\(\int \frac {50 x^4+10 x^5-10 x^6+e^x (-50 x^2-10 x^3+10 x^4)+(100 x^3+10 x^4-20 x^5+e^x (-100 x-10 x^2+20 x^3)) \log (x)+(50 x^2-10 x^4+e^x (-50+10 x^2)) \log ^2(x)+(-51 x^4-9 x^5+8 x^6+e^x (x^2+24 x^3+7 x^4-5 x^5)+(-100 x^3-8 x^4+16 x^5+e^x (48 x^2+9 x^3-10 x^4)) \log (x)+(-50 x^2+8 x^4+e^x (25 x+2 x^2-5 x^3)) \log ^2(x)) \log (x^2)+(10 x^4+2 x^5-2 x^6+e^x (-10 x^2-2 x^3+2 x^4)+(20 x^3+2 x^4-4 x^5+e^x (-20 x-2 x^2+4 x^3)) \log (x)+(10 x^2-2 x^4+e^x (-10+2 x^2)) \log ^2(x)+(-10 x^4-2 x^5+2 x^6+e^x (5 x^3+x^4-x^5)+(-20 x^3-2 x^4+4 x^5+e^x (10 x^2+x^3-2 x^4)) \log (x)+(-10 x^2+2 x^4+e^x (5 x-x^3)) \log ^2(x)) \log (x^2)) \log (\frac {5 x+x^2-x^3+(5-x^2) \log (x)}{x+\log (x)})}{-5 x^7-x^8+x^9+e^{2 x} (-5 x^3-x^4+x^5)+e^x (10 x^5+2 x^6-2 x^7)+(-10 x^6-x^7+2 x^8+e^{2 x} (-10 x^2-x^3+2 x^4)+e^x (20 x^4+2 x^5-4 x^6)) \log (x)+(-5 x^5+x^7+e^{2 x} (-5 x+x^3)+e^x (10 x^3-2 x^5)) \log ^2(x)} \, dx\) [656]

Optimal result

Integrand size = 613, antiderivative size = 35 \[ \int \frac {50 x^4+10 x^5-10 x^6+e^x \left (-50 x^2-10 x^3+10 x^4\right )+\left (100 x^3+10 x^4-20 x^5+e^x \left (-100 x-10 x^2+20 x^3\right )\right ) \log (x)+\left (50 x^2-10 x^4+e^x \left (-50+10 x^2\right )\right ) \log ^2(x)+\left (-51 x^4-9 x^5+8 x^6+e^x \left (x^2+24 x^3+7 x^4-5 x^5\right )+\left (-100 x^3-8 x^4+16 x^5+e^x \left (48 x^2+9 x^3-10 x^4\right )\right ) \log (x)+\left (-50 x^2+8 x^4+e^x \left (25 x+2 x^2-5 x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )+\left (10 x^4+2 x^5-2 x^6+e^x \left (-10 x^2-2 x^3+2 x^4\right )+\left (20 x^3+2 x^4-4 x^5+e^x \left (-20 x-2 x^2+4 x^3\right )\right ) \log (x)+\left (10 x^2-2 x^4+e^x \left (-10+2 x^2\right )\right ) \log ^2(x)+\left (-10 x^4-2 x^5+2 x^6+e^x \left (5 x^3+x^4-x^5\right )+\left (-20 x^3-2 x^4+4 x^5+e^x \left (10 x^2+x^3-2 x^4\right )\right ) \log (x)+\left (-10 x^2+2 x^4+e^x \left (5 x-x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )\right ) \log \left (\frac {5 x+x^2-x^3+\left (5-x^2\right ) \log (x)}{x+\log (x)}\right )}{-5 x^7-x^8+x^9+e^{2 x} \left (-5 x^3-x^4+x^5\right )+e^x \left (10 x^5+2 x^6-2 x^7\right )+\left (-10 x^6-x^7+2 x^8+e^{2 x} \left (-10 x^2-x^3+2 x^4\right )+e^x \left (20 x^4+2 x^5-4 x^6\right )\right ) \log (x)+\left (-5 x^5+x^7+e^{2 x} \left (-5 x+x^3\right )+e^x \left (10 x^3-2 x^5\right )\right ) \log ^2(x)} \, dx=\frac {\log \left (x^2\right ) \left (5+\log \left (5+x \left (-x+\frac {x}{x+\log (x)}\right )\right )\right )}{e^x-x^2} \] Output:

(5+ln(5+x*(x/(x+ln(x))-x)))/(exp(x)-x^2)*ln(x^2)
 

Mathematica [A] (verified)

Time = 0.78 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.31 \[ \int \frac {50 x^4+10 x^5-10 x^6+e^x \left (-50 x^2-10 x^3+10 x^4\right )+\left (100 x^3+10 x^4-20 x^5+e^x \left (-100 x-10 x^2+20 x^3\right )\right ) \log (x)+\left (50 x^2-10 x^4+e^x \left (-50+10 x^2\right )\right ) \log ^2(x)+\left (-51 x^4-9 x^5+8 x^6+e^x \left (x^2+24 x^3+7 x^4-5 x^5\right )+\left (-100 x^3-8 x^4+16 x^5+e^x \left (48 x^2+9 x^3-10 x^4\right )\right ) \log (x)+\left (-50 x^2+8 x^4+e^x \left (25 x+2 x^2-5 x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )+\left (10 x^4+2 x^5-2 x^6+e^x \left (-10 x^2-2 x^3+2 x^4\right )+\left (20 x^3+2 x^4-4 x^5+e^x \left (-20 x-2 x^2+4 x^3\right )\right ) \log (x)+\left (10 x^2-2 x^4+e^x \left (-10+2 x^2\right )\right ) \log ^2(x)+\left (-10 x^4-2 x^5+2 x^6+e^x \left (5 x^3+x^4-x^5\right )+\left (-20 x^3-2 x^4+4 x^5+e^x \left (10 x^2+x^3-2 x^4\right )\right ) \log (x)+\left (-10 x^2+2 x^4+e^x \left (5 x-x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )\right ) \log \left (\frac {5 x+x^2-x^3+\left (5-x^2\right ) \log (x)}{x+\log (x)}\right )}{-5 x^7-x^8+x^9+e^{2 x} \left (-5 x^3-x^4+x^5\right )+e^x \left (10 x^5+2 x^6-2 x^7\right )+\left (-10 x^6-x^7+2 x^8+e^{2 x} \left (-10 x^2-x^3+2 x^4\right )+e^x \left (20 x^4+2 x^5-4 x^6\right )\right ) \log (x)+\left (-5 x^5+x^7+e^{2 x} \left (-5 x+x^3\right )+e^x \left (10 x^3-2 x^5\right )\right ) \log ^2(x)} \, dx=\frac {\log \left (x^2\right ) \left (5+\log \left (\frac {x \left (5+x-x^2\right )-\left (-5+x^2\right ) \log (x)}{x+\log (x)}\right )\right )}{e^x-x^2} \] Input:

Integrate[(50*x^4 + 10*x^5 - 10*x^6 + E^x*(-50*x^2 - 10*x^3 + 10*x^4) + (1 
00*x^3 + 10*x^4 - 20*x^5 + E^x*(-100*x - 10*x^2 + 20*x^3))*Log[x] + (50*x^ 
2 - 10*x^4 + E^x*(-50 + 10*x^2))*Log[x]^2 + (-51*x^4 - 9*x^5 + 8*x^6 + E^x 
*(x^2 + 24*x^3 + 7*x^4 - 5*x^5) + (-100*x^3 - 8*x^4 + 16*x^5 + E^x*(48*x^2 
 + 9*x^3 - 10*x^4))*Log[x] + (-50*x^2 + 8*x^4 + E^x*(25*x + 2*x^2 - 5*x^3) 
)*Log[x]^2)*Log[x^2] + (10*x^4 + 2*x^5 - 2*x^6 + E^x*(-10*x^2 - 2*x^3 + 2* 
x^4) + (20*x^3 + 2*x^4 - 4*x^5 + E^x*(-20*x - 2*x^2 + 4*x^3))*Log[x] + (10 
*x^2 - 2*x^4 + E^x*(-10 + 2*x^2))*Log[x]^2 + (-10*x^4 - 2*x^5 + 2*x^6 + E^ 
x*(5*x^3 + x^4 - x^5) + (-20*x^3 - 2*x^4 + 4*x^5 + E^x*(10*x^2 + x^3 - 2*x 
^4))*Log[x] + (-10*x^2 + 2*x^4 + E^x*(5*x - x^3))*Log[x]^2)*Log[x^2])*Log[ 
(5*x + x^2 - x^3 + (5 - x^2)*Log[x])/(x + Log[x])])/(-5*x^7 - x^8 + x^9 + 
E^(2*x)*(-5*x^3 - x^4 + x^5) + E^x*(10*x^5 + 2*x^6 - 2*x^7) + (-10*x^6 - x 
^7 + 2*x^8 + E^(2*x)*(-10*x^2 - x^3 + 2*x^4) + E^x*(20*x^4 + 2*x^5 - 4*x^6 
))*Log[x] + (-5*x^5 + x^7 + E^(2*x)*(-5*x + x^3) + E^x*(10*x^3 - 2*x^5))*L 
og[x]^2),x]
 

Output:

(Log[x^2]*(5 + Log[(x*(5 + x - x^2) - (-5 + x^2)*Log[x])/(x + Log[x])]))/( 
E^x - x^2)
 

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.

