**4+64*x**3+128*x)*ln(x)+(2*(32*x**3+160*x **2)*ln(2)+8*x**4+32*x**3-64*x**2-128*x)*exp(x)+4*(64*x**3+128*x**2+256)*l n(2)**2+2*(32*x**4+64*x**3+128*x)*ln(2)+4*x**5+8*x**4+16*x**2)*exp(((8*x** 3+32*x**2-16*x-64)*ln(x)+(8*x**2+32*x)*exp(x)+2*(8*x**3+32*x**2-16*x-64)*l n(2)+2*x**4+8*x**3-4*x**2-16*x)/(4*x*ln(x)+8*x*ln(2)+x**2))/(16*x**2*ln(x) **2+(64*x**2*ln(2)+8*x**3)*ln(x)+64*x**2*ln(2)**2+16*x**3*ln(2)+x**4),x)
exp((2*x**4 + 8*x**3 - 4*x**2 - 16*x + (8*x**2 + 32*x)*exp(x) + (8*x**3 + 32*x**2 - 16*x - 64)*log(x) + (16*x**3 + 64*x**2 - 32*x - 128)*log(2))/(x* *2 + 4*x*log(x) + 8*x*log(2)))
Timed out. \[ \int \frac {e^{\frac {-16 x-4 x^2+8 x^3+2 x^4+e^x \left (32 x+8 x^2\right )+\left (-64-16 x+32 x^2+8 x^3\right ) \log (4)+\left (-64-16 x+32 x^2+8 x^3\right ) \log (x)}{x^2+4 x \log (4)+4 x \log (x)}} \left (16 x^2+8 x^4+4 x^5+\left (128 x+64 x^3+32 x^4\right ) \log (4)+\left (256+128 x^2+64 x^3\right ) \log ^2(4)+e^x \left (-128 x-64 x^2+32 x^3+8 x^4+\left (160 x^2+32 x^3\right ) \log (4)\right )+\left (128 x+64 x^3+32 x^4+e^x \left (160 x^2+32 x^3\right )+\left (512+256 x^2+128 x^3\right ) \log (4)\right ) \log (x)+\left (256+128 x^2+64 x^3\right ) \log ^2(x)\right )}{x^4+8 x^3 \log (4)+16 x^2 \log ^2(4)+\left (8 x^3+32 x^2 \log (4)\right ) \log (x)+16 x^2 \log ^2(x)} \, dx=\text {Timed out} \]
integrate(((64*x^3+128*x^2+256)*log(x)^2+((32*x^3+160*x^2)*exp(x)+2*(128*x ^3+256*x^2+512)*log(2)+32*x^4+64*x^3+128*x)*log(x)+(2*(32*x^3+160*x^2)*log (2)+8*x^4+32*x^3-64*x^2-128*x)*exp(x)+4*(64*x^3+128*x^2+256)*log(2)^2+2*(3 2*x^4+64*x^3+128*x)*log(2)+4*x^5+8*x^4+16*x^2)*exp(((8*x^3+32*x^2-16*x-64) *log(x)+(8*x^2+32*x)*exp(x)+2*(8*x^3+32*x^2-16*x-64)*log(2)+2*x^4+8*x^3-4* x^2-16*x)/(4*x*log(x)+8*x*log(2)+x^2))/(16*x^2*log(x)^2+(64*x^2*log(2)+8*x ^3)*log(x)+64*x^2*log(2)^2+16*x^3*log(2)+x^4),x, algorithm=\
Leaf count of result is larger than twice the leaf count of optimal. 302 vs. \(2 (31) = 62\).
