\(\int \frac {e^{-\frac {1}{-x+(-15+9 x-3 \log (4)+e^x (5-3 x+\log (4))) \log (x)}} (-15+8 x-3 \log (4)+e^x (5-3 x+\log (4))+(9 x+e^x (2 x-3 x^2+x \log (4))) \log (x))}{x^3+(30 x^2-18 x^3+6 x^2 \log (4)+e^x (-10 x^2+6 x^3-2 x^2 \log (4))) \log (x)+(225 x-270 x^2+81 x^3+(90 x-54 x^2) \log (4)+9 x \log ^2(4)+e^x (-150 x+180 x^2-54 x^3+(-60 x+36 x^2) \log (4)-6 x \log ^2(4))+e^{2 x} (25 x-30 x^2+9 x^3+(10 x-6 x^2) \log (4)+x \log ^2(4))) \log ^2(x)} \, dx\) [1379]

Optimal result

Integrand size = 240, antiderivative size = 26 \[ \int \frac {e^{-\frac {1}{-x+\left (-15+9 x-3 \log (4)+e^x (5-3 x+\log (4))\right ) \log (x)}} \left (-15+8 x-3 \log (4)+e^x (5-3 x+\log (4))+\left (9 x+e^x \left (2 x-3 x^2+x \log (4)\right )\right ) \log (x)\right )}{x^3+\left (30 x^2-18 x^3+6 x^2 \log (4)+e^x \left (-10 x^2+6 x^3-2 x^2 \log (4)\right )\right ) \log (x)+\left (225 x-270 x^2+81 x^3+\left (90 x-54 x^2\right ) \log (4)+9 x \log ^2(4)+e^x \left (-150 x+180 x^2-54 x^3+\left (-60 x+36 x^2\right ) \log (4)-6 x \log ^2(4)\right )+e^{2 x} \left (25 x-30 x^2+9 x^3+\left (10 x-6 x^2\right ) \log (4)+x \log ^2(4)\right )\right ) \log ^2(x)} \, dx=e^{\frac {1}{x-\left (3-e^x\right ) (-5+3 x-\log (4)) \log (x)}} \] Output:

exp(1/(x-ln(x)*(-exp(x)+3)*(3*x-2*ln(2)-5)))
 

Mathematica [A] (verified)

Time = 0.14 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.88 \[ \int \frac {e^{-\frac {1}{-x+\left (-15+9 x-3 \log (4)+e^x (5-3 x+\log (4))\right ) \log (x)}} \left (-15+8 x-3 \log (4)+e^x (5-3 x+\log (4))+\left (9 x+e^x \left (2 x-3 x^2+x \log (4)\right )\right ) \log (x)\right )}{x^3+\left (30 x^2-18 x^3+6 x^2 \log (4)+e^x \left (-10 x^2+6 x^3-2 x^2 \log (4)\right )\right ) \log (x)+\left (225 x-270 x^2+81 x^3+\left (90 x-54 x^2\right ) \log (4)+9 x \log ^2(4)+e^x \left (-150 x+180 x^2-54 x^3+\left (-60 x+36 x^2\right ) \log (4)-6 x \log ^2(4)\right )+e^{2 x} \left (25 x-30 x^2+9 x^3+\left (10 x-6 x^2\right ) \log (4)+x \log ^2(4)\right )\right ) \log ^2(x)} \, dx=e^{\frac {1}{x+\left (-3+e^x\right ) (-5+3 x-\log (4)) \log (x)}} \] Input:

Integrate[(-15 + 8*x - 3*Log[4] + E^x*(5 - 3*x + Log[4]) + (9*x + E^x*(2*x 
 - 3*x^2 + x*Log[4]))*Log[x])/(E^(-x + (-15 + 9*x - 3*Log[4] + E^x*(5 - 3* 
x + Log[4]))*Log[x])^(-1)*(x^3 + (30*x^2 - 18*x^3 + 6*x^2*Log[4] + E^x*(-1 
0*x^2 + 6*x^3 - 2*x^2*Log[4]))*Log[x] + (225*x - 270*x^2 + 81*x^3 + (90*x 
- 54*x^2)*Log[4] + 9*x*Log[4]^2 + E^x*(-150*x + 180*x^2 - 54*x^3 + (-60*x 
+ 36*x^2)*Log[4] - 6*x*Log[4]^2) + E^(2*x)*(25*x - 30*x^2 + 9*x^3 + (10*x 
- 6*x^2)*Log[4] + x*Log[4]^2))*Log[x]^2)),x]
 

Output:

E^(x + (-3 + E^x)*(-5 + 3*x - Log[4])*Log[x])^(-1)
 

Rubi [F]

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.