\(\displaystyle \int \frac {-10 x^6+10 x^5+50 x^4+\left (-10 x^4+50 x^2+e^x \left (10 x^2-50\right )\right ) \log ^2(x)+e^x \left (10 x^4-10 x^3-50 x^2\right )+\left (-20 x^5+10 x^4+100 x^3+e^x \left (20 x^3-10 x^2-100 x\right )\right ) \log (x)+\left (8 x^6-9 x^5-51 x^4+\left (8 x^4-50 x^2+e^x \left (-5 x^3+2 x^2+25 x\right )\right ) \log ^2(x)+e^x \left (-5 x^5+7 x^4+24 x^3+x^2\right )+\left (16 x^5-8 x^4-100 x^3+e^x \left (-10 x^4+9 x^3+48 x^2\right )\right ) \log (x)\right ) \log \left (x^2\right )+\left (-2 x^6+2 x^5+10 x^4+\left (-2 x^4+10 x^2+e^x \left (2 x^2-10\right )\right ) \log ^2(x)+e^x \left (2 x^4-2 x^3-10 x^2\right )+\left (-4 x^5+2 x^4+20 x^3+e^x \left (4 x^3-2 x^2-20 x\right )\right ) \log (x)+\left (2 x^6-2 x^5-10 x^4+e^x \left (-x^5+x^4+5 x^3\right )+\left (2 x^4+e^x \left (5 x-x^3\right )-10 x^2\right ) \log ^2(x)+\left (4 x^5-2 x^4-20 x^3+e^x \left (-2 x^4+x^3+10 x^2\right )\right ) \log (x)\right ) \log \left (x^2\right )\right ) \log \left (\frac {-x^3+x^2+\left (5-x^2\right ) \log (x)+5 x}{x+\log (x)}\right )}{x^9-x^8-5 x^7+e^x \left (-2 x^7+2 x^6+10 x^5\right )+\left (x^7-5 x^5+e^{2 x} \left (x^3-5 x\right )+e^x \left (10 x^3-2 x^5\right )\right ) \log ^2(x)+e^{2 x} \left (x^5-x^4-5 x^3\right )+\left (2 x^8-x^7-10 x^6+e^x \left (-4 x^6+2 x^5+20 x^4\right )+e^{2 x} \left (2 x^4-x^3-10 x^2\right )\right ) \log (x)} \, dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {-10 x^6+10 x^5+50 x^4+10 e^x \left (x^2-x-5\right ) x^2+10 \left (e^x-x^2\right ) \left (x^2-5\right ) \log ^2(x)+\left (\left (x^2-x-5\right ) x^2+\left (x^2-5\right ) \log ^2(x)+\left (2 x^2-x-10\right ) x \log (x)\right ) \left (2 \left (e^x-x^2\right )-\left (e^x-2 x\right ) x \log \left (x^2\right )\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+10 \left (e^x-x^2\right ) \left (2 x^2-x-10\right ) x \log (x)+x \left (\left (e^x \left (-10 x^2+9 x+48\right )+4 x \left (4 x^2-2 x-25\right )\right ) x \log (x)+\left (8 x^2-9 x-51\right ) x^3+e^x \left (-5 x^3+7 x^2+24 x+1\right ) x+\left (8 x^3+e^x \left (-5 x^2+2 x+25\right )-50 x\right ) \log ^2(x)\right ) \log \left (x^2\right )}{x \left (e^x-x^2\right )^2 \left (\left (x^2-x-5\right ) x^2+\left (x^2-5\right ) \log ^2(x)+\left (2 x^2-x-10\right ) x \log (x)\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {5 \log \left (x^2\right ) x^5+\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^5+10 \log (x) \log \left (x^2\right ) x^4-7 \log \left (x^2\right ) x^4+2 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-10 x^4-20 \log (x) x^3+5 \log ^2(x) \log \left (x^2\right ) x^3-9 \log (x) \log \left (x^2\right ) x^3-24 \log \left (x^2\right ) x^3-4 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+\log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-\log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-5 \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+10 x^3-10 \log ^2(x) x^2+10 \log (x) x^2-2 \log ^2(x) \log \left (x^2\right ) x^2-48 \log (x) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2-2 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+2 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2-10 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+10 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+50 x^2+100 \log (x) x-25 \log ^2(x) \log \left (x^2\right ) x+20 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x-5 \log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x+50 \log ^2(x)+10 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )}{x \left (x^2-e^x\right ) (x+\log (x)) \left (x^3+\log (x) x^2-x^2-5 x-5 \log (x)\right )}-\frac {(x-2) x \log \left (x^2\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )}{\left (x^2-e^x\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\log ^2(x) \left (2 \left (e^x-x^2\right ) \left (x^2-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (8 x^3-5 e^x x^2-\left (e^x-2 x\right ) \left (x^2-5\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+2 e^x x-50 x+25 e^x\right )\right )+x \log (x) \left (2 \left (e^x-x^2\right ) \left (2 x^2-x-10\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (16 x^3-10 e^x x^2-8 x^2-\left (e^x-2 x\right ) \left (2 x^2-x-10\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+9 e^x x-100 x+48 e^x\right )\right )+x^2 \left (2 \left (e^x-x^2\right ) \left (x^2-x-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+\log \left (x^2\right ) \left (8 x^4-5 e^x x^3-9 x^3+7 e^x x^2-51 x^2-\left (e^x-2 x\right ) \left (x^2-x-5\right ) x \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+24 e^x x+e^x\right )\right )}{x \left (e^x-x^2\right )^2 (x+\log (x)) \left (x \left (x^2-x-5\right )+\left (x^2-5\right ) \log (x)\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {5 \log \left (x^2\right ) x^5+\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^5+10 \log (x) \log \left (x^2\right ) x^4-7 \log \left (x^2\right ) x^4+2 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-10 x^4-20 \log (x) x^3+5 \log ^2(x) \log \left (x^2\right ) x^3-9 \log (x) \log \left (x^2\right ) x^3-24 \log \left (x^2\right ) x^3-4 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+\log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-\log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-5 \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+10 x^3-10 \log ^2(x) x^2+10 \log (x) x^2-2 \log ^2(x) \log \left (x^2\right ) x^2-48 \log (x) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2-2 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+2 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2-10 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+10 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+50 x^2+100 \log (x) x-25 \log ^2(x) \log \left (x^2\right ) x+20 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x-5 \log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x+50 \log ^2(x)+10 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )}{x \left (x^2-e^x\right ) (x+\log (x)) \left (x^3+\log (x) x^2-x^2-5 x-5 \log (x)\right )}-\frac {(x-2) x \log \left (x^2\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )}{\left (x^2-e^x\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\log ^2(x) \left (2 \left (e^x-x^2\right ) \left (x^2-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (8 x^3-5 e^x x^2-\left (e^x-2 x\right ) \left (x^2-5\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+2 e^x x-50 x+25 e^x\right )\right )+x \log (x) \left (2 \left (e^x-x^2\right ) \left (2 x^2-x-10\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (16 x^3-10 e^x x^2-8 x^2-\left (e^x-2 x\right ) \left (2 x^2-x-10\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+9 e^x x-100 x+48 e^x\right )\right )+x^2 \left (2 \left (e^x-x^2\right ) \left (x^2-x-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+\log \left (x^2\right ) \left (8 x^4-5 e^x x^3-9 x^3+7 e^x x^2-51 x^2-\left (e^x-2 x\right ) \left (x^2-x-5\right ) x \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+24 e^x x+e^x\right )\right )}{x \left (e^x-x^2\right )^2 (x+\log (x)) \left (x \left (x^2-x-5\right )+\left (x^2-5\right ) \log (x)\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {5 \log \left (x^2\right ) x^5+\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^5+10 \log (x) \log \left (x^2\right ) x^4-7 \log \left (x^2\right ) x^4+2 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-10 x^4-20 \log (x) x^3+5 \log ^2(x) \log \left (x^2\right ) x^3-9 \log (x) \log \left (x^2\right ) x^3-24 \log \left (x^2\right ) x^3-4 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+\log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-\log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-5 \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+10 x^3-10 \log ^2(x) x^2+10 \log (x) x^2-2 \log ^2(x) \log \left (x^2\right ) x^2-48 \log (x) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2-2 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+2 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2-10 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+10 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+50 x^2+100 \log (x) x-25 \log ^2(x) \log \left (x^2\right ) x+20 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x-5 \log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x+50 \log ^2(x)+10 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )}{x \left (x^2-e^x\right ) (x+\log (x)) \left (x^3+\log (x) x^2-x^2-5 x-5 \log (x)\right )}-\frac {(x-2) x \log \left (x^2\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )}{\left (x^2-e^x\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\log ^2(x) \left (2 \left (e^x-x^2\right ) \left (x^2-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (8 x^3-5 e^x x^2-\left (e^x-2 x\right ) \left (x^2-5\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+2 e^x x-50 x+25 e^x\right )\right )+x \log (x) \left (2 \left (e^x-x^2\right ) \left (2 x^2-x-10\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (16 x^3-10 e^x x^2-8 x^2-\left (e^x-2 x\right ) \left (2 x^2-x-10\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+9 e^x x-100 x+48 e^x\right )\right )+x^2 \left (2 \left (e^x-x^2\right ) \left (x^2-x-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+\log \left (x^2\right ) \left (8 x^4-5 e^x x^3-9 x^3+7 e^x x^2-51 x^2-\left (e^x-2 x\right ) \left (x^2-x-5\right ) x \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+24 e^x x+e^x\right )\right )}{x \left (e^x-x^2\right )^2 (x+\log (x)) \left (x \left (x^2-x-5\right )+\left (x^2-5\right ) \log (x)\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {5 \log \left (x^2\right ) x^5+\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^5+10 \log (x) \log \left (x^2\right ) x^4-7 \log \left (x^2\right ) x^4+2 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-10 x^4-20 \log (x) x^3+5 \log ^2(x) \log \left (x^2\right ) x^3-9 \log (x) \log \left (x^2\right ) x^3-24 \log \left (x^2\right ) x^3-4 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+\log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-\log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-5 \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+10 x^3-10 \log ^2(x) x^2+10 \log (x) x^2-2 \log ^2(x) \log \left (x^2\right ) x^2-48 \log (x) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2-2 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+2 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2-10 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+10 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+50 x^2+100 \log (x) x-25 \log ^2(x) \log \left (x^2\right ) x+20 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x-5 \log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x+50 \log ^2(x)+10 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )}{x \left (x^2-e^x\right ) (x+\log (x)) \left (x^3+\log (x) x^2-x^2-5 x-5 \log (x)\right )}-\frac {(x-2) x \log \left (x^2\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )}{\left (x^2-e^x\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\log ^2(x) \left (2 \left (e^x-x^2\right ) \left (x^2-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (8 x^3-5 e^x x^2-\left (e^x-2 x\right ) \left (x^2-5\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+2 e^x x-50 x+25 e^x\right )\right )+x \log (x) \left (2 \left (e^x-x^2\right ) \left (2 x^2-x-10\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (16 x^3-10 e^x x^2-8 x^2-\left (e^x-2 x\right ) \left (2 x^2-x-10\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+9 e^x x-100 x+48 e^x\right )\right )+x^2 \left (2 \left (e^x-x^2\right ) \left (x^2-x-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+\log \left (x^2\right ) \left (8 x^4-5 e^x x^3-9 x^3+7 e^x x^2-51 x^2-\left (e^x-2 x\right ) \left (x^2-x-5\right ) x \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+24 e^x x+e^x\right )\right )}{x \left (e^x-x^2\right )^2 (x+\log (x)) \left (x \left (x^2-x-5\right )+\left (x^2-5\right ) \log (x)\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {5 \log \left (x^2\right ) x^5+\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^5+10 \log (x) \log \left (x^2\right ) x^4-7 \log \left (x^2\right ) x^4+2 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-10 x^4-20 \log (x) x^3+5 \log ^2(x) \log \left (x^2\right ) x^3-9 \log (x) \log \left (x^2\right ) x^3-24 \log \left (x^2\right ) x^3-4 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+\log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-\log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-5 \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+10 x^3-10 \log ^2(x) x^2+10 \log (x) x^2-2 \log ^2(x) \log \left (x^2\right ) x^2-48 \log (x) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2-2 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+2 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2-10 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+10 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+50 x^2+100 \log (x) x-25 \log ^2(x) \log \left (x^2\right ) x+20 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x-5 \log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x+50 \log ^2(x)+10 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )}{x \left (x^2-e^x\right ) (x+\log (x)) \left (x^3+\log (x) x^2-x^2-5 x-5 \log (x)\right )}-\frac {(x-2) x \log \left (x^2\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )}{\left (x^2-e^x\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\log ^2(x) \left (2 \left (e^x-x^2\right ) \left (x^2-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (8 x^3-5 e^x x^2-\left (e^x-2 x\right ) \left (x^2-5\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+2 e^x x-50 x+25 e^x\right )\right )+x \log (x) \left (2 \left (e^x-x^2\right ) \left (2 x^2-x-10\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (16 x^3-10 e^x x^2-8 x^2-\left (e^x-2 x\right ) \left (2 x^2-x-10\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+9 e^x x-100 x+48 e^x\right )\right )+x^2 \left (2 \left (e^x-x^2\right ) \left (x^2-x-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+\log \left (x^2\right ) \left (8 x^4-5 e^x x^3-9 x^3+7 e^x x^2-51 x^2-\left (e^x-2 x\right ) \left (x^2-x-5\right ) x \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+24 e^x x+e^x\right )\right )}{x \left (e^x-x^2\right )^2 (x+\log (x)) \left (x \left (x^2-x-5\right )+\left (x^2-5\right ) \log (x)\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {5 \log \left (x^2\right ) x^5+\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^5+10 \log (x) \log \left (x^2\right ) x^4-7 \log \left (x^2\right ) x^4+2 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-10 x^4-20 \log (x) x^3+5 \log ^2(x) \log \left (x^2\right ) x^3-9 \log (x) \log \left (x^2\right ) x^3-24 \log \left (x^2\right ) x^3-4 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+\log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-\log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-5 \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+10 x^3-10 \log ^2(x) x^2+10 \log (x) x^2-2 \log ^2(x) \log \left (x^2\right ) x^2-48 \log (x) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2-2 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+2 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2-10 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+10 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+50 x^2+100 \log (x) x-25 \log ^2(x) \log \left (x^2\right ) x+20 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x-5 \log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x+50 \log ^2(x)+10 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )}{x \left (x^2-e^x\right ) (x+\log (x)) \left (x^3+\log (x) x^2-x^2-5 x-5 \log (x)\right )}-\frac {(x-2) x \log \left (x^2\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )}{\left (x^2-e^x\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\log ^2(x) \left (2 \left (e^x-x^2\right ) \left (x^2-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (8 x^3-5 e^x x^2-\left (e^x-2 x\right ) \left (x^2-5\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+2 e^x x-50 x+25 e^x\right )\right )+x \log (x) \left (2 \left (e^x-x^2\right ) \left (2 x^2-x-10\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (16 x^3-10 e^x x^2-8 x^2-\left (e^x-2 x\right ) \left (2 x^2-x-10\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+9 e^x x-100 x+48 e^x\right )\right )+x^2 \left (2 \left (e^x-x^2\right ) \left (x^2-x-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+\log \left (x^2\right ) \left (8 x^4-5 e^x x^3-9 x^3+7 e^x x^2-51 x^2-\left (e^x-2 x\right ) \left (x^2-x-5\right ) x \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+24 e^x x+e^x\right )\right )}{x \left (e^x-x^2\right )^2 (x+\log (x)) \left (x \left (x^2-x-5\right )+\left (x^2-5\right ) \log (x)\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {5 \log \left (x^2\right ) x^5+\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^5+10 \log (x) \log \left (x^2\right ) x^4-7 \log \left (x^2\right ) x^4+2 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-10 x^4-20 \log (x) x^3+5 \log ^2(x) \log \left (x^2\right ) x^3-9 \log (x) \log \left (x^2\right ) x^3-24 \log \left (x^2\right ) x^3-4 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+\log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-\log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-5 \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+10 x^3-10 \log ^2(x) x^2+10 \log (x) x^2-2 \log ^2(x) \log \left (x^2\right ) x^2-48 \log (x) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2-2 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+2 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2-10 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+10 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+50 x^2+100 \log (x) x-25 \log ^2(x) \log \left (x^2\right ) x+20 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x-5 \log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x+50 \log ^2(x)+10 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )}{x \left (x^2-e^x\right ) (x+\log (x)) \left (x^3+\log (x) x^2-x^2-5 x-5 \log (x)\right )}-\frac {(x-2) x \log \left (x^2\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )}{\left (x^2-e^x\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\log ^2(x) \left (2 \left (e^x-x^2\right ) \left (x^2-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (8 x^3-5 e^x x^2-\left (e^x-2 x\right ) \left (x^2-5\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+2 e^x x-50 x+25 e^x\right )\right )+x \log (x) \left (2 \left (e^x-x^2\right ) \left (2 x^2-x-10\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (16 x^3-10 e^x x^2-8 x^2-\left (e^x-2 x\right ) \left (2 x^2-x-10\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+9 e^x x-100 x+48 e^x\right )\right )+x^2 \left (2 \left (e^x-x^2\right ) \left (x^2-x-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+\log \left (x^2\right ) \left (8 x^4-5 e^x x^3-9 x^3+7 e^x x^2-51 