Time = 1.07 (sec) , antiderivative size = 302, normalized size of antiderivative = 9.44 \[ \int \frac {e^{\frac {-16 x-4 x^2+8 x^3+2 x^4+e^x \left (32 x+8 x^2\right )+\left (-64-16 x+32 x^2+8 x^3\right ) \log (4)+\left (-64-16 x+32 x^2+8 x^3\right ) \log (x)}{x^2+4 x \log (4)+4 x \log (x)}} \left (16 x^2+8 x^4+4 x^5+\left (128 x+64 x^3+32 x^4\right ) \log (4)+\left (256+128 x^2+64 x^3\right ) \log ^2(4)+e^x \left (-128 x-64 x^2+32 x^3+8 x^4+\left (160 x^2+32 x^3\right ) \log (4)\right )+\left (128 x+64 x^3+32 x^4+e^x \left (160 x^2+32 x^3\right )+\left (512+256 x^2+128 x^3\right ) \log (4)\right ) \log (x)+\left (256+128 x^2+64 x^3\right ) \log ^2(x)\right )}{x^4+8 x^3 \log (4)+16 x^2 \log ^2(4)+\left (8 x^3+32 x^2 \log (4)\right ) \log (x)+16 x^2 \log ^2(x)} \, dx=e^{\left (\frac {2 \, x^{4}}{x^{2} + 8 \, x \log \left (2\right ) + 4 \, x \log \left (x\right )} + \frac {16 \, x^{3} \log \left (2\right )}{x^{2} + 8 \, x \log \left (2\right ) + 4 \, x \log \left (x\right )} + \frac {8 \, x^{3} \log \left (x\right )}{x^{2} + 8 \, x \log \left (2\right ) + 4 \, x \log \left (x\right )} + \frac {8 \, x^{3}}{x^{2} + 8 \, x \log \left (2\right ) + 4 \, x \log \left (x\right )} + \frac {8 \, x^{2} e^{x}}{x^{2} + 8 \, x \log \left (2\right ) + 4 \, x \log \left (x\right )} + \frac {64 \, x^{2} \log \left (2\right )}{x^{2} + 8 \, x \log \left (2\right ) + 4 \, x \log \left (x\right )} + \frac {32 \, x^{2} \log \left (x\right )}{x^{2} + 8 \, x \log \left (2\right ) + 4 \, x \log \left (x\right )} - \frac {4 \, x^{2}}{x^{2} + 8 \, x \log \left (2\right ) + 4 \, x \log \left (x\right )} + \frac {32 \, x e^{x}}{x^{2} + 8 \, x \log \left (2\right ) + 4 \, x \log \left (x\right )} - \frac {32 \, x \log \left (2\right )}{x^{2} + 8 \, x \log \left (2\right ) + 4 \, x \log \left (x\right )} - \frac {16 \, x \log \left (x\right )}{x^{2} + 8 \, x \log \left (2\right ) + 4 \, x \log \left (x\right )} - \frac {16 \, x}{x^{2} + 8 \, x \log \left (2\right ) + 4 \, x \log \left (x\right )} - \frac {128 \, \log \left (2\right )}{x^{2} + 8 \, x \log \left (2\right ) + 4 \, x \log \left (x\right )} - \frac {64 \, \log \left (x\right )}{x^{2} + 8 \, x \log \left (2\right ) + 4 \, x \log \left (x\right )}\right )} \]
integrate(((64*x^3+128*x^2+256)*log(x)^2+((32*x^3+160*x^2)*exp(x)+2*(128*x ^3+256*x^2+512)*log(2)+32*x^4+64*x^3+128*x)*log(x)+(2*(32*x^3+160*x^2)*log (2)+8*x^4+32*x^3-64*x^2-128*x)*exp(x)+4*(64*x^3+128*x^2+256)*log(2)^2+2*(3 2*x^4+64*x^3+128*x)*log(2)+4*x^5+8*x^4+16*x^2)*exp(((8*x^3+32*x^2-16*x-64) *log(x)+(8*x^2+32*x)*exp(x)+2*(8*x^3+32*x^2-16*x-64)*log(2)+2*x^4+8*x^3-4* x^2-16*x)/(4*x*log(x)+8*x*log(2)+x^2))/(16*x^2*log(x)^2+(64*x^2*log(2)+8*x ^3)*log(x)+64*x^2*log(2)^2+16*x^3*log(2)+x^4),x, algorithm=\
e^(2*x^4/(x^2 + 8*x*log(2) + 4*x*log(x)) + 16*x^3*log(2)/(x^2 + 8*x*log(2) + 4*x*log(x)) + 8*x^3*log(x)/(x^2 + 8*x*log(2) + 4*x*log(x)) + 8*x^3/(x^2 + 8*x*log(2) + 4*x*log(x)) + 8*x^2*e^x/(x^2 + 8*x*log(2) + 4*x*log(x)) + 64*x^2*log(2)/(x^2 + 8*x*log(2) + 4*x*log(x)) + 32*x^2*log(x)/(x^2 + 8*x*l og(2) + 4*x*log(x)) - 4*x^2/(x^2 + 8*x*log(2) + 4*x*log(x)) + 32*x*e^x/(x^ 2 + 8*x*log(2) + 4*x*log(x)) - 32*x*log(2)/(x^2 + 8*x*log(2) + 4*x*log(x)) - 16*x*log(x)/(x^2 + 8*x*log(2) + 4*x*log(x)) - 16*x/(x^2 + 8*x*log(2) + 4*x*log(x)) - 128*log(2)/(x^2 + 8*x*log(2) + 4*x*log(x)) - 64*log(x)/(x^2 + 8*x*log(2) + 4*x*log(x)))