\(\displaystyle \int \frac {\left (\left (e^x \left (-3 x^2+2 x+x \log (4)\right )+9 x\right ) \log (x)+8 x+e^x (-3 x+5+\log (4))-15-3 \log (4)\right ) \exp \left (-\frac {1}{\left (9 x+e^x (-3 x+5+\log (4))-15-3 \log (4)\right ) \log (x)-x}\right )}{x^3+\left (81 x^3-270 x^2+\left (90 x-54 x^2\right ) \log (4)+e^x \left (-54 x^3+180 x^2+\left (36 x^2-60 x\right ) \log (4)-150 x-6 x \log ^2(4)\right )+e^{2 x} \left (9 x^3-30 x^2+\left (10 x-6 x^2\right ) \log (4)+25 x+x \log ^2(4)\right )+225 x+9 x \log ^2(4)\right ) \log ^2(x)+\left (-18 x^3+30 x^2+6 x^2 \log (4)+e^x \left (6 x^3-10 x^2-2 x^2 \log (4)\right )\right ) \log (x)} \, dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (8 x-\left (x \left (e^x (3 x-2-\log (4))-9\right ) \log (x)\right )+e^x (-3 x+5+\log (4))-15 \left (1+\frac {2 \log (2)}{5}\right )\right )}{x \left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (27 x^2 \log ^2(x)-3 x^2 \log (x)-3 x-90 x \left (1+\frac {2 \log (2)}{5}\right ) \log ^2(x)+75 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log ^2(x)+5 x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)-5 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+5 \left (1+\frac {2 \log (2)}{5}\right )\right )}{(-3 x+5+\log (4)) \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )^2}+\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (3 x^2 \log (x)+3 x-2 x (1+\log (2)) \log (x)-5 \left (1+\frac {2 \log (2)}{5}\right )\right )}{x (-3 x+5+\log (4)) \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (x \left (e^x \left (9 x^2-3 x (7+\log (16))+10+4 \log ^2(2)+\log (16384)\right )-27 x+45-12 \log ^2(2)+\log (262144)+\log (4) \log (64)\right ) \log (x)+(3 x-5-\log (4)) \left (-8 x+e^x (3 x-5-\log (4))+15+\log (64)\right )\right )}{x (-3 x+5+\log (4)) \left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-81 x^3 \log ^2(x)+9 x^3 \log (x)+9 x^2+405 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log ^2(x)-30 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)-675 x \left (1+\frac {\log ^2(4) \log (64)+\log (4) (\log (16) \log (64)+\log (262144))+\log (64) (\log (16384)+2 \log (1048576))}{75 \log (64)}\right ) \log ^2(x)+375 \left (1+\frac {(5+\log (4)) \left (\log (4) \left (\log ^2(64)+3 \log (262144)\right )+3 \log (64) \log (16384)\right )}{375 \log (64)}+\frac {2 \log (2)}{5}\right ) \log ^2(x)+40 x \left (1+\frac {1}{20} \log (2) (13+\log (4))\right ) \log (x)-30 x \left (1+\frac {2 \log (2)}{5}\right )-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (x)+25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right )\right )}{(-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )^2}+\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-9 x^3 \log (x)-9 x^2+21 x^2 \left (1+\frac {4 \log (2)}{7}\right ) \log (x)-10 x \left (1+\frac {1}{5} \log (2) (7+\log (4))\right ) \log (x)+30 x \left (1+\frac {2 \log (2)}{5}\right )-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right )\right )}{x (-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )}\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-9 x^3 \log (x)-9 x^2+21 x^2 \left (1+\frac {4 \log (2)}{7}\right ) \log (x)-10 x \left (1+\frac {7}{5} \log (2) \left (1+\frac {\log ^2(4)}{\log (16384)}\right )\right ) \log (x)+30 x \left (1+\frac {2 \log (2)}{5}\right )-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right )\right )}{x (-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )}+\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-81 x^3 \log (64) \log ^2(x)+9 x^3 \log (64) \log (x)+405 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log (64) \log ^2(x)-30 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log (64) \log (x)+9 x^2 \log (64)-675 x \log (64) \left (1+\frac {9 \log ^2(4) \log (64)+\log ^2(262144)+\log ^2(18014398509481984)+9 \log (4) \log (16) \log (64)}{675 \log (64)}\right ) \log ^2(x)+40 x \left (1+\frac {1}{40} \left (\log ^2(4)+26 \log (2)\right )\right ) \log (64) \log (x)+375 \log (64) \left (1+\frac {\log ^2(4) \log ^2(64)+3 (5+\log (4)) (\log (4) \log (262144)+\log (64) \log (16777216))}{375 \log (64)}\right ) \log ^2(x)-30 x \left (1+\frac {2 \log (2)}{5}\right ) \log (64)-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (64) \log (x)+25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (64)\right )}{\log (64) (-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-\frac {\left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right ) \left (x \left (9 x^2 \log (16384)-3 x (7+\log (16)) \log (16384)+14 \log (2) \log ^2(4)+\log (16384) (10+\log (16384))\right ) \log (x)+\log (16384) (-3 x+5+\log (4))^2\right )}{x \log (16384)}+\frac {\left (-81 x^3 \log (64)+81 x^2 (5+\log (4)) \log (64)-x \left (9 \left (75+\log ^2(4)+\log (4) \log (16)\right ) \log (64)+\log ^2(262144)+\log ^2(18014398509481984)\right )+\log ^2(64) \left (\log ^2(4)+\log (16777216)\right )+15 \log (64) (25+\log (16777216))+3 \log (4) (5+\log (4)) \log (262144)\right ) \log ^2(x)}{\log (64)}+\left (9 x^3-6 x^2 (5+\log (4))+x \left (40+\log ^2(4)+26 \log (2)\right )-(5+\log (4))^2\right ) \log (x)+(-3 x+5+\log (4))^2\right )}{(-3 x+5+\log (4))^2 \log (x) \left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-9 x^3 \log (16384) \log (x)+21 x^2 \left (1+\frac {4 \log (2)}{7}\right ) \log (16384) \log (x)-9 x^2 \log (16384)-14 x \log (2) \log ^2(4) \left (1+\frac {(5+\log (128)) \log (16384)}{7 \log (2) \log ^2(4)}\right ) \log (x)+30 x \left (1+\frac {2 \log (2)}{5}\right ) \log (16384)-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (16384)\right )}{x \log (16384) (-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )}+\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-81 x^3 \log (64) \log ^2(x)+9 x^3 \log (64) \log (x)+405 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log (64) \log ^2(x)-30 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log (64) \log (x)+9 x^2 \log (64)-675 x \log (64) \left (1+\frac {9 \log ^2(4) \log (64)+\log ^2(262144)+\log ^2(18014398509481984)+9 \log (4) \log (16) \log (64)}{675 \log (64)}\right ) \log ^2(x)+40 x \left (1+\frac {1}{40} \left (\log ^2(4)+26 \log (2)\right )\right ) \log (64) \log (x)+375 \log (64) \left (1+\frac {\log ^2(4) \log ^2(64)+3 (5+\log (4)) (\log (4) \log (262144)+\log (64) \log (16777216))}{375 \log (64)}\right ) \log ^2(x)-30 x \left (1+\frac {2 \log (2)}{5}\right ) \log (64)-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (64) \log (x)+25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (64)\right )}{\log (64) (-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-\frac {\left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right ) \left (x \left (9 x^2 \log (16384)-3 x (7+\log (16)) \log (16384)+14 \log (2) \log ^2(4)+\log (16384) (10+\log (16384))\right ) \log (x)+\log (16384) (-3 x+5+\log (4))^2\right )}{x \log (16384)}+\frac {\left (-81 x^3 \log (64)+81 x^2 (5+\log (4)) \log (64)-x \left (9 \left (75+\log ^2(4)+\log (4) \log (16)\right ) \log (64)+\log ^2(262144)+\log ^2(18014398509481984)\right )+\log ^2(64) \left (\log ^2(4)+\log (16777216)\right )+15 \log (64) (25+\log (16777216))+3 \log (4) (5+\log (4)) \log (262144)\right ) \log ^2(x)}{\log (64)}+\left (9 x^3-6 x^2 (5+\log (4))+x \left (40+\log ^2(4)+26 \log (2)\right )-(5+\log (4))^2\right ) \log (x)+(-3 x+5+\log (4))^2\right )}{(-3 x+5+\log (4))^2 \log (x) \left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-9 x^3 \log (16384) \log (x)+21 x^2 \left (1+\frac {4 \log (2)}{7}\right ) \log (16384) \log (x)-9 x^2 \log (16384)-14 x \log (2) \log ^2(4) \left (1+\frac {(5+\log (128)) \log (16384)}{7 \log (2) \log ^2(4)}\right ) \log (x)+30 x \left (1+\frac {2 \log (2)}{5}\right ) \log (16384)-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (16384)\right )}{x \log (16384) (-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )}+\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-81 x^3 \log (64) \log ^2(x)+9 x^3 \log (64) \log (x)+405 