x^2-\left (e^x-2 x\right ) \left (x^2-x-5\right ) x \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+24 e^x x+e^x\right )\right )}{x \left (e^x-x^2\right )^2 (x+\log (x)) \left (x \left (x^2-x-5\right )+\left (x^2-5\right ) \log (x)\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {5 \log \left (x^2\right ) x^5+\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^5+10 \log (x) \log \left (x^2\right ) x^4-7 \log \left (x^2\right ) x^4+2 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-10 x^4-20 \log (x) x^3+5 \log ^2(x) \log \left (x^2\right ) x^3-9 \log (x) \log \left (x^2\right ) x^3-24 \log \left (x^2\right ) x^3-4 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+\log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-\log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-5 \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+10 x^3-10 \log ^2(x) x^2+10 \log (x) x^2-2 \log ^2(x) \log \left (x^2\right ) x^2-48 \log (x) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2-2 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+2 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2-10 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+10 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+50 x^2+100 \log (x) x-25 \log ^2(x) \log \left (x^2\right ) x+20 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x-5 \log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x+50 \log ^2(x)+10 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )}{x \left (x^2-e^x\right ) (x+\log (x)) \left (x^3+\log (x) x^2-x^2-5 x-5 \log (x)\right )}-\frac {(x-2) x \log \left (x^2\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )}{\left (x^2-e^x\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\log ^2(x) \left (2 \left (e^x-x^2\right ) \left (x^2-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (8 x^3-5 e^x x^2-\left (e^x-2 x\right ) \left (x^2-5\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+2 e^x x-50 x+25 e^x\right )\right )+x \log (x) \left (2 \left (e^x-x^2\right ) \left (2 x^2-x-10\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (16 x^3-10 e^x x^2-8 x^2-\left (e^x-2 x\right ) \left (2 x^2-x-10\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+9 e^x x-100 x+48 e^x\right )\right )+x^2 \left (2 \left (e^x-x^2\right ) \left (x^2-x-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+\log \left (x^2\right ) \left (8 x^4-5 e^x x^3-9 x^3+7 e^x x^2-51 x^2-\left (e^x-2 x\right ) \left (x^2-x-5\right ) x \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+24 e^x x+e^x\right )\right )}{x \left (e^x-x^2\right )^2 (x+\log (x)) \left (x \left (x^2-x-5\right )+\left (x^2-5\right ) \log (x)\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {5 \log \left (x^2\right ) x^5+\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^5+10 \log (x) \log \left (x^2\right ) x^4-7 \log \left (x^2\right ) x^4+2 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-10 x^4-20 \log (x) x^3+5 \log ^2(x) \log \left (x^2\right ) x^3-9 \log (x) \log \left (x^2\right ) x^3-24 \log \left (x^2\right ) x^3-4 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+\log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-\log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-5 \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+10 x^3-10 \log ^2(x) x^2+10 \log (x) x^2-2 \log ^2(x) \log \left (x^2\right ) x^2-48 \log (x) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2-2 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+2 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2-10 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+10 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+50 x^2+100 \log (x) x-25 \log ^2(x) \log \left (x^2\right ) x+20 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x-5 \log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x+50 \log ^2(x)+10 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )}{x \left (x^2-e^x\right ) (x+\log (x)) \left (x^3+\log (x) x^2-x^2-5 x-5 \log (x)\right )}-\frac {(x-2) x \log \left (x^2\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )}{\left (x^2-e^x\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\log ^2(x) \left (2 \left (e^x-x^2\right ) \left (x^2-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (8 x^3-5 e^x x^2-\left (e^x-2 x\right ) \left (x^2-5\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+2 e^x x-50 x+25 e^x\right )\right )+x \log (x) \left (2 \left (e^x-x^2\right ) \left (2 x^2-x-10\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (16 x^3-10 e^x x^2-8 x^2-\left (e^x-2 x\right ) \left (2 x^2-x-10\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+9 e^x x-100 x+48 e^x\right )\right )+x^2 \left (2 \left (e^x-x^2\right ) \left (x^2-x-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+\log \left (x^2\right ) \left (8 x^4-5 e^x x^3-9 x^3+7 e^x x^2-51 x^2-\left (e^x-2 x\right ) \left (x^2-x-5\right ) x \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+24 e^x x+e^x\right )\right )}{x \left (e^x-x^2\right )^2 (x+\log (x)) \left (x \left (x^2-x-5\right )+\left (x^2-5\right ) \log (x)\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {5 \log \left (x^2\right ) x^5+\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^5+10 \log (x) \log \left (x^2\right ) x^4-7 \log \left (x^2\right ) x^4+2 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-10 x^4-20 \log (x) x^3+5 \log ^2(x) \log \left (x^2\right ) x^3-9 \log (x) \log \left (x^2\right ) x^3-24 \log \left (x^2\right ) x^3-4 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+\log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-\log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-5 \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+10 x^3-10 \log ^2(x) x^2+10 \log (x) x^2-2 \log ^2(x) \log \left (x^2\right ) x^2-48 \log (x) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2-2 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+2 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2-10 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+10 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+50 x^2+100 \log (x) x-25 \log ^2(x) \log \left (x^2\right ) x+20 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x-5 \log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x+50 \log ^2(x)+10 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )}{x \left (x^2-e^x\right ) (x+\log (x)) \left (x^3+\log (x) x^2-x^2-5 x-5 \log (x)\right )}-\frac {(x-2) x \log \left (x^2\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )}{\left (x^2-e^x\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\log ^2(x) \left (2 \left (e^x-x^2\right ) \left (x^2-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (8 x^3-5 e^x x^2-\left (e^x-2 x\right ) \left (x^2-5\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+2 e^x x-50 x+25 e^x\right )\right )+x \log (x) \left (2 \left (e^x-x^2\right ) \left (2 x^2-x-10\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (16 x^3-10 e^x x^2-8 x^2-\left (e^x-2 x\right ) \left (2 x^2-x-10\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+9 e^x x-100 x+48 e^x\right )\right )+x^2 \left (2 \left (e^x-x^2\right ) \left (x^2-x-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+\log \left (x^2\right ) \left (8 x^4-5 e^x x^3-9 x^3+7 e^x x^2-51 x^2-\left (e^x-2 x\right ) \left (x^2-x-5\right ) x \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+24 e^x x+e^x\right )\right )}{x \left (e^x-x^2\right )^2 (x+\log (x)) \left (x \left (x^2-x-5\right )+\left (x^2-5\right ) \log (x)\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {5 \log \left (x^2\right ) x^5+\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^5+10 \log (x) \log \left (x^2\right ) x^4-7 \log \left (x^2\right ) x^4+2 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-10 x^4-20 \log (x) x^3+5 \log ^2(x) \log \left (x^2\right ) x^3-9 \log (x) \log \left (x^2\right ) x^3-24 \log \left (x^2\right ) x^3-4 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+\log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-\log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-5 \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+10 x^3-10 \log ^2(x) x^2+10 \log (x) x^2-2 \log ^2(x) \log \left (x^2\right ) x^2-48 \log (x) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2-2 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+2 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2-10 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+10 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+50 x^2+100 \log (x) x-25 \log ^2(x) \log \left (x^2\right ) x+20 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x-5 \log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x+50 \log ^2(x)+10 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )}{x \left (x^2-e^x\right ) (x+\log (x)) \left (x^3+\log (x) x^2-x^2-5 x-5 \log (x)\right )}-\frac {(x-2) x \log \left (x^2\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )}{\left (x^2-e^x\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\log ^2(x) \left (2 \left (e^x-x^2\right ) \left (x^2-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (8 x^3-5 e^x x^2-\left (e^x-2 x\right ) \left (x^2-5\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+2 e^x x-50 x+25 e^x\right )\right )+x \log (x) \left (2 \left (e^x-x^2\right ) \left (2 x^2-x-10\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (16 x^3-10 e^x x^2-8 x^2-\left (e^x-2 x\right ) \left (2 x^2-x-10\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+9 e^x x-100 x+48 e^x\right )\right )+x^2 \left (2 \left (e^x-x^2\right ) \left (x^2-x-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+\log \left (x^2\right ) \left (8 x^4-5 e^x x^3-9 x^3+7 e^x x^2-51 x^2-\left (e^x-2 x\right ) \left (x^2-x-5\right ) x \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+24 e^x x+e^x\right )\right )}{x \left (e^x-x^2\right )^2 (x+\log (x)) \left (x \left (x^2-x-5\right )+\left (x^2-5\right ) \log (x)\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {5 \log \left (x^2\right ) x^5+\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^5+10 \log (x) \log \left (x^2\right ) x^4-7 \log \left (x^2\right ) x^4+2 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-10 x^4-20 \log (x) x^3+5 \log ^2(x) \log \left (x^2\right ) x^3-9 \log (x) \log \left (x^2\right ) x^3-24 \log \left (x^2\right ) x^3-4 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+\log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-\log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-5 \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+10 x^3-10 \log ^2(x) x^2+10 \log (x) x^2-2 \log ^2(x) \log \left (x^2\right ) x^2-48 \log (x) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2-2 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+2 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2-10 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+10 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+50 x^2+100 \log (x) x-25 \log ^2(x) \log \left (x^2\right ) x+20 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x-5 \log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x+50 \log ^2(x)+10 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )}{x \left (x^2-e^x\right ) (x+\log (x)) \left (x^3+\log (x) x^2-x^2-5 x-5 \log (x)\right )}-\frac {(x-2) x \log \left (x^2\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )}{\left (x^2-e^x\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\log ^2(x) \left (2 \left (e^x-x^2\right ) \left (x^2-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (8 x^3-5 e^x x^2-\left (e^x-2 x\right ) \left (x^2-5\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+2 e^x x-50 x+25 e^x\right )\right )+x \log (x) \left (2 \left (e^x-x^2\right ) \left (2 x^2-x-10\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (16 x^3-10 e^x x^2-8 x^2-\left (e^x-2 x\right ) \left (2 x^2-x-10\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+9 e^x x-100 x+48 e^x\right )\right )+x^2 \left (2 \left (e^x-x^2\right ) \left (x^2-x-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+\log \left (x^2\right ) \left (8 x^4-5 e^x x^3-9 x^3+7 e^x x^2-51 x^2-\left (e^x-2 x\right ) \left (x^2-x-5\right ) x \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+24 e^x x+e^x\right )\right )}{x \left (e^x-x^2\right )^2 (x+\log (x)) \left (x \left (x^2-x-5\right )+\left (x^2-5\right ) \log (x)\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {5 \log \left (x^2\right ) x^5+\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^5+10 \log (x) \log \left (x^2\right ) x^4-7 \log \left (x^2\right ) x^4+2 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-10 x^4-20 \log (x) x^3+5 \log ^2(x) \log \left (x^2\right ) x^3-9 \log (x) \log \left (x^2\right ) x^3-24 \log \left (x^2\right ) x^3-4 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+\log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-\log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-5 \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+10 x^3-10 \log ^2(x) x^2+10 \log (x) x^2-2 \log ^2(x) \log \left (x^2\right ) x^2-48 \log (x) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2-2 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+2 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2-10 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+10 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+50 x^2+100 \log (x) x-25 \log ^2(x) \log \left (x^2\right ) x+20 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x-5 \log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x+50 \log ^2(x)+10 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )}{x \left (x^2-e^x\right ) (x+\log (x)) \left (x^3+\log (x) x^2-x^2-5 x-5 \log (x)\right )}-\frac {(x-2) x \log \left (x^2\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )}{\left (x^2-e^x\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\log ^2(x) \left (2 \left (e^x-x^2\right ) \left (x^2-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (8 x^3-5 e^x x^2-\left (e^x-2 x\right ) \left (x^2-5\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+2 e^x x-50 x+25 e^x\right )\right )+x \log (x) \left (2 \left (e^x-x^2\right ) \left (2 x^2-x-10\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (16 x^3-10 e^x x^2-8 x^2-\left (e^x-2 x\right ) \left (2 x^2-x-10\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+9 e^x x-100 x+48 e^x\right )\right )+x^2 \left (2 \left (e^x-x^2\right ) \left (x^2-x-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+\log \left (x^2\right ) \left (8 x^4-5 e^x x^3-9 x^3+7 e^x x^2-51 x^2-\left (e^x-2 x\right ) \left (x^2-x-5\right ) x \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+24 e^x x+e^x\right )\right )}{x \left (e^x-x^2\right )^2 (x+\log (x)) \left (x \left (x^2-x-5\right )+\left (x^2-5\right ) \log (x)\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {5 \log \left (x^2\right ) x^5+\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^5+10 \log (x) \log \left (x^2\right ) x^4-7 \log \left (x^2\right ) x^4+2 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-10 x^4-20 \log (x) x^3+5 \log ^2(x) \log \left (x^2\right ) x^3-9 \log (x) \log \left (x^2\right ) x^3-24 \log \left (x^2\right ) x^3-4 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+\log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-\log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-5 \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+10 x^3-10 \log ^2(x) x^2+10 \log (x) x^2-2 \log ^2(x) \log \left (x^2\right ) x^2-48 \log (x) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2-2 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+2 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2-10 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+10 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+50 x^2+100 \log (x) x-25 \log ^2(x) \log \left (x^2\right ) x+20 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x-5 \log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x+50 \log ^2(x)+10 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )}{x \left (x^2-e^x\right ) (x+\log (x)) \left (x^3+\log (x) x^2-x^2-5 x-5 \log (x)\right )}-\frac {(x-2) x \log \left (x^2\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )}{\left (x^2-e^x\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\log ^2(x) \left (2 \left (e^x-x^2\right ) \left (x^2-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (8 x^3-5 e^x x^2-\left (e^x-2 x\right ) \left (x^2-5\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+2 e^x x-50 x+25 e^x\right )\right )+x \log (x) \left (2 \left (e^x-x^2\right ) \left (2 x^2-x-10\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+x \log \left (x^2\right ) \left (16 x^3-10 e^x x^2-8 x^2-\left (e^x-2 x\right ) \left (2 x^2-x-10\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+9 e^x x-100 x+48 e^x\right )\right )+x^2 \left (2 \left (e^x-x^2\right ) \left (x^2-x-5\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )+\log \left (x^2\right ) \left (8 x^4-5 e^x x^3-9 x^3+7 e^x x^2-51 x^2-\left (e^x-2 x\right ) \left (x^2-x-5\right ) x \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+24 e^x x+e^x\right )\right )}{x \left (e^x-x^2\right )^2 (x+\log (x)) \left (x \left (x^2-x-5\right )+\left (x^2-5\right ) \log (x)\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {5 \log \left (x^2\right ) x^5+\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^5+10 \log (x) \log \left (x^2\right ) x^4-7 \log \left (x^2\right ) x^4+2 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-\log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^4-10 x^4-20 \log (x) x^3+5 \log ^2(x) \log \left (x^2\right ) x^3-9 \log (x) \log \left (x^2\right ) x^3-24 \log \left (x^2\right ) x^3-4 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+\log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-\log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3-5 \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+2 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^3+10 x^3-10 \log ^2(x) x^2+10 \log (x) x^2-2 \log ^2(x) \log \left (x^2\right ) x^2-48 \log (x) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2-2 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+2 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2-10 \log (x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+10 \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x^2+50 x^2+100 \log (x) x-25 \log ^2(x) \log \left (x^2\right ) x+20 \log (x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x-5 \log ^2(x) \log \left (x^2\right ) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right ) x+50 \log ^2(x)+10 \log ^2(x) \log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )}{x \left (x^2-e^x\right ) (x+\log (x)) \left (x^3+\log (x) x^2-x^2-5 x-5 \log (x)\right )}-\frac {(x-2) x \log \left (x^2\right ) \left (\log \left (\frac {x \left (-x^2+x+5\right )-\left (x^2-5\right ) \log (x)}{x+\log (x)}\right )+5\right )}{\left (x^2-e^x\right )^2}\right )dx\)