Time = 15.05 (sec) , antiderivative size = 223, normalized size of antiderivative = 6.97 \[ \int \frac {e^{\frac {-16 x-4 x^2+8 x^3+2 x^4+e^x \left (32 x+8 x^2\right )+\left (-64-16 x+32 x^2+8 x^3\right ) \log (4)+\left (-64-16 x+32 x^2+8 x^3\right ) \log (x)}{x^2+4 x \log (4)+4 x \log (x)}} \left (16 x^2+8 x^4+4 x^5+\left (128 x+64 x^3+32 x^4\right ) \log (4)+\left (256+128 x^2+64 x^3\right ) \log ^2(4)+e^x \left (-128 x-64 x^2+32 x^3+8 x^4+\left (160 x^2+32 x^3\right ) \log (4)\right )+\left (128 x+64 x^3+32 x^4+e^x \left (160 x^2+32 x^3\right )+\left (512+256 x^2+128 x^3\right ) \log (4)\right ) \log (x)+\left (256+128 x^2+64 x^3\right ) \log ^2(x)\right )}{x^4+8 x^3 \log (4)+16 x^2 \log ^2(4)+\left (8 x^3+32 x^2 \log (4)\right ) \log (x)+16 x^2 \log ^2(x)} \, dx=2^{\frac {64\,\left (x^2-2\right )}{8\,x\,\ln \left (2\right )+4\,x\,\ln \left (x\right )+x^2}+\frac {16\,\left (x^2-2\right )}{x+8\,\ln \left (2\right )+4\,\ln \left (x\right )}}\,x^{\frac {8\,\left (x^2+4\,x\right )}{x+8\,\ln \left (2\right )+4\,\ln \left (x\right )}-\frac {16\,\left (x+4\right )}{8\,x\,\ln \left (2\right )+4\,x\,\ln \left (x\right )+x^2}}\,{\mathrm {e}}^{\frac {8\,x^2\,{\mathrm {e}}^x}{8\,x\,\ln \left (2\right )+4\,x\,\ln \left (x\right )+x^2}}\,{\mathrm {e}}^{-\frac {4\,x^2}{8\,x\,\ln \left (2\right )+4\,x\,\ln \left (x\right )+x^2}}\,{\mathrm {e}}^{\frac {2\,x^4}{8\,x\,\ln \left (2\right )+4\,x\,\ln \left (x\right )+x^2}}\,{\mathrm {e}}^{\frac {8\,x^3}{8\,x\,\ln \left (2\right )+4\,x\,\ln \left (x\right )+x^2}}\,{\mathrm {e}}^{\frac {32\,x\,{\mathrm {e}}^x}{8\,x\,\ln \left (2\right )+4\,x\,\ln \left (x\right )+x^2}}\,{\mathrm {e}}^{-\frac {16\,x}{8\,x\,\ln \left (2\right )+4\,x\,\ln \left (x\right )+x^2}} \]
int((exp(-(16*x + 2*log(2)*(16*x - 32*x^2 - 8*x^3 + 64) - exp(x)*(32*x + 8 *x^2) + 4*x^2 - 8*x^3 - 2*x^4 + log(x)*(16*x - 32*x^2 - 8*x^3 + 64))/(8*x* log(2) + 4*x*log(x) + x^2))*(2*log(2)*(128*x + 64*x^3 + 32*x^4) + log(x)^2 *(128*x^2 + 64*x^3 + 256) + log(x)*(128*x + exp(x)*(160*x^2 + 32*x^3) + 2* log(2)*(256*x^2 + 128*x^3 + 512) + 64*x^3 + 32*x^4) + exp(x)*(2*log(2)*(16 0*x^2 + 32*x^3) - 128*x - 64*x^2 + 32*x^3 + 8*x^4) + 16*x^2 + 8*x^4 + 4*x^ 5 + 4*log(2)^2*(128*x^2 + 64*x^3 + 256)))/(64*x^2*log(2)^2 + 16*x^2*log(x) ^2 + log(x)*(64*x^2*log(2) + 8*x^3) + 16*x^3*log(2) + x^4),x)
2^((64*(x^2 - 2))/(8*x*log(2) + 4*x*log(x) + x^2) + (16*(x^2 - 2))/(x + 8* log(2) + 4*log(x)))*x^((8*(4*x + x^2))/(x + 8*log(2) + 4*log(x)) - (16*(x + 4))/(8*x*log(2) + 4*x*log(x) + x^2))*exp((8*x^2*exp(x))/(8*x*log(2) + 4* x*log(x) + x^2))*exp(-(4*x^2)/(8*x*log(2) + 4*x*log(x) + x^2))*exp((2*x^4) /(8*x*log(2) + 4*x*log(x) + x^2))*exp((8*x^3)/(8*x*log(2) + 4*x*log(x) + x ^2))*exp((32*x*exp(x))/(8*x*log(2) + 4*x*log(x) + x^2))*exp(-(16*x)/(8*x*l og(2) + 4*x*log(x) + x^2))