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log (64) \log ^2(x)-30 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log (64) \log (x)+9 x^2 \log (64)-675 x \log (64) \left (1+\frac {9 \log ^2(4) \log (64)+\log ^2(262144)+\log ^2(18014398509481984)+9 \log (4) \log (16) \log (64)}{675 \log (64)}\right ) \log ^2(x)+40 x \left (1+\frac {1}{40} \left (\log ^2(4)+26 \log (2)\right )\right ) \log (64) \log (x)+375 \log (64) \left (1+\frac {\log ^2(4) \log ^2(64)+3 (5+\log (4)) (\log (4) \log (262144)+\log (64) \log (16777216))}{375 \log (64)}\right ) \log ^2(x)-30 x \left (1+\frac {2 \log (2)}{5}\right ) \log (64)-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (64) \log (x)+25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (64)\right )}{\log (64) (-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-\frac {\left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right ) \left (x \left (9 x^2 \log (16384)-3 x (7+\log (16)) \log (16384)+14 \log (2) \log ^2(4)+\log (16384) (10+\log (16384))\right ) \log (x)+\log (16384) (-3 x+5+\log (4))^2\right )}{x \log (16384)}+\frac {\left (-81 x^3 \log (64)+81 x^2 (5+\log (4)) \log (64)-x \left (9 \left (75+\log ^2(4)+\log (4) \log (16)\right ) \log (64)+\log ^2(262144)+\log ^2(18014398509481984)\right )+\log ^2(64) \left (\log ^2(4)+\log (16777216)\right )+15 \log (64) (25+\log (16777216))+3 \log (4) (5+\log (4)) \log (262144)\right ) \log ^2(x)}{\log (64)}+\left (9 x^3-6 x^2 (5+\log (4))+x \left (40+\log ^2(4)+26 \log (2)\right )-(5+\log (4))^2\right ) \log (x)+(-3 x+5+\log (4))^2\right )}{(-3 x+5+\log (4))^2 \log (x) \left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-9 x^3 \log (16384) \log (x)+21 x^2 \left (1+\frac {4 \log (2)}{7}\right ) \log (16384) \log (x)-9 x^2 \log (16384)-14 x \log (2) \log ^2(4) \left (1+\frac {(5+\log (128)) \log (16384)}{7 \log (2) \log ^2(4)}\right ) \log (x)+30 x \left (1+\frac {2 \log (2)}{5}\right ) \log (16384)-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (16384)\right )}{x \log (16384) (-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )}+\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-81 x^3 \log (64) \log ^2(x)+9 x^3 \log (64) \log (x)+405 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log (64) \log ^2(x)-30 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log (64) \log (x)+9 x^2 \log (64)-675 x \log (64) \left (1+\frac {9 \log ^2(4) \log (64)+\log ^2(262144)+\log ^2(18014398509481984)+9 \log (4) \log (16) \log (64)}{675 \log (64)}\right ) \log ^2(x)+40 x \left (1+\frac {1}{40} \left (\log ^2(4)+26 \log (2)\right )\right ) \log (64) \log (x)+375 \log (64) \left (1+\frac {\log ^2(4) \log ^2(64)+3 (5+\log (4)) (\log (4) \log (262144)+\log (64) \log (16777216))}{375 \log (64)}\right ) \log ^2(x)-30 x \left (1+\frac {2 \log (2)}{5}\right ) \log (64)-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (64) \log (x)+25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (64)\right )}{\log (64) (-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-\frac {\left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right ) \left (x \left (9 x^2 \log (16384)-3 x (7+\log (16)) \log (16384)+14 \log (2) \log ^2(4)+\log (16384) (10+\log (16384))\right ) \log (x)+\log (16384) (-3 x+5+\log (4))^2\right )}{x \log (16384)}+\frac {\left (-81 x^3 \log (64)+81 x^2 (5+\log (4)) \log (64)-x \left (9 \left (75+\log ^2(4)+\log (4) \log (16)\right ) \log (64)+\log ^2(262144)+\log ^2(18014398509481984)\right )+\log ^2(64) \left (\log ^2(4)+\log (16777216)\right )+15 \log (64) (25+\log (16777216))+3 \log (4) (5+\log (4)) \log (262144)\right ) \log ^2(x)}{\log (64)}+\left (9 x^3-6 x^2 (5+\log (4))+x \left (40+\log ^2(4)+26 \log (2)\right )-(5+\log (4))^2\right ) \log (x)+(-3 x+5+\log (4))^2\right )}{(-3 x+5+\log (4))^2 \log (x) \left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-9 x^3 \log (16384) \log (x)+21 x^2 \left (1+\frac {4 \log (2)}{7}\right ) \log (16384) \log (x)-9 x^2 \log (16384)-14 x \log (2) \log ^2(4) \left (1+\frac {(5+\log (128)) \log (16384)}{7 \log (2) \log ^2(4)}\right ) \log (x)+30 x \left (1+\frac {2 \log (2)}{5}\right ) \log (16384)-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (16384)\right )}{x \log (16384) (-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )}+\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-81 x^3 \log (64) \log ^2(x)+9 x^3 \log (64) \log (x)+405 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log (64) \log ^2(x)-30 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log (64) \log (x)+9 x^2 \log (64)-675 x \log (64) \left (1+\frac {9 \log ^2(4) \log (64)+\log ^2(262144)+\log ^2(18014398509481984)+9 \log (4) \log (16) \log (64)}{675 \log (64)}\right ) \log ^2(x)+40 x \left (1+\frac {1}{40} \left (\log ^2(4)+26 \log (2)\right )\right ) \log (64) \log (x)+375 \log (64) \left (1+\frac {\log ^2(4) \log ^2(64)+3 (5+\log (4)) (\log (4) \log (262144)+\log (64) \log (16777216))}{375 \log (64)}\right ) \log ^2(x)-30 x \left (1+\frac {2 \log (2)}{5}\right ) \log (64)-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (64) \log (x)+25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (64)\right )}{\log (64) (-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-\frac {\left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right ) \left (x \left (9 x^2 \log (16384)-3 x (7+\log (16)) \log (16384)+14 \log (2) \log ^2(4)+\log (16384) (10+\log (16384))\right ) \log (x)+\log (16384) (-3 x+5+\log (4))^2\right )}{x \log (16384)}+\frac {\left (-81 x^3 \log (64)+81 x^2 (5+\log (4)) \log (64)-x \left (9 \left (75+\log ^2(4)+\log (4) \log (16)\right ) \log (64)+\log ^2(262144)+\log ^2(18014398509481984)\right )+\log ^2(64) \left (\log ^2(4)+\log (16777216)\right )+15 \log (64) (25+\log (16777216))+3 \log (4) (5+\log (4)) \log (262144)\right ) \log ^2(x)}{\log (64)}+\left (9 x^3-6 x^2 (5+\log (4))+x \left (40+\log ^2(4)+26 \log (2)\right )-(5+\log (4))^2\right ) \log (x)+(-3 x+5+\log (4))^2\right )}{(-3 x+5+\log (4))^2 \log (x) \left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-9 x^3 \log (16384) \log (x)+21 x^2 \left (1+\frac {4 \log (2)}{7}\right ) \log (16384) \log (x)-9 x^2 \log (16384)-14 x \log (2) \log ^2(4) \left (1+\frac {(5+\log (128)) \log (16384)}{7 \log (2) \log ^2(4)}\right ) \log (x)+30 x \left (1+\frac {2 \log (2)}{5}\right ) \log (16384)-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (16384)\right )}{x \log (16384) (-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )}+\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-81 x^3 \log (64) \log ^2(x)+9 x^3 \log (64) \log (x)+405 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log (64) \log ^2(x)-30 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log (64) \log (x)+9 x^2 \log (64)-675 x \log (64) \left (1+\frac {9 \log ^2(4) \log (64)+\log ^2(262144)+\log ^2(18014398509481984)+9 \log (4) \log (16) \log (64)}{675 \log (64)}\right ) \log ^2(x)+40 x \left (1+\frac {1}{40} \left (\log ^2(4)+26 \log (2)\right )\right ) \log (64) \log (x)+375 \log (64) \left (1+\frac {\log ^2(4) \log ^2(64)+3 (5+\log (4)) (\log (4) \log (262144)+\log (64) \log (16777216))}{375 \log (64)}\right ) \log ^2(x)-30 x \left (1+\frac {2 \log (2)}{5}\right ) \log (64)-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (64) \log (x)+25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (64)\right )}{\log (64) (-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-\frac {\left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right ) \left (x \left (9 x^2 \log (16384)-3 x (7+\log (16)) \log (16384)+14 \log (2) \log ^2(4)+\log (16384) (10+\log (16384))\right ) \log (x)+\log (16384) (-3 x+5+\log (4))^2\right )}{x \log (16384)}+\frac {\left (-81 x^3 \log (64)+81 x^2 (5+\log (4)) \log (64)-x \left (9 \left (75+\log ^2(4)+\log (4) \log (16)\right ) \log (64)+\log ^2(262144)+\log ^2(18014398509481984)\right )+\log ^2(64) \left (\log ^2(4)+\log (16777216)\right )+15 \log (64) (25+\log (16777216))+3 \log (4) (5+\log (4)) \log (262144)\right ) \log ^2(x)}{\log (64)}+\left (9 x^3-6 x^2 (5+\log (4))+x \left (40+\log ^2(4)+26 \log (2)\right )-(5+\log (4))^2\right ) \log (x)+(-3 x+5+\log (4))^2\right )}{(-3 x+5+\log (4))^2 \log (x) \left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-9 x^3 \log (16384) \log (x)+21 x^2 \left (1+\frac {4 \log (2)}{7}\right ) \log (16384) \log (x)-9 x^2 \log (16384)-14 x \log (2) \log ^2(4) \left (1+\frac {(5+\log (128)) \log (16384)}{7 \log (2) \log ^2(4)}\right ) \log (x)+30 x \left (1+\frac {2 \log (2)}{5}\right ) \log (16384)-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (16384)\right )}{x \log (16384) (-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )}+\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-81 x^3 \log (64) \log ^2(x)+9 x^3 \log (64) \log (x)+405 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log (64) \log ^2(x)-30 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log (64) \log (x)+9 x^2 \log (64)-675 x \log (64) \left (1+\frac {9 \log ^2(4) \log (64)+\log ^2(262144)+\log ^2(18014398509481984)+9 \log (4) \log (16) \log (64)}{675 \log (64)}\right ) \log ^2(x)+40 x \left (1+\frac {1}{40} \left (\log ^2(4)+26 \log (2)\right )\right ) \log (64) \log (x)+375 \log (64) \left (1+\frac {\log ^2(4) \log ^2(64)+3 (5+\log (4)) (\log (4) \log (262144)+\log (64) \log (16777216))}{375 \log (64)}\right ) \log ^2(x)-30 x \left (1+\frac {2 \log (2)}{5}\right ) \log (64)-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (64) \log (x)+25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (64)\right )}{\log (64) (-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-\frac {\left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right ) \left (x \left (9 x^2 \log (16384)-3 x (7+\log (16)) \log (16384)+14 \log (2) \log ^2(4)+\log (16384) (10+\log (16384))\right ) \log (x)+\log (16384) (-3 x+5+\log (4))^2\right )}{x \log (16384)}+\frac {\left (-81 x^3 \log (64)+81 x^2 (5+\log (4)) \log (64)-x \left (9 \left (75+\log ^2(4)+\log (4) \log (16)\right ) \log (64)+\log ^2(262144)+\log ^2(18014398509481984)\right )+\log ^2(64) \left (\log ^2(4)+\log (16777216)\right )+15 \log (64) (25+\log (16777216))+3 \log (4) (5+\log (4)) \log (262144)\right ) \log ^2(x)}{\log (64)}+\left (9 x^3-6 x^2 (5+\log (4))+x \left (40+\log ^2(4)+26 \log (2)\right )-(5+\log (4))^2\right ) \log (x)+(-3 x+5+\log (4))^2\right )}{(-3 x+5+\log (4))^2 \log (x) \left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-9 x^3 \log (16384) \log (x)+21 x^2 \left (1+\frac {4 \log (2)}{7}\right ) \log (16384) \log (x)-9 x^2 \log (16384)-14 x \log (2) \log ^2(4) \left (1+\frac {(5+\log (128)) \log (16384)}{7 \log (2) \log ^2(4)}\right ) \log (x)+30 x \left (1+\frac {2 \log (2)}{5}\right ) \log (16384)-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (16384)\right )}{x \log (16384) (-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )}+\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-81 x^3 \log (64) \log ^2(x)+9 x^3 \log (64) \log (x)+405 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log (64) \log ^2(x)-30 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log (64) \log (x)+9 x^2 \log (64)-675 x \log (64) \left (1+\frac {9 \log ^2(4) \log (64)+\log ^2(262144)+\log ^2(18014398509481984)+9 \log (4) \log (16) \log (64)}{675 \log (64)}\right ) \log ^2(x)+40 x \left (1+\frac {1}{40} \left (\log ^2(4)+26 \log (2)\right )\right ) \log (64) \log (x)+375 \log (64) \left (1+\frac {\log ^2(4) \log ^2(64)+3 (5+\log (4)) (\log (4) \log (262144)+\log (64) \log (16777216))}{375 \log (64)}\right ) \log ^2(x)-30 x \left (1+\frac {2 \log (2)}{5}\right ) \log (64)-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (64) \log (x)+25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (64)\right )}{\log (64) (-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-\frac {\left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right ) \left (x \left (9 x^2 \log (16384)-3 x (7+\log (16)) \log (16384)+14 \log (2) \log ^2(4)+\log (16384) (10+\log (16384))\right ) \log (x)+\log (16384) (-3 x+5+\log (4))^2\right )}{x \log (16384)}+\frac {\left (-81 x^3 \log (64)+81 x^2 (5+\log (4)) \log (64)-x \left (9 \left (75+\log ^2(4)+\log (4) \log (16)\right ) \log (64)+\log ^2(262144)+\log ^2(18014398509481984)\right )+\log ^2(64) \left (\log ^2(4)+\log (16777216)\right )+15 \log (64) (25+\log (16777216))+3 \log (4) (5+\log (4)) \log (262144)\right ) \log ^2(x)}{\log (64)}+\left (9 x^3-6 x^2 (5+\log (4))+x \left (40+\log ^2(4)+26 \log (2)\right )-(5+\log (4))^2\right ) \log (x)+(-3 x+5+\log (4))^2\right )}{(-3 x+5+\log (4))^2 \log (x) \left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-9 x^3 \log (16384) \log (x)+21 x^2 \left (1+\frac {4 \log (2)}{7}\right ) \log (16384) \log (x)-9 x^2 \log (16384)-14 x \log (2) \log ^2(4) \left (1+\frac {(5+\log (128)) \log (16384)}{7 \log (2) \log ^2(4)}\right ) \log (x)+30 x \left (1+\frac {2 \log (2)}{5}\right ) \log (16384)-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (16384)\right )}{x \log (16384) (-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )}+\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-81 x^3 \log (64) \log ^2(x)+9 x^3 \log (64) \log (x)+405 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log (64) \log ^2(x)-30 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log (64) \log (x)+9 x^2 \log (64)-675 x \log (64) \left (1+\frac {9 \log ^2(4) \log (64)+\log ^2(262144)+\log ^2(18014398509481984)+9 \log (4) \log (16) \log (64)}{675 \log (64)}\right ) \log ^2(x)+40 x \left (1+\frac {1}{40} \left (\log ^2(4)+26 \log (2)\right )\right ) \log (64) \log (x)+375 \log (64) \left (1+\frac {\log ^2(4) \log ^2(64)+3 (5+\log (4)) (\log (4) \log (262144)+\log (64) \log (16777216))}{375 \log (64)}\right ) \log ^2(x)-30 x \left (1+\frac {2 \log (2)}{5}\right ) \log (64)-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (64) \log (x)+25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (64)\right )}{\log (64) (-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-\frac {\left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right ) \left (x \left (9 x^2 \log (16384)-3 x (7+\log (16)) \log (16384)+14 \log (2) \log ^2(4)+\log (16384) (10+\log (16384))\right ) \log (x)+\log (16384) (-3 x+5+\log (4))^2\right )}{x \log (16384)}+\frac {\left (-81 x^3 \log (64)+81 x^2 (5+\log (4)) \log (64)-x \left (9 \left (75+\log ^2(4)+\log (4) \log (16)\right ) \log (64)+\log ^2(262144)+\log ^2(18014398509481984)\right )+\log ^2(64) \left (\log ^2(4)+\log (16777216)\right )+15 \log (64) (25+\log (16777216))+3 \log (4) (5+\log (4)) \log (262144)\right ) \log ^2(x)}{\log (64)}+\left (9 x^3-6 x^2 (5+\log (4))+x \left (40+\log ^2(4)+26 \log (2)\right )-(5+\log (4))^2\right ) \log (x)+(-3 x+5+\log (4))^2\right )}{(-3 x+5+\log (4))^2 \log (x) \left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-9 x^3 \log (16384) \log (x)+21 x^2 \left (1+\frac {4 \log (2)}{7}\right ) \log (16384) \log (x)-9 x^2 \log (16384)-14 x \log (2) \log ^2(4) \left (1+\frac {(5+\log (128)) \log (16384)}{7 \log (2) \log ^2(4)}\right ) \log (x)+30 x \left (1+\frac {2 \log (2)}{5}\right ) \log (16384)-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (16384)\right )}{x \log (16384) (-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )}+\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-81 x^3 \log (64) \log ^2(x)+9 x^3 \log (64) \log (x)+405 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log (64) \log ^2(x)-30 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log (64) \log (x)+9 x^2 \log (64)-675 x \log (64) \left (1+\frac {9 \log ^2(4) \log (64)+\log ^2(262144)+\log ^2(18014398509481984)+9 \log (4) \log (16) \log (64)}{675 \log (64)}\right ) \log ^2(x)+40 x \left (1+\frac {1}{40} \left (\log ^2(4)+26 \log (2)\right )\right ) \log (64) \log (x)+375 \log (64) \left (1+\frac {\log ^2(4) \log ^2(64)+3 (5+\log (4)) (\log (4) \log (262144)+\log (64) \log (16777216))}{375 \log (64)}\right ) \log ^2(x)-30 x \left (1+\frac {2 \log (2)}{5}\right ) \log (64)-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (64) \log (x)+25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (64)\right )}{\log (64) (-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-\frac {\left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right ) \left (x \left (9 x^2 \log (16384)-3 x (7+\log (16)) \log (16384)+14 \log (2) \log ^2(4)+\log (16384) (10+\log (16384))\right ) \log (x)+\log (16384) (-3 x+5+\log (4))^2\right )}{x \log (16384)}+\frac {\left (-81 x^3 \log (64)+81 x^2 (5+\log (4)) \log (64)-x \left (9 \left (75+\log ^2(4)+\log (4) \log (16)\right ) \log (64)+\log ^2(262144)+\log ^2(18014398509481984)\right )+\log ^2(64) \left (\log ^2(4)+\log (16777216)\right )+15 \log (64) (25+\log (16777216))+3 \log (4) (5+\log (4)) \log (262144)\right ) \log ^2(x)}{\log (64)}+\left (9 x^3-6 x^2 (5+\log (4))+x \left (40+\log ^2(4)+26 \log (2)\right )-(5+\log (4))^2\right ) \log (x)+(-3 x+5+\log (4))^2\right )}{(-3 x+5+\log (4))^2 \log (x) \left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-9 x^3 \log (16384) \log (x)+21 x^2 \left (1+\frac {4 \log (2)}{7}\right ) \log (16384) \log (x)-9 x^2 \log (16384)-14 x \log (2) \log ^2(4) \left (1+\frac {(5+\log (128)) \log (16384)}{7 \log (2) \log ^2(4)}\right ) \log (x)+30 x \left (1+\frac {2 \log (2)}{5}\right ) \log (16384)-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (16384)\right )}{x \log (16384) (-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )}+\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-81 x^3 \log (64) \log ^2(x)+9 x^3 \log (64) \log (x)+405 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log (64) \log ^2(x)-30 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log (64) \log (x)+9 x^2 \log (64)-675 x \log (64) \left (1+\frac {9 \log ^2(4) \log (64)+\log ^2(262144)+\log ^2(18014398509481984)+9 \log (4) \log (16) \log (64)}{675 \log (64)}\right ) \log ^2(x)+40 x \left (1+\frac {1}{40} \left (\log ^2(4)+26 \log (2)\right )\right ) \log (64) \log (x)+375 \log (64) \left (1+\frac {\log ^2(4) \log ^2(64)+3 (5+\log (4)) (\log (4) \log (262144)+\log (64) \log (16777216))}{375 \log (64)}\right ) \log ^2(x)-30 x \left (1+\frac {2 \log (2)}{5}\right ) \log (64)-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (64) \log (x)+25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (64)\right )}{\log (64) (-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-\frac {\left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right ) \left (x \left (9 x^2 \log (16384)-3 x (7+\log (16)) \log (16384)+14 \log (2) \log ^2(4)+\log (16384) (10+\log (16384))\right ) \log (x)+\log (16384) (-3 x+5+\log (4))^2\right )}{x \log (16384)}+\frac {\left (-81 x^3 \log (64)+81 x^2 (5+\log (4)) \log (64)-x \left (9 \left (75+\log ^2(4)+\log (4) \log (16)\right ) \log (64)+\log ^2(262144)+\log ^2(18014398509481984)\right )+\log ^2(64) \left (\log ^2(4)+\log (16777216)\right )+15 \log (64) (25+\log (16777216))+3 \log (4) (5+\log (4)) \log (262144)\right ) \log ^2(x)}{\log (64)}+\left (9 x^3-6 x^2 (5+\log (4))+x \left (40+\log ^2(4)+26 \log (2)\right )-(5+\log (4))^2\right ) \log (x)+(-3 x+5+\log (4))^2\right )}{(-3 x+5+\log (4))^2 \log (x) \left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-9 x^3 \log (16384) \log (x)+21 x^2 \left (1+\frac {4 \log (2)}{7}\right ) \log (16384) \log (x)-9 x^2 \log (16384)-14 x \log (2) \log ^2(4) \left (1+\frac {(5+\log (128)) \log (16384)}{7 \log (2) \log ^2(4)}\right ) \log (x)+30 x \left (1+\frac {2 \log (2)}{5}\right ) \log (16384)-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (16384)\right )}{x \log (16384) (-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )}+\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-81 x^3 \log (64) \log ^2(x)+9 x^3 \log (64) \log (x)+405 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log (64) \log ^2(x)-30 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log (64) \log (x)+9 x^2 \log (64)-675 x \log (64) \left (1+\frac {9 \log ^2(4) \log (64)+\log ^2(262144)+\log ^2(18014398509481984)+9 \log (4) \log (16) \log (64)}{675 \log (64)}\right ) \log ^2(x)+40 x \left (1+\frac {1}{40} \left (\log ^2(4)+26 \log (2)\right )\right ) \log (64) \log (x)+375 \log (64) \left (1+\frac {\log ^2(4) \log ^2(64)+3 (5+\log (4)) (\log (4) \log (262144)+\log (64) \log (16777216))}{375 \log (64)}\right ) \log ^2(x)-30 x \left (1+\frac {2 \log (2)}{5}\right ) \log (64)-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (64) \log (x)+25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (64)\right )}{\log (64) (-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-\frac {\left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right ) \left (x \left (9 x^2 \log (16384)-3 x (7+\log (16)) \log (16384)+14 \log (2) \log ^2(4)+\log (16384) (10+\log (16384))\right ) \log (x)+\log (16384) (-3 x+5+\log (4))^2\right )}{x \log (16384)}+\frac {\left (-81 x^3 \log (64)+81 x^2 (5+\log (4)) \log (64)-x \left (9 \left (75+\log ^2(4)+\log (4) \log (16)\right ) \log (64)+\log ^2(262144)+\log ^2(18014398509481984)\right )+\log ^2(64) \left (\log ^2(4)+\log (16777216)\right )+15 \log (64) (25+\log (16777216))+3 \log (4) (5+\log (4)) \log (262144)\right ) \log ^2(x)}{\log (64)}+\left (9 x^3-6 x^2 (5+\log (4))+x \left (40+\log ^2(4)+26 \log (2)\right )-(5+\log (4))^2\right ) \log (x)+(-3 x+5+\log (4))^2\right )}{(-3 x+5+\log (4))^2 \log (x) \left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-9 x^3 \log (16384) \log (x)+21 x^2 \left (1+\frac {4 \log (2)}{7}\right ) \log (16384) \log (x)-9 x^2 \log (16384)-14 x \log (2) \log ^2(4) \left (1+\frac {(5+\log (128)) \log (16384)}{7 \log (2) \log ^2(4)}\right ) \log (x)+30 x \left (1+\frac {2 \log (2)}{5}\right ) \log (16384)-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (16384)\right )}{x \log (16384) (-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )}+\frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-81 x^3 \log (64) \log ^2(x)+9 x^3 \log (64) \log (x)+405 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log (64) \log ^2(x)-30 x^2 \left (1+\frac {2 \log (2)}{5}\right ) \log (64) \log (x)+9 x^2 \log (64)-675 x \log (64) \left (1+\frac {9 \log ^2(4) \log (64)+\log ^2(262144)+\log ^2(18014398509481984)+9 \log (4) \log (16) \log (64)}{675 \log (64)}\right ) \log ^2(x)+40 x \left (1+\frac {1}{40} \left (\log ^2(4)+26 \log (2)\right )\right ) \log (64) \log (x)+375 \log (64) \left (1+\frac {\log ^2(4) \log ^2(64)+3 (5+\log (4)) (\log (4) \log (262144)+\log (64) \log (16777216))}{375 \log (64)}\right ) \log ^2(x)-30 x \left (1+\frac {2 \log (2)}{5}\right ) \log (64)-25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (64) \log (x)+25 \left (1+\frac {2}{25} (5+\log (2)) \log (4)\right ) \log (64)\right )}{\log (64) (-3 x+5+\log (4))^2 \log (x) \left (x+3 e^x x \log (x)-9 x \log (x)-5 e^x \left (1+\frac {2 \log (2)}{5}\right ) \log (x)+15 \left (1+\frac {2 \log (2)}{5}\right ) \log (x)\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {1}{x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)}} \left (-\frac {\left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right ) \left (x \left (9 x^2 \log (16384)-3 x (7+\log (16)) \log (16384)+14 \log (2) \log ^2(4)+\log (16384) (10+\log (16384))\right ) \log (x)+\log (16384) (-3 x+5+\log (4))^2\right )}{x \log (16384)}+\frac {\left (-81 x^3 \log (64)+81 x^2 (5+\log (4)) \log (64)-x \left (9 \left (75+\log ^2(4)+\log (4) \log (16)\right ) \log (64)+\log ^2(262144)+\log ^2(18014398509481984)\right )+\log ^2(64) \left (\log ^2(4)+\log (16777216)\right )+15 \log (64) (25+\log (16777216))+3 \log (4) (5+\log (4)) \log (262144)\right ) \log ^2(x)}{\log (64)}+\left (9 x^3-6 x^2 (5+\log (4))+x \left (40+\log ^2(4)+26 \log (2)\right )-(5+\log (4))^2\right ) \log (x)+(-3 x+5+\log (4))^2\right )}{(-3 x+5+\log (4))^2 \log (x) \left (x+\left (e^x-3\right ) (3 x-5-\log (4)) \log (x)\right )^2}dx\)