Input:

Int[(50*x^4 + 10*x^5 - 10*x^6 + E^x*(-50*x^2 - 10*x^3 + 10*x^4) + (100*x^3 
 + 10*x^4 - 20*x^5 + E^x*(-100*x - 10*x^2 + 20*x^3))*Log[x] + (50*x^2 - 10 
*x^4 + E^x*(-50 + 10*x^2))*Log[x]^2 + (-51*x^4 - 9*x^5 + 8*x^6 + E^x*(x^2 
+ 24*x^3 + 7*x^4 - 5*x^5) + (-100*x^3 - 8*x^4 + 16*x^5 + E^x*(48*x^2 + 9*x 
^3 - 10*x^4))*Log[x] + (-50*x^2 + 8*x^4 + E^x*(25*x + 2*x^2 - 5*x^3))*Log[ 
x]^2)*Log[x^2] + (10*x^4 + 2*x^5 - 2*x^6 + E^x*(-10*x^2 - 2*x^3 + 2*x^4) + 
 (20*x^3 + 2*x^4 - 4*x^5 + E^x*(-20*x - 2*x^2 + 4*x^3))*Log[x] + (10*x^2 - 
 2*x^4 + E^x*(-10 + 2*x^2))*Log[x]^2 + (-10*x^4 - 2*x^5 + 2*x^6 + E^x*(5*x 
^3 + x^4 - x^5) + (-20*x^3 - 2*x^4 + 4*x^5 + E^x*(10*x^2 + x^3 - 2*x^4))*L 
og[x] + (-10*x^2 + 2*x^4 + E^x*(5*x - x^3))*Log[x]^2)*Log[x^2])*Log[(5*x + 
 x^2 - x^3 + (5 - x^2)*Log[x])/(x + Log[x])])/(-5*x^7 - x^8 + x^9 + E^(2*x 
)*(-5*x^3 - x^4 + x^5) + E^x*(10*x^5 + 2*x^6 - 2*x^7) + (-10*x^6 - x^7 + 2 
*x^8 + E^(2*x)*(-10*x^2 - x^3 + 2*x^4) + E^x*(20*x^4 + 2*x^5 - 4*x^6))*Log 
[x] + (-5*x^5 + x^7 + E^(2*x)*(-5*x + x^3) + E^x*(10*x^3 - 2*x^5))*Log[x]^ 
2),x]
 

