3.20.96 \(\int \frac {-1500 e^{15-3 x} x^5+e^{20-4 x} (-2500 x^5+2500 x^6)+e^x (e^{20-4 x} (2500 x^3-2500 x^4)+e^{15-3 x} (-1500 x^3+1500 x^4))+(-2700 e^{10-2 x} x^5+e^{15-3 x} (-6000 x^5+4500 x^6)+e^x (e^{15-3 x} (6000 x^3-4500 x^4)+e^{10-2 x} (-2700 x^3+2700 x^4))) \log (\frac {-e^x+x^2}{2 x})+(-1620 e^{5-x} x^5+e^{10-2 x} (-5400 x^5+2700 x^6)+e^x (e^{10-2 x} (5400 x^3-2700 x^4)+e^{5-x} (-1620 x^3+1620 x^4))) \log ^2(\frac {-e^x+x^2}{2 x})+(-324 x^5+e^{5-x} (-2160 x^5+540 x^6)+e^x (-324 x^3+324 x^4+e^{5-x} (2160 x^3-540 x^4))) \log ^3(\frac {-e^x+x^2}{2 x})+(324 e^x x^3-324 x^5) \log ^4(\frac {-e^x+x^2}{2 x})}{81 e^x-81 x^2} \, dx\) [1996]

3.20.96.1 Optimal result

Integrand size = 390, antiderivative size = 32 \[ \int \frac {-1500 e^{15-3 x} x^5+e^{20-4 x} \left (-2500 x^5+2500 x^6\right )+e^x \left (e^{20-4 x} \left (2500 x^3-2500 x^4\right )+e^{15-3 x} \left (-1500 x^3+1500 x^4\right )\right )+\left (-2700 e^{10-2 x} x^5+e^{15-3 x} \left (-6000 x^5+4500 x^6\right )+e^x \left (e^{15-3 x} \left (6000 x^3-4500 x^4\right )+e^{10-2 x} \left (-2700 x^3+2700 x^4\right )\right )\right ) \log \left (\frac {-e^x+x^2}{2 x}\right )+\left (-1620 e^{5-x} x^5+e^{10-2 x} \left (-5400 x^5+2700 x^6\right )+e^x \left (e^{10-2 x} \left (5400 x^3-2700 x^4\right )+e^{5-x} \left (-1620 x^3+1620 x^4\right )\right )\right ) \log ^2\left (\frac {-e^x+x^2}{2 x}\right )+\left (-324 x^5+e^{5-x} \left (-2160 x^5+540 x^6\right )+e^x \left (-324 x^3+324 x^4+e^{5-x} \left (2160 x^3-540 x^4\right )\right )\right ) \log ^3\left (\frac {-e^x+x^2}{2 x}\right )+\left (324 e^x x^3-324 x^5\right ) \log ^4\left (\frac {-e^x+x^2}{2 x}\right )}{81 e^x-81 x^2} \, dx=\left (\frac {5}{3} e^{5-x} x+x \log \left (\frac {1}{2} \left (-\frac {e^x}{x}+x\right )\right )\right )^4 \]

output

(x*ln(1/2*x-1/2*exp(x)/x)+5/3*x*exp(5-x))^4
 

3.20.96.2 Mathematica [A] (verified)

Time = 0.40 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.31 \[ \int \frac {-1500 e^{15-3 x} x^5+e^{20-4 x} \left (-2500 x^5+2500 x^6\right )+e^x \left (e^{20-4 x} \left (2500 x^3-2500 x^4\right )+e^{15-3 x} \left (-1500 x^3+1500 x^4\right )\right )+\left (-2700 e^{10-2 x} x^5+e^{15-3 x} \left (-6000 x^5+4500 x^6\right )+e^x \left (e^{15-3 x} \left (6000 x^3-4500 x^4\right )+e^{10-2 x} \left (-2700 x^3+2700 x^4\right )\right )\right ) \log \left (\frac {-e^x+x^2}{2 x}\right )+\left (-1620 e^{5-x} x^5+e^{10-2 x} \left (-5400 x^5+2700 x^6\right )+e^x \left (e^{10-2 x} \left (5400 x^3-2700 x^4\right )+e^{5-x} \left (-1620 x^3+1620 x^4\right )\right )\right ) \log ^2\left (\frac {-e^x+x^2}{2 x}\right )+\left (-324 x^5+e^{5-x} \left (-2160 x^5+540 x^6\right )+e^x \left (-324 x^3+324 x^4+e^{5-x} \left (2160 x^3-540 x^4\right )\right )\right ) \log ^3\left (\frac {-e^x+x^2}{2 x}\right )+\left (324 e^x x^3-324 x^5\right ) \log ^4\left (\frac {-e^x+x^2}{2 x}\right )}{81 e^x-81 x^2} \, dx=\frac {1}{81} e^{-4 x} x^4 \left (5 e^5+3 e^x \log \left (\frac {-e^x+x^2}{2 x}\right )\right )^4 \]