Input:

Int[(-15 + 8*x - 3*Log[4] + E^x*(5 - 3*x + Log[4]) + (9*x + E^x*(2*x - 3*x 
^2 + x*Log[4]))*Log[x])/(E^(-x + (-15 + 9*x - 3*Log[4] + E^x*(5 - 3*x + Lo 
g[4]))*Log[x])^(-1)*(x^3 + (30*x^2 - 18*x^3 + 6*x^2*Log[4] + E^x*(-10*x^2 
+ 6*x^3 - 2*x^2*Log[4]))*Log[x] + (225*x - 270*x^2 + 81*x^3 + (90*x - 54*x 
^2)*Log[4] + 9*x*Log[4]^2 + E^x*(-150*x + 180*x^2 - 54*x^3 + (-60*x + 36*x 
^2)*Log[4] - 6*x*Log[4]^2) + E^(2*x)*(25*x - 30*x^2 + 9*x^3 + (10*x - 6*x^ 
2)*Log[4] + x*Log[4]^2))*Log[x]^2)),x]
 

Output:

$Aborted
 

Maple [A] (verified)

Time = 0.10 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.77

\[{\mathrm e}^{-\frac {1}{2 \ln \left (x \right ) {\mathrm e}^{x} \ln \left (2\right )-3 x \,{\mathrm e}^{x} \ln \left (x \right )+5 \,{\mathrm e}^{x} \ln \left (x \right )-6 \ln \left (2\right ) \ln \left (x \right )+9 x \ln \left (x \right )-15 \ln \left (x \right )-x}}\]

Input:

int((((2*x*ln(2)-3*x^2+2*x)*exp(x)+9*x)*ln(x)+(2*ln(2)-3*x+5)*exp(x)-6*ln( 
2)+8*x-15)*exp(-1/(((2*ln(2)-3*x+5)*exp(x)-6*ln(2)+9*x-15)*ln(x)-x))/(((4* 
x*ln(2)^2+2*(-6*x^2+10*x)*ln(2)+9*x^3-30*x^2+25*x)*exp(x)^2+(-24*x*ln(2)^2 
+2*(36*x^2-60*x)*ln(2)-54*x^3+180*x^2-150*x)*exp(x)+36*x*ln(2)^2+2*(-54*x^ 
2+90*x)*ln(2)+81*x^3-270*x^2+225*x)*ln(x)^2+((-4*x^2*ln(2)+6*x^3-10*x^2)*e 
xp(x)+12*x^2*ln(2)-18*x^3+30*x^2)*ln(x)+x^3),x)
 

Output:

exp(-1/(2*ln(x)*exp(x)*ln(2)-3*x*exp(x)*ln(x)+5*exp(x)*ln(x)-6*ln(2)*ln(x) 
+9*x*ln(x)-15*ln(x)-x))
 

Fricas [A] (verification not implemented)