Output:

$Aborted
 

Maple [C] (warning: unable to verify)

Result contains higher order function than in optimal. Order 9 vs. order 3.

Time = 0.12 (sec) , antiderivative size = 1449, normalized size of antiderivative = 41.40

\[\text {Expression too large to display}\]

Input:

int((((((-x^3+5*x)*exp(x)+2*x^4-10*x^2)*ln(x)^2+((-2*x^4+x^3+10*x^2)*exp(x 
)+4*x^5-2*x^4-20*x^3)*ln(x)+(-x^5+x^4+5*x^3)*exp(x)+2*x^6-2*x^5-10*x^4)*ln 
(x^2)+((2*x^2-10)*exp(x)-2*x^4+10*x^2)*ln(x)^2+((4*x^3-2*x^2-20*x)*exp(x)- 
4*x^5+2*x^4+20*x^3)*ln(x)+(2*x^4-2*x^3-10*x^2)*exp(x)-2*x^6+2*x^5+10*x^4)* 
ln(((-x^2+5)*ln(x)-x^3+x^2+5*x)/(x+ln(x)))+(((-5*x^3+2*x^2+25*x)*exp(x)+8* 
x^4-50*x^2)*ln(x)^2+((-10*x^4+9*x^3+48*x^2)*exp(x)+16*x^5-8*x^4-100*x^3)*l 
n(x)+(-5*x^5+7*x^4+24*x^3+x^2)*exp(x)+8*x^6-9*x^5-51*x^4)*ln(x^2)+((10*x^2 
-50)*exp(x)-10*x^4+50*x^2)*ln(x)^2+((20*x^3-10*x^2-100*x)*exp(x)-20*x^5+10 
*x^4+100*x^3)*ln(x)+(10*x^4-10*x^3-50*x^2)*exp(x)-10*x^6+10*x^5+50*x^4)/(( 
(x^3-5*x)*exp(x)^2+(-2*x^5+10*x^3)*exp(x)+x^7-5*x^5)*ln(x)^2+((2*x^4-x^3-1 
0*x^2)*exp(x)^2+(-4*x^6+2*x^5+20*x^4)*exp(x)+2*x^8-x^7-10*x^6)*ln(x)+(x^5- 
x^4-5*x^3)*exp(x)^2+(-2*x^7+2*x^6+10*x^5)*exp(x)+x^9-x^8-5*x^7),x)
 

Output:

-1/2*(4*ln(x)-I*Pi*csgn(I*x^2)^3+2*I*Pi*csgn(I*x^2)^2*csgn(I*x)-I*Pi*csgn( 
I*x^2)*csgn(I*x)^2)/(-exp(x)+x^2)*ln(x^3+(ln(x)-1)*x^2-5*x-5*ln(x))+1/4*(- 
40*ln(x)-20*I*Pi*csgn(I*x^2)^2*csgn(I*x)+10*I*Pi*csgn(I*x^2)*csgn(I*x)^2-2 
*I*Pi*csgn(I*x^2)^3*ln(x+ln(x))-Pi^2*csgn(I*x^2)^3*csgn(I/(x+ln(x)))*csgn( 
I/(x+ln(x))*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))^2-Pi^2*csgn(I*x^2)^3*csgn(I*( 
x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))*csgn(I/(x+ln(x))*(x^3+(ln(x)-1)*x^2-5*x-5* 
ln(x)))^2+Pi^2*csgn(I*x^2)*csgn(I/(x+ln(x)))*csgn(I*(x^3+(ln(x)-1)*x^2-5*x 
-5*ln(x)))*csgn(I/(x+ln(x))*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))*csgn(I*x)^2-2 
*Pi^2*csgn(I*x^2)^2*csgn(I/(x+ln(x)))*csgn(I*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x 
)))*csgn(I/(x+ln(x))*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))*csgn(I*x)-4*I*Pi*csg 
n(I/(x+ln(x))*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))^3*ln(x)-Pi^2*csgn(I*x^2)*cs 
gn(I/(x+ln(x))*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))^3*csgn(I*x)^2+2*Pi^2*csgn( 
I*x^2)^3*csgn(I/(x+ln(x))*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))^2+2*Pi^2*csgn(I 
*x^2)^2*csgn(I/(x+ln(x))*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))^3*csgn(I*x)+4*I* 
Pi*csgn(I/(x+ln(x)))*csgn(I*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))*csgn(I/(x+ln( 
x))*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))*ln(x)+8*ln(x)*ln(x+ln(x))-Pi^2*csgn(I 
*x^2)*csgn(I/(x+ln(x)))*csgn(I/(x+ln(x))*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))^ 
2*csgn(I*x)^2-Pi^2*csgn(I*x^2)*csgn(I*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))*csg 
n(I/(x+ln(x))*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))^2*csgn(I*x)^2+Pi^2*csgn(I*x 
^2)^3*csgn(I/(x+ln(x)))*csgn(I*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))*csgn(I/...
 

Fricas [A] (verification not implemented)

Time = 0.11 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.40 \[ \int \frac {50 x^4+10 x^5-10 x^6+e^x \left (-50 x^2-10 x^3+10 x^4\right )+\left (100 x^3+10 x^4-20 x^5+e^x \left (-100 x-10 x^2+20 x^3\right )\right ) \log (x)+\left (50 x^2-10 x^4+e^x \left (-50+10 x^2\right )\right ) \log ^2(x)+\left (-51 x^4-9 x^5+8 x^6+e^x \left (x^2+24 x^3+7 x^4-5 x^5\right )+\left (-100 x^3-8 x^4+16 x^5+e^x \left (48 x^2+9 x^3-10 x^4\right )\right ) \log (x)+\left (-50 x^2+8 x^4+e^x \left (25 x+2 x^2-5 x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )+\left (10 x^4+2 x^5-2 x^6+e^x \left (-10 x^2-2 x^3+2 x^4\right )+\left (20 x^3+2 x^4-4 x^5+e^x \left (-20 x-2 x^2+4 x^3\right )\right ) \log (x)+\left (10 x^2-2 x^4+e^x \left (-10+2 x^2\right )\right ) \log ^2(x)+\left (-10 x^4-2 x^5+2 x^6+e^x \left (5 x^3+x^4-x^5\right )+\left (-20 x^3-2 x^4+4 x^5+e^x \left (10 x^2+x^3-2 x^4\right )\right ) \log (x)+\left (-10 x^2+2 x^4+e^x \left (5 x-x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )\right ) \log \left (\frac {5 x+x^2-x^3+\left (5-x^2\right ) \log (x)}{x+\log (x)}\right )}{-5 x^7-x^8+x^9+e^{2 x} \left (-5 x^3-x^4+x^5\right )+e^x \left (10 x^5+2 x^6-2 x^7\right )+\left (-10 x^6-x^7+2 x^8+e^{2 x} \left (-10 x^2-x^3+2 x^4\right )+e^x \left (20 x^4+2 x^5-4 x^6\right )\right ) \log (x)+\left (-5 x^5+x^7+e^{2 x} \left (-5 x+x^3\right )+e^x \left (10 x^3-2 x^5\right )\right ) \log ^2(x)} \, dx=-\frac {2 \, {\left (\log \left (x\right ) \log \left (-\frac {x^{3} - x^{2} + {\left (x^{2} - 5\right )} \log \left (x\right ) - 5 \, x}{x + \log \left (x\right )}\right ) + 5 \, \log \left (x\right )\right )}}{x^{2} - e^{x}} \] Input:

integrate((((((-x^3+5*x)*exp(x)+2*x^4-10*x^2)*log(x)^2+((-2*x^4+x^3+10*x^2 
)*exp(x)+4*x^5-2*x^4-20*x^3)*log(x)+(-x^5+x^4+5*x^3)*exp(x)+2*x^6-2*x^5-10 
*x^4)*log(x^2)+((2*x^2-10)*exp(x)-2*x^4+10*x^2)*log(x)^2+((4*x^3-2*x^2-20* 
x)*exp(x)-4*x^5+2*x^4+20*x^3)*log(x)+(2*x^4-2*x^3-10*x^2)*exp(x)-2*x^6+2*x 
^5+10*x^4)*log(((-x^2+5)*log(x)-x^3+x^2+5*x)/(x+log(x)))+(((-5*x^3+2*x^2+2 
5*x)*exp(x)+8*x^4-50*x^2)*log(x)^2+((-10*x^4+9*x^3+48*x^2)*exp(x)+16*x^5-8 
*x^4-100*x^3)*log(x)+(-5*x^5+7*x^4+24*x^3+x^2)*exp(x)+8*x^6-9*x^5-51*x^4)* 
log(x^2)+((10*x^2-50)*exp(x)-10*x^4+50*x^2)*log(x)^2+((20*x^3-10*x^2-100*x 
)*exp(x)-20*x^5+10*x^4+100*x^3)*log(x)+(10*x^4-10*x^3-50*x^2)*exp(x)-10*x^ 
6+10*x^5+50*x^4)/(((x^3-5*x)*exp(x)^2+(-2*x^5+10*x^3)*exp(x)+x^7-5*x^5)*lo 
g(x)^2+((2*x^4-x^3-10*x^2)*exp(x)^2+(-4*x^6+2*x^5+20*x^4)*exp(x)+2*x^8-x^7 
-10*x^6)*log(x)+(x^5-x^4-5*x^3)*exp(x)^2+(-2*x^7+2*x^6+10*x^5)*exp(x)+x^9- 
x^8-5*x^7),x, algorithm="fricas")
 

Output:

-2*(log(x)*log(-(x^3 - x^2 + (x^2 - 5)*log(x) - 5*x)/(x + log(x))) + 5*log 
(x))/(x^2 - e^x)
 

Sympy [A] (verification not implemented)

Time = 0.80 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.17 \[ \int \frac {50 x^4+10 x^5-10 x^6+e^x \left (-50 x^2-10 x^3+10 x^4\right )+\left (100 x^3+10 x^4-20 x^5+e^x \left (-100 x-10 x^2+20 x^3\right )\right ) \log (x)+\left (50 x^2-10 x^4+e^x \left (-50+10 x^2\right )\right ) \log ^2(x)+\left (-51 x^4-9 x^5+8 x^6+e^x \left (x^2+24 x^3+7 x^4-5 x^5\right )+\left (-100 x^3-8 x^4+16 x^5+e^x \left (48 x^2+9 x^3-10 x^4\right )\right ) \log (x)+\left (-50 x^2+8 x^4+e^x \left (25 x+2 x^2-5 x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )+\left (10 x^4+2 x^5-2 x^6+e^x \left (-10 x^2-2 x^3+2 x^4\right )+\left (20 x^3+2 x^4-4 x^5+e^x \left (-20 x-2 x^2+4 x^3\right )\right ) \log (x)+\left (10 x^2-2 x^4+e^x \left (-10+2 x^2\right )\right ) \log ^2(x)+\left (-10 x^4-2 x^5+2 x^6+e^x \left (5 x^3+x^4-x^5\right )+\left (-20 x^3-2 x^4+4 x^5+e^x \left (10 x^2+x^3-2 x^4\right )\right ) \log (x)+\left (-10 x^2+2 x^4+e^x \left (5 x-x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )\right ) \log \left (\frac {5 x+x^2-x^3+\left (5-x^2\right ) \log (x)}{x+\log (x)}\right )}{-5 x^7-x^8+x^9+e^{2 x} \left (-5 x^3-x^4+x^5\right )+e^x \left (10 x^5+2 x^6-2 x^7\right )+\left (-10 x^6-x^7+2 x^8+e^{2 x} \left (-10 x^2-x^3+2 x^4\right )+e^x \left (20 x^4+2 x^5-4 x^6\right )\right ) \log (x)+\left (-5 x^5+x^7+e^{2 x} \left (-5 x+x^3\right )+e^x \left (10 x^3-2 x^5\right )\right ) \log ^2(x)} \, dx=\frac {2 \log {\left (x \right )} \log {\left (\frac {- x^{3} + x^{2} + 5 x + \left (5 - x^{2}\right ) \log {\left (x \right )}}{x + \log {\left (x \right )}} \right )} + 10 \log {\left (x \right )}}{- x^{2} + e^{x}} \] Input:

integrate((((((-x**3+5*x)*exp(x)+2*x**4-10*x**2)*ln(x)**2+((-2*x**4+x**3+1 
0*x**2)*exp(x)+4*x**5-2*x**4-20*x**3)*ln(x)+(-x**5+x**4+5*x**3)*exp(x)+2*x 
**6-2*x**5-10*x**4)*ln(x**2)+((2*x**2-10)*exp(x)-2*x**4+10*x**2)*ln(x)**2+ 
((4*x**3-2*x**2-20*x)*exp(x)-4*x**5+2*x**4+20*x**3)*ln(x)+(2*x**4-2*x**3-1 
0*x**2)*exp(x)-2*x**6+2*x**5+10*x**4)*ln(((-x**2+5)*ln(x)-x**3+x**2+5*x)/( 
x+ln(x)))+(((-5*x**3+2*x**2+25*x)*exp(x)+8*x**4-50*x**2)*ln(x)**2+((-10*x* 
*4+9*x**3+48*x**2)*exp(x)+16*x**5-8*x**4-100*x**3)*ln(x)+(-5*x**5+7*x**4+2 
4*x**3+x**2)*exp(x)+8*x**6-9*x**5-51*x**4)*ln(x**2)+((10*x**2-50)*exp(x)-1 
0*x**4+50*x**2)*ln(x)**2+((20*x**3-10*x**2-100*x)*exp(x)-20*x**5+10*x**4+1 
00*x**3)*ln(x)+(10*x**4-10*x**3-50*x**2)*exp(x)-10*x**6+10*x**5+50*x**4)/( 
((x**3-5*x)*exp(x)**2+(-2*x**5+10*x**3)*exp(x)+x**7-5*x**5)*ln(x)**2+((2*x 
**4-x**3-10*x**2)*exp(x)**2+(-4*x**6+2*x**5+20*x**4)*exp(x)+2*x**8-x**7-10 
*x**6)*ln(x)+(x**5-x**4-5*x**3)*exp(x)**2+(-2*x**7+2*x**6+10*x**5)*exp(x)+ 
x**9-x**8-5*x**7),x)
 