Time = 0.07 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.12 \[ \int \frac {e^{-\frac {1}{-x+\left (-15+9 x-3 \log (4)+e^x (5-3 x+\log (4))\right ) \log (x)}} \left (-15+8 x-3 \log (4)+e^x (5-3 x+\log (4))+\left (9 x+e^x \left (2 x-3 x^2+x \log (4)\right )\right ) \log (x)\right )}{x^3+\left (30 x^2-18 x^3+6 x^2 \log (4)+e^x \left (-10 x^2+6 x^3-2 x^2 \log (4)\right )\right ) \log (x)+\left (225 x-270 x^2+81 x^3+\left (90 x-54 x^2\right ) \log (4)+9 x \log ^2(4)+e^x \left (-150 x+180 x^2-54 x^3+\left (-60 x+36 x^2\right ) \log (4)-6 x \log ^2(4)\right )+e^{2 x} \left (25 x-30 x^2+9 x^3+\left (10 x-6 x^2\right ) \log (4)+x \log ^2(4)\right )\right ) \log ^2(x)} \, dx=e^{\left (\frac {1}{{\left ({\left (3 \, x - 2 \, \log \left (2\right ) - 5\right )} e^{x} - 9 \, x + 6 \, \log \left (2\right ) + 15\right )} \log \left (x\right ) + x}\right )} \] Input:

integrate((((2*x*log(2)-3*x^2+2*x)*exp(x)+9*x)*log(x)+(2*log(2)-3*x+5)*exp 
(x)-6*log(2)+8*x-15)*exp(-1/(((2*log(2)-3*x+5)*exp(x)-6*log(2)+9*x-15)*log 
(x)-x))/(((4*x*log(2)^2+2*(-6*x^2+10*x)*log(2)+9*x^3-30*x^2+25*x)*exp(x)^2 
+(-24*x*log(2)^2+2*(36*x^2-60*x)*log(2)-54*x^3+180*x^2-150*x)*exp(x)+36*x* 
log(2)^2+2*(-54*x^2+90*x)*log(2)+81*x^3-270*x^2+225*x)*log(x)^2+((-4*x^2*l 
og(2)+6*x^3-10*x^2)*exp(x)+12*x^2*log(2)-18*x^3+30*x^2)*log(x)+x^3),x, alg 
orithm="fricas")
 

Output:

e^(1/(((3*x - 2*log(2) - 5)*e^x - 9*x + 6*log(2) + 15)*log(x) + x))
 

Sympy [A] (verification not implemented)

Time = 17.07 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.23 \[ \int \frac {e^{-\frac {1}{-x+\left (-15+9 x-3 \log (4)+e^x (5-3 x+\log (4))\right ) \log (x)}} \left (-15+8 x-3 \log (4)+e^x (5-3 x+\log (4))+\left (9 x+e^x \left (2 x-3 x^2+x \log (4)\right )\right ) \log (x)\right )}{x^3+\left (30 x^2-18 x^3+6 x^2 \log (4)+e^x \left (-10 x^2+6 x^3-2 x^2 \log (4)\right )\right ) \log (x)+\left (225 x-270 x^2+81 x^3+\left (90 x-54 x^2\right ) \log (4)+9 x \log ^2(4)+e^x \left (-150 x+180 x^2-54 x^3+\left (-60 x+36 x^2\right ) \log (4)-6 x \log ^2(4)\right )+e^{2 x} \left (25 x-30 x^2+9 x^3+\left (10 x-6 x^2\right ) \log (4)+x \log ^2(4)\right )\right ) \log ^2(x)} \, dx=e^{- \frac {1}{- x + \left (9 x + \left (- 3 x + 2 \log {\left (2 \right )} + 5\right ) e^{x} - 15 - 6 \log {\left (2 \right )}\right ) \log {\left (x \right )}}} \] Input:

integrate((((2*x*ln(2)-3*x**2+2*x)*exp(x)+9*x)*ln(x)+(2*ln(2)-3*x+5)*exp(x 
)-6*ln(2)+8*x-15)*exp(-1/(((2*ln(2)-3*x+5)*exp(x)-6*ln(2)+9*x-15)*ln(x)-x) 
)/(((4*x*ln(2)**2+2*(-6*x**2+10*x)*ln(2)+9*x**3-30*x**2+25*x)*exp(x)**2+(- 
24*x*ln(2)**2+2*(36*x**2-60*x)*ln(2)-54*x**3+180*x**2-150*x)*exp(x)+36*x*l 
n(2)**2+2*(-54*x**2+90*x)*ln(2)+81*x**3-270*x**2+225*x)*ln(x)**2+((-4*x**2 
*ln(2)+6*x**3-10*x**2)*exp(x)+12*x**2*ln(2)-18*x**3+30*x**2)*ln(x)+x**3),x 
)
 

Output:

exp(-1/(-x + (9*x + (-3*x + 2*log(2) + 5)*exp(x) - 15 - 6*log(2))*log(x)))
 

Maxima [A] (verification not implemented)

Time = 0.33 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.12 \[ \int \frac {e^{-\frac {1}{-x+\left (-15+9 x-3 \log (4)+e^x (5-3 x+\log (4))\right ) \log (x)}} \left (-15+8 x-3 \log (4)+e^x (5-3 x+\log (4))+\left (9 x+e^x \left (2 x-3 x^2+x \log (4)\right )\right ) \log (x)\right )}{x^3+\left (30 x^2-18 x^3+6 x^2 \log (4)+e^x \left (-10 x^2+6 x^3-2 x^2 \log (4)\right )\right ) \log (x)+\left (225 x-270 x^2+81 x^3+\left (90 x-54 x^2\right ) \log (4)+9 x \log ^2(4)+e^x \left (-150 x+180 x^2-54 x^3+\left (-60 x+36 x^2\right ) \log (4)-6 x \log ^2(4)\right )+e^{2 x} \left (25 x-30 x^2+9 x^3+\left (10 x-6 x^2\right ) \log (4)+x \log ^2(4)\right )\right ) \log ^2(x)} \, dx=e^{\left (\frac {1}{{\left ({\left (3 \, x - 2 \, \log \left (2\right ) - 5\right )} e^{x} - 9 \, x + 6 \, \log \left (2\right ) + 15\right )} \log \left (x\right ) + x}\right )} \] Input:

integrate((((2*x*log(2)-3*x^2+2*x)*exp(x)+9*x)*log(x)+(2*log(2)-3*x+5)*exp 
(x)-6*log(2)+8*x-15)*exp(-1/(((2*log(2)-3*x+5)*exp(x)-6*log(2)+9*x-15)*log 
(x)-x))/(((4*x*log(2)^2+2*(-6*x^2+10*x)*log(2)+9*x^3-30*x^2+25*x)*exp(x)^2 
+(-24*x*log(2)^2+2*(36*x^2-60*x)*log(2)-54*x^3+180*x^2-150*x)*exp(x)+36*x* 
log(2)^2+2*(-54*x^2+90*x)*log(2)+81*x^3-270*x^2+225*x)*log(x)^2+((-4*x^2*l 
og(2)+6*x^3-10*x^2)*exp(x)+12*x^2*log(2)-18*x^3+30*x^2)*log(x)+x^3),x, alg 
orithm="maxima")
 

Output:

e^(1/(((3*x - 2*log(2) - 5)*e^x - 9*x + 6*log(2) + 15)*log(x) + x))
 

Giac [A] (verification not implemented)