Output:

(2*log(x)*log((-x**3 + x**2 + 5*x + (5 - x**2)*log(x))/(x + log(x))) + 10* 
log(x))/(-x**2 + exp(x))
 

Maxima [A] (verification not implemented)

Time = 0.32 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.46 \[ \int \frac {50 x^4+10 x^5-10 x^6+e^x \left (-50 x^2-10 x^3+10 x^4\right )+\left (100 x^3+10 x^4-20 x^5+e^x \left (-100 x-10 x^2+20 x^3\right )\right ) \log (x)+\left (50 x^2-10 x^4+e^x \left (-50+10 x^2\right )\right ) \log ^2(x)+\left (-51 x^4-9 x^5+8 x^6+e^x \left (x^2+24 x^3+7 x^4-5 x^5\right )+\left (-100 x^3-8 x^4+16 x^5+e^x \left (48 x^2+9 x^3-10 x^4\right )\right ) \log (x)+\left (-50 x^2+8 x^4+e^x \left (25 x+2 x^2-5 x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )+\left (10 x^4+2 x^5-2 x^6+e^x \left (-10 x^2-2 x^3+2 x^4\right )+\left (20 x^3+2 x^4-4 x^5+e^x \left (-20 x-2 x^2+4 x^3\right )\right ) \log (x)+\left (10 x^2-2 x^4+e^x \left (-10+2 x^2\right )\right ) \log ^2(x)+\left (-10 x^4-2 x^5+2 x^6+e^x \left (5 x^3+x^4-x^5\right )+\left (-20 x^3-2 x^4+4 x^5+e^x \left (10 x^2+x^3-2 x^4\right )\right ) \log (x)+\left (-10 x^2+2 x^4+e^x \left (5 x-x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )\right ) \log \left (\frac {5 x+x^2-x^3+\left (5-x^2\right ) \log (x)}{x+\log (x)}\right )}{-5 x^7-x^8+x^9+e^{2 x} \left (-5 x^3-x^4+x^5\right )+e^x \left (10 x^5+2 x^6-2 x^7\right )+\left (-10 x^6-x^7+2 x^8+e^{2 x} \left (-10 x^2-x^3+2 x^4\right )+e^x \left (20 x^4+2 x^5-4 x^6\right )\right ) \log (x)+\left (-5 x^5+x^7+e^{2 x} \left (-5 x+x^3\right )+e^x \left (10 x^3-2 x^5\right )\right ) \log ^2(x)} \, dx=-\frac {2 \, {\left (\log \left (-x^{3} + x^{2} - {\left (x^{2} - 5\right )} \log \left (x\right ) + 5 \, x\right ) \log \left (x\right ) - \log \left (x + \log \left (x\right )\right ) \log \left (x\right ) + 5 \, \log \left (x\right )\right )}}{x^{2} - e^{x}} \] Input:

integrate((((((-x^3+5*x)*exp(x)+2*x^4-10*x^2)*log(x)^2+((-2*x^4+x^3+10*x^2 
)*exp(x)+4*x^5-2*x^4-20*x^3)*log(x)+(-x^5+x^4+5*x^3)*exp(x)+2*x^6-2*x^5-10 
*x^4)*log(x^2)+((2*x^2-10)*exp(x)-2*x^4+10*x^2)*log(x)^2+((4*x^3-2*x^2-20* 
x)*exp(x)-4*x^5+2*x^4+20*x^3)*log(x)+(2*x^4-2*x^3-10*x^2)*exp(x)-2*x^6+2*x 
^5+10*x^4)*log(((-x^2+5)*log(x)-x^3+x^2+5*x)/(x+log(x)))+(((-5*x^3+2*x^2+2 
5*x)*exp(x)+8*x^4-50*x^2)*log(x)^2+((-10*x^4+9*x^3+48*x^2)*exp(x)+16*x^5-8 
*x^4-100*x^3)*log(x)+(-5*x^5+7*x^4+24*x^3+x^2)*exp(x)+8*x^6-9*x^5-51*x^4)* 
log(x^2)+((10*x^2-50)*exp(x)-10*x^4+50*x^2)*log(x)^2+((20*x^3-10*x^2-100*x 
)*exp(x)-20*x^5+10*x^4+100*x^3)*log(x)+(10*x^4-10*x^3-50*x^2)*exp(x)-10*x^ 
6+10*x^5+50*x^4)/(((x^3-5*x)*exp(x)^2+(-2*x^5+10*x^3)*exp(x)+x^7-5*x^5)*lo 
g(x)^2+((2*x^4-x^3-10*x^2)*exp(x)^2+(-4*x^6+2*x^5+20*x^4)*exp(x)+2*x^8-x^7 
-10*x^6)*log(x)+(x^5-x^4-5*x^3)*exp(x)^2+(-2*x^7+2*x^6+10*x^5)*exp(x)+x^9- 
x^8-5*x^7),x, algorithm="maxima")
 

Output:

-2*(log(-x^3 + x^2 - (x^2 - 5)*log(x) + 5*x)*log(x) - log(x + log(x))*log( 
x) + 5*log(x))/(x^2 - e^x)
 

Giac [A] (verification not implemented)

Time = 1.20 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.51 \[ \int \frac {50 x^4+10 x^5-10 x^6+e^x \left (-50 x^2-10 x^3+10 x^4\right )+\left (100 x^3+10 x^4-20 x^5+e^x \left (-100 x-10 x^2+20 x^3\right )\right ) \log (x)+\left (50 x^2-10 x^4+e^x \left (-50+10 x^2\right )\right ) \log ^2(x)+\left (-51 x^4-9 x^5+8 x^6+e^x \left (x^2+24 x^3+7 x^4-5 x^5\right )+\left (-100 x^3-8 x^4+16 x^5+e^x \left (48 x^2+9 x^3-10 x^4\right )\right ) \log (x)+\left (-50 x^2+8 x^4+e^x \left (25 x+2 x^2-5 x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )+\left (10 x^4+2 x^5-2 x^6+e^x \left (-10 x^2-2 x^3+2 x^4\right )+\left (20 x^3+2 x^4-4 x^5+e^x \left (-20 x-2 x^2+4 x^3\right )\right ) \log (x)+\left (10 x^2-2 x^4+e^x \left (-10+2 x^2\right )\right ) \log ^2(x)+\left (-10 x^4-2 x^5+2 x^6+e^x \left (5 x^3+x^4-x^5\right )+\left (-20 x^3-2 x^4+4 x^5+e^x \left (10 x^2+x^3-2 x^4\right )\right ) \log (x)+\left (-10 x^2+2 x^4+e^x \left (5 x-x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )\right ) \log \left (\frac {5 x+x^2-x^3+\left (5-x^2\right ) \log (x)}{x+\log (x)}\right )}{-5 x^7-x^8+x^9+e^{2 x} \left (-5 x^3-x^4+x^5\right )+e^x \left (10 x^5+2 x^6-2 x^7\right )+\left (-10 x^6-x^7+2 x^8+e^{2 x} \left (-10 x^2-x^3+2 x^4\right )+e^x \left (20 x^4+2 x^5-4 x^6\right )\right ) \log (x)+\left (-5 x^5+x^7+e^{2 x} \left (-5 x+x^3\right )+e^x \left (10 x^3-2 x^5\right )\right ) \log ^2(x)} \, dx=-\frac {2 \, {\left (\log \left (-x^{3} - x^{2} \log \left (x\right ) + x^{2} + 5 \, x + 5 \, \log \left (x\right )\right ) \log \left (x\right ) - \log \left (x + \log \left (x\right )\right ) \log \left (x\right ) + 5 \, \log \left (x\right )\right )}}{x^{2} - e^{x}} \] Input:

integrate((((((-x^3+5*x)*exp(x)+2*x^4-10*x^2)*log(x)^2+((-2*x^4+x^3+10*x^2 
)*exp(x)+4*x^5-2*x^4-20*x^3)*log(x)+(-x^5+x^4+5*x^3)*exp(x)+2*x^6-2*x^5-10 
*x^4)*log(x^2)+((2*x^2-10)*exp(x)-2*x^4+10*x^2)*log(x)^2+((4*x^3-2*x^2-20* 
x)*exp(x)-4*x^5+2*x^4+20*x^3)*log(x)+(2*x^4-2*x^3-10*x^2)*exp(x)-2*x^6+2*x 
^5+10*x^4)*log(((-x^2+5)*log(x)-x^3+x^2+5*x)/(x+log(x)))+(((-5*x^3+2*x^2+2 
5*x)*exp(x)+8*x^4-50*x^2)*log(x)^2+((-10*x^4+9*x^3+48*x^2)*exp(x)+16*x^5-8 
*x^4-100*x^3)*log(x)+(-5*x^5+7*x^4+24*x^3+x^2)*exp(x)+8*x^6-9*x^5-51*x^4)* 
log(x^2)+((10*x^2-50)*exp(x)-10*x^4+50*x^2)*log(x)^2+((20*x^3-10*x^2-100*x 
)*exp(x)-20*x^5+10*x^4+100*x^3)*log(x)+(10*x^4-10*x^3-50*x^2)*exp(x)-10*x^ 
6+10*x^5+50*x^4)/(((x^3-5*x)*exp(x)^2+(-2*x^5+10*x^3)*exp(x)+x^7-5*x^5)*lo 
g(x)^2+((2*x^4-x^3-10*x^2)*exp(x)^2+(-4*x^6+2*x^5+20*x^4)*exp(x)+2*x^8-x^7 
-10*x^6)*log(x)+(x^5-x^4-5*x^3)*exp(x)^2+(-2*x^7+2*x^6+10*x^5)*exp(x)+x^9- 
x^8-5*x^7),x, algorithm="giac")
 

Output:

-2*(log(-x^3 - x^2*log(x) + x^2 + 5*x + 5*log(x))*log(x) - log(x + log(x)) 
*log(x) + 5*log(x))/(x^2 - e^x)
 