Time = 0.12 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.58 \[ \int \frac {e^{-\frac {1}{-x+\left (-15+9 x-3 \log (4)+e^x (5-3 x+\log (4))\right ) \log (x)}} \left (-15+8 x-3 \log (4)+e^x (5-3 x+\log (4))+\left (9 x+e^x \left (2 x-3 x^2+x \log (4)\right )\right ) \log (x)\right )}{x^3+\left (30 x^2-18 x^3+6 x^2 \log (4)+e^x \left (-10 x^2+6 x^3-2 x^2 \log (4)\right )\right ) \log (x)+\left (225 x-270 x^2+81 x^3+\left (90 x-54 x^2\right ) \log (4)+9 x \log ^2(4)+e^x \left (-150 x+180 x^2-54 x^3+\left (-60 x+36 x^2\right ) \log (4)-6 x \log ^2(4)\right )+e^{2 x} \left (25 x-30 x^2+9 x^3+\left (10 x-6 x^2\right ) \log (4)+x \log ^2(4)\right )\right ) \log ^2(x)} \, dx=e^{\left (\frac {1}{3 \, x e^{x} \log \left (x\right ) - 2 \, e^{x} \log \left (2\right ) \log \left (x\right ) - 9 \, x \log \left (x\right ) - 5 \, e^{x} \log \left (x\right ) + 6 \, \log \left (2\right ) \log \left (x\right ) + x + 15 \, \log \left (x\right )}\right )} \] Input:

integrate((((2*x*log(2)-3*x^2+2*x)*exp(x)+9*x)*log(x)+(2*log(2)-3*x+5)*exp 
(x)-6*log(2)+8*x-15)*exp(-1/(((2*log(2)-3*x+5)*exp(x)-6*log(2)+9*x-15)*log 
(x)-x))/(((4*x*log(2)^2+2*(-6*x^2+10*x)*log(2)+9*x^3-30*x^2+25*x)*exp(x)^2 
+(-24*x*log(2)^2+2*(36*x^2-60*x)*log(2)-54*x^3+180*x^2-150*x)*exp(x)+36*x* 
log(2)^2+2*(-54*x^2+90*x)*log(2)+81*x^3-270*x^2+225*x)*log(x)^2+((-4*x^2*l 
og(2)+6*x^3-10*x^2)*exp(x)+12*x^2*log(2)-18*x^3+30*x^2)*log(x)+x^3),x, alg 
orithm="giac")
 

Output:

e^(1/(3*x*e^x*log(x) - 2*e^x*log(2)*log(x) - 9*x*log(x) - 5*e^x*log(x) + 6 
*log(2)*log(x) + x + 15*log(x)))
 

Mupad [B] (verification not implemented)

Time = 3.83 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.58 \[ \int \frac {e^{-\frac {1}{-x+\left (-15+9 x-3 \log (4)+e^x (5-3 x+\log (4))\right ) \log (x)}} \left (-15+8 x-3 \log (4)+e^x (5-3 x+\log (4))+\left (9 x+e^x \left (2 x-3 x^2+x \log (4)\right )\right ) \log (x)\right )}{x^3+\left (30 x^2-18 x^3+6 x^2 \log (4)+e^x \left (-10 x^2+6 x^3-2 x^2 \log (4)\right )\right ) \log (x)+\left (225 x-270 x^2+81 x^3+\left (90 x-54 x^2\right ) \log (4)+9 x \log ^2(4)+e^x \left (-150 x+180 x^2-54 x^3+\left (-60 x+36 x^2\right ) \log (4)-6 x \log ^2(4)\right )+e^{2 x} \left (25 x-30 x^2+9 x^3+\left (10 x-6 x^2\right ) \log (4)+x \log ^2(4)\right )\right ) \log ^2(x)} \, dx={\mathrm {e}}^{\frac {1}{x+15\,\ln \left (x\right )-5\,{\mathrm {e}}^x\,\ln \left (x\right )+6\,\ln \left (2\right )\,\ln \left (x\right )-9\,x\,\ln \left (x\right )-2\,{\mathrm {e}}^x\,\ln \left (2\right )\,\ln \left (x\right )+3\,x\,{\mathrm {e}}^x\,\ln \left (x\right )}} \] Input:

int((exp(1/(x - log(x)*(9*x - 6*log(2) + exp(x)*(2*log(2) - 3*x + 5) - 15) 
))*(8*x - 6*log(2) + exp(x)*(2*log(2) - 3*x + 5) + log(x)*(9*x + exp(x)*(2 
*x + 2*x*log(2) - 3*x^2)) - 15))/(log(x)^2*(225*x + exp(2*x)*(25*x + 2*log 
(2)*(10*x - 6*x^2) + 4*x*log(2)^2 - 30*x^2 + 9*x^3) + 2*log(2)*(90*x - 54* 
x^2) + 36*x*log(2)^2 - exp(x)*(150*x + 2*log(2)*(60*x - 36*x^2) + 24*x*log 
(2)^2 - 180*x^2 + 54*x^3) - 270*x^2 + 81*x^3) + log(x)*(12*x^2*log(2) - ex 
p(x)*(4*x^2*log(2) + 10*x^2 - 6*x^3) + 30*x^2 - 18*x^3) + x^3),x)
                                                                                    
                                                                                    
 

Output:

exp(1/(x + 15*log(x) - 5*exp(x)*log(x) + 6*log(2)*log(x) - 9*x*log(x) - 2* 
exp(x)*log(2)*log(x) + 3*x*exp(x)*log(x)))
 

Reduce [B] (verification not implemented)

Time = 0.34 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.88 \[ \int \frac {e^{-\frac {1}{-x+\left (-15+9 x-3 \log (4)+e^x (5-3 x+\log (4))\right ) \log (x)}} \left (-15+8 x-3 \log (4)+e^x (5-3 x+\log (4))+\left (9 x+e^x \left (2 x-3 x^2+x \log (4)\right )\right ) \log (x)\right )}{x^3+\left (30 x^2-18 x^3+6 x^2 \log (4)+e^x \left (-10 x^2+6 x^3-2 x^2 \log (4)\right )\right ) \log (x)+\left (225 x-270 x^2+81 x^3+\left (90 x-54 x^2\right ) \log (4)+9 x \log ^2(4)+e^x \left (-150 x+180 x^2-54 x^3+\left (-60 x+36 x^2\right ) \log (4)-6 x \log ^2(4)\right )+e^{2 x} \left (25 x-30 x^2+9 x^3+\left (10 x-6 x^2\right ) \log (4)+x \log ^2(4)\right )\right ) \log ^2(x)} \, dx=\frac {1}{e^{\frac {1}{2 e^{x} \mathrm {log}\left (x \right ) \mathrm {log}\left (2\right )-3 e^{x} \mathrm {log}\left (x \right ) x +5 e^{x} \mathrm {log}\left (x \right )-6 \,\mathrm {log}\left (x \right ) \mathrm {log}\left (2\right )+9 \,\mathrm {log}\left (x \right ) x -15 \,\mathrm {log}\left (x \right )-x}}} \] Input:

int((((2*x*log(2)-3*x^2+2*x)*exp(x)+9*x)*log(x)+(2*log(2)-3*x+5)*exp(x)-6* 
log(2)+8*x-15)*exp(-1/(((2*log(2)-3*x+5)*exp(x)-6*log(2)+9*x-15)*log(x)-x) 
)/(((4*x*log(2)^2+2*(-6*x^2+10*x)*log(2)+9*x^3-30*x^2+25*x)*exp(x)^2+(-24* 
x*log(2)^2+2*(36*x^2-60*x)*log(2)-54*x^3+180*x^2-150*x)*exp(x)+36*x*log(2) 
^2+2*(-54*x^2+90*x)*log(2)+81*x^3-270*x^2+225*x)*log(x)^2+((-4*x^2*log(2)+ 
6*x^3-10*x^2)*exp(x)+12*x^2*log(2)-18*x^3+30*x^2)*log(x)+x^3),x)
 

Output:

1/e**(1/(2*e**x*log(x)*log(2) - 3*e**x*log(x)*x + 5*e**x*log(x) - 6*log(x) 
*log(2) + 9*log(x)*x - 15*log(x) - x))