Mupad [B] (verification not implemented)

Time = 3.41 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.37 \[ \int \frac {50 x^4+10 x^5-10 x^6+e^x \left (-50 x^2-10 x^3+10 x^4\right )+\left (100 x^3+10 x^4-20 x^5+e^x \left (-100 x-10 x^2+20 x^3\right )\right ) \log (x)+\left (50 x^2-10 x^4+e^x \left (-50+10 x^2\right )\right ) \log ^2(x)+\left (-51 x^4-9 x^5+8 x^6+e^x \left (x^2+24 x^3+7 x^4-5 x^5\right )+\left (-100 x^3-8 x^4+16 x^5+e^x \left (48 x^2+9 x^3-10 x^4\right )\right ) \log (x)+\left (-50 x^2+8 x^4+e^x \left (25 x+2 x^2-5 x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )+\left (10 x^4+2 x^5-2 x^6+e^x \left (-10 x^2-2 x^3+2 x^4\right )+\left (20 x^3+2 x^4-4 x^5+e^x \left (-20 x-2 x^2+4 x^3\right )\right ) \log (x)+\left (10 x^2-2 x^4+e^x \left (-10+2 x^2\right )\right ) \log ^2(x)+\left (-10 x^4-2 x^5+2 x^6+e^x \left (5 x^3+x^4-x^5\right )+\left (-20 x^3-2 x^4+4 x^5+e^x \left (10 x^2+x^3-2 x^4\right )\right ) \log (x)+\left (-10 x^2+2 x^4+e^x \left (5 x-x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )\right ) \log \left (\frac {5 x+x^2-x^3+\left (5-x^2\right ) \log (x)}{x+\log (x)}\right )}{-5 x^7-x^8+x^9+e^{2 x} \left (-5 x^3-x^4+x^5\right )+e^x \left (10 x^5+2 x^6-2 x^7\right )+\left (-10 x^6-x^7+2 x^8+e^{2 x} \left (-10 x^2-x^3+2 x^4\right )+e^x \left (20 x^4+2 x^5-4 x^6\right )\right ) \log (x)+\left (-5 x^5+x^7+e^{2 x} \left (-5 x+x^3\right )+e^x \left (10 x^3-2 x^5\right )\right ) \log ^2(x)} \, dx=\frac {\ln \left (x^2\right )\,\left (\ln \left (\frac {5\,x+5\,\ln \left (x\right )-x^2\,\ln \left (x\right )+x^2-x^3}{x+\ln \left (x\right )}\right )+5\right )}{{\mathrm {e}}^x-x^2} \] Input:

int(-(log(x)*(100*x^3 + 10*x^4 - 20*x^5 - exp(x)*(100*x + 10*x^2 - 20*x^3) 
) - exp(x)*(50*x^2 + 10*x^3 - 10*x^4) + log(x)^2*(exp(x)*(10*x^2 - 50) + 5 
0*x^2 - 10*x^4) + log((5*x - log(x)*(x^2 - 5) + x^2 - x^3)/(x + log(x)))*( 
log(x)*(20*x^3 + 2*x^4 - 4*x^5 - exp(x)*(20*x + 2*x^2 - 4*x^3)) - exp(x)*( 
10*x^2 + 2*x^3 - 2*x^4) + log(x)^2*(exp(x)*(2*x^2 - 10) + 10*x^2 - 2*x^4) 
+ log(x^2)*(log(x)^2*(exp(x)*(5*x - x^3) - 10*x^2 + 2*x^4) - log(x)*(20*x^ 
3 + 2*x^4 - 4*x^5 - exp(x)*(10*x^2 + x^3 - 2*x^4)) - 10*x^4 - 2*x^5 + 2*x^ 
6 + exp(x)*(5*x^3 + x^4 - x^5)) + 10*x^4 + 2*x^5 - 2*x^6) + log(x^2)*(exp( 
x)*(x^2 + 24*x^3 + 7*x^4 - 5*x^5) + log(x)^2*(8*x^4 - 50*x^2 + exp(x)*(25* 
x + 2*x^2 - 5*x^3)) + log(x)*(exp(x)*(48*x^2 + 9*x^3 - 10*x^4) - 100*x^3 - 
 8*x^4 + 16*x^5) - 51*x^4 - 9*x^5 + 8*x^6) + 50*x^4 + 10*x^5 - 10*x^6)/(ex 
p(2*x)*(5*x^3 + x^4 - x^5) - exp(x)*(10*x^5 + 2*x^6 - 2*x^7) + log(x)*(exp 
(2*x)*(10*x^2 + x^3 - 2*x^4) - exp(x)*(20*x^4 + 2*x^5 - 4*x^6) + 10*x^6 + 
x^7 - 2*x^8) + log(x)^2*(exp(2*x)*(5*x - x^3) - exp(x)*(10*x^3 - 2*x^5) + 
5*x^5 - x^7) + 5*x^7 + x^8 - x^9),x)
 

Output:

(log(x^2)*(log((5*x + 5*log(x) - x^2*log(x) + x^2 - x^3)/(x + log(x))) + 5 
))/(exp(x) - x^2)
 

Reduce [B] (verification not implemented)

Time = 0.65 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.40 \[ \int \frac {50 x^4+10 x^5-10 x^6+e^x \left (-50 x^2-10 x^3+10 x^4\right )+\left (100 x^3+10 x^4-20 x^5+e^x \left (-100 x-10 x^2+20 x^3\right )\right ) \log (x)+\left (50 x^2-10 x^4+e^x \left (-50+10 x^2\right )\right ) \log ^2(x)+\left (-51 x^4-9 x^5+8 x^6+e^x \left (x^2+24 x^3+7 x^4-5 x^5\right )+\left (-100 x^3-8 x^4+16 x^5+e^x \left (48 x^2+9 x^3-10 x^4\right )\right ) \log (x)+\left (-50 x^2+8 x^4+e^x \left (25 x+2 x^2-5 x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )+\left (10 x^4+2 x^5-2 x^6+e^x \left (-10 x^2-2 x^3+2 x^4\right )+\left (20 x^3+2 x^4-4 x^5+e^x \left (-20 x-2 x^2+4 x^3\right )\right ) \log (x)+\left (10 x^2-2 x^4+e^x \left (-10+2 x^2\right )\right ) \log ^2(x)+\left (-10 x^4-2 x^5+2 x^6+e^x \left (5 x^3+x^4-x^5\right )+\left (-20 x^3-2 x^4+4 x^5+e^x \left (10 x^2+x^3-2 x^4\right )\right ) \log (x)+\left (-10 x^2+2 x^4+e^x \left (5 x-x^3\right )\right ) \log ^2(x)\right ) \log \left (x^2\right )\right ) \log \left (\frac {5 x+x^2-x^3+\left (5-x^2\right ) \log (x)}{x+\log (x)}\right )}{-5 x^7-x^8+x^9+e^{2 x} \left (-5 x^3-x^4+x^5\right )+e^x \left (10 x^5+2 x^6-2 x^7\right )+\left (-10 x^6-x^7+2 x^8+e^{2 x} \left (-10 x^2-x^3+2 x^4\right )+e^x \left (20 x^4+2 x^5-4 x^6\right )\right ) \log (x)+\left (-5 x^5+x^7+e^{2 x} \left (-5 x+x^3\right )+e^x \left (10 x^3-2 x^5\right )\right ) \log ^2(x)} \, dx=\frac {\mathrm {log}\left (x^{2}\right ) \left (\mathrm {log}\left (\frac {-\mathrm {log}\left (x \right ) x^{2}+5 \,\mathrm {log}\left (x \right )-x^{3}+x^{2}+5 x}{\mathrm {log}\left (x \right )+x}\right )+5\right )}{e^{x}-x^{2}} \] Input:

int((((((-x^3+5*x)*exp(x)+2*x^4-10*x^2)*log(x)^2+((-2*x^4+x^3+10*x^2)*exp( 
x)+4*x^5-2*x^4-20*x^3)*log(x)+(-x^5+x^4+5*x^3)*exp(x)+2*x^6-2*x^5-10*x^4)* 
log(x^2)+((2*x^2-10)*exp(x)-2*x^4+10*x^2)*log(x)^2+((4*x^3-2*x^2-20*x)*exp 
(x)-4*x^5+2*x^4+20*x^3)*log(x)+(2*x^4-2*x^3-10*x^2)*exp(x)-2*x^6+2*x^5+10* 
x^4)*log(((-x^2+5)*log(x)-x^3+x^2+5*x)/(x+log(x)))+(((-5*x^3+2*x^2+25*x)*e 
xp(x)+8*x^4-50*x^2)*log(x)^2+((-10*x^4+9*x^3+48*x^2)*exp(x)+16*x^5-8*x^4-1 
00*x^3)*log(x)+(-5*x^5+7*x^4+24*x^3+x^2)*exp(x)+8*x^6-9*x^5-51*x^4)*log(x^ 
2)+((10*x^2-50)*exp(x)-10*x^4+50*x^2)*log(x)^2+((20*x^3-10*x^2-100*x)*exp( 
x)-20*x^5+10*x^4+100*x^3)*log(x)+(10*x^4-10*x^3-50*x^2)*exp(x)-10*x^6+10*x 
^5+50*x^4)/(((x^3-5*x)*exp(x)^2+(-2*x^5+10*x^3)*exp(x)+x^7-5*x^5)*log(x)^2 
+((2*x^4-x^3-10*x^2)*exp(x)^2+(-4*x^6+2*x^5+20*x^4)*exp(x)+2*x^8-x^7-10*x^ 
6)*log(x)+(x^5-x^4-5*x^3)*exp(x)^2+(-2*x^7+2*x^6+10*x^5)*exp(x)+x^9-x^8-5* 
x^7),x)
 

Output:

(log(x**2)*(log(( - log(x)*x**2 + 5*log(x) - x**3 + x**2 + 5*x)/(log(x) + 
x)) + 5))/(e**x - x**2)