input

Integrate[(-1500*E^(15 - 3*x)*x^5 + E^(20 - 4*x)*(-2500*x^5 + 2500*x^6) + 
E^x*(E^(20 - 4*x)*(2500*x^3 - 2500*x^4) + E^(15 - 3*x)*(-1500*x^3 + 1500*x 
^4)) + (-2700*E^(10 - 2*x)*x^5 + E^(15 - 3*x)*(-6000*x^5 + 4500*x^6) + E^x 
*(E^(15 - 3*x)*(6000*x^3 - 4500*x^4) + E^(10 - 2*x)*(-2700*x^3 + 2700*x^4) 
))*Log[(-E^x + x^2)/(2*x)] + (-1620*E^(5 - x)*x^5 + E^(10 - 2*x)*(-5400*x^ 
5 + 2700*x^6) + E^x*(E^(10 - 2*x)*(5400*x^3 - 2700*x^4) + E^(5 - x)*(-1620 
*x^3 + 1620*x^4)))*Log[(-E^x + x^2)/(2*x)]^2 + (-324*x^5 + E^(5 - x)*(-216 
0*x^5 + 540*x^6) + E^x*(-324*x^3 + 324*x^4 + E^(5 - x)*(2160*x^3 - 540*x^4 
)))*Log[(-E^x + x^2)/(2*x)]^3 + (324*E^x*x^3 - 324*x^5)*Log[(-E^x + x^2)/( 
2*x)]^4)/(81*E^x - 81*x^2),x]
 

output

(x^4*(5*E^5 + 3*E^x*Log[(-E^x + x^2)/(2*x)])^4)/(81*E^(4*x))
 

3.20.96.3 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.

\(\displaystyle \int \frac {-1500 e^{15-3 x} x^5+e^{20-4 x} \left (2500 x^6-2500 x^5\right )+e^x \left (e^{20-4 x} \left (2500 x^3-2500 x^4\right )+e^{15-3 x} \left (1500 x^4-1500 x^3\right )\right )+\left (324 e^x x^3-324 x^5\right ) \log ^4\left (\frac {x^2-e^x}{2 x}\right )+\left (-324 x^5+e^{5-x} \left (540 x^6-2160 x^5\right )+e^x \left (324 x^4-324 x^3+e^{5-x} \left (2160 x^3-540 x^4\right )\right )\right ) \log ^3\left (\frac {x^2-e^x}{2 x}\right )+\left (-1620 e^{5-x} x^5+e^{10-2 x} \left (2700 x^6-5400 x^5\right )+e^x \left (e^{10-2 x} \left (5400 x^3-2700 x^4\right )+e^{5-x} \left (1620 x^4-1620 x^3\right )\right )\right ) \log ^2\left (\frac {x^2-e^x}{2 x}\right )+\left (-2700 e^{10-2 x} x^5+e^{15-3 x} \left (4500 x^6-6000 x^5\right )+e^x \left (e^{15-3 x} \left (6000 x^3-4500 x^4\right )+e^{10-2 x} \left (2700 x^4-2700 x^3\right )\right )\right ) \log \left (\frac {x^2-e^x}{2 x}\right )}{81 e^x-81 x^2} \, dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {4 e^{-4 x} x^3 \left (3 e^x \log \left (\frac {x^2-e^x}{2 x}\right )+5 e^5\right )^3 \left (-3 e^x x^2+5 e^5 (x-1) x^2+3 e^x \left (e^x-x^2\right ) \log \left (\frac {x^2-e^x}{2 x}\right )+3 e^{2 x} (x-1)-5 e^{x+5} (x-1)\right )}{81 \left (e^x-x^2\right )}dx\)

\(\Big \downarrow \) 27

\(\displaystyle \frac {4}{81} \int -\frac {e^{-4 x} x^3 \left (3 e^x \log \left (-\frac {e^x-x^2}{2 x}\right )+5 e^5\right )^3 \left (3 e^x x^2+5 e^5 (1-x) x^2+3 e^{2 x} (1-x)-5 e^{x+5} (1-x)-3 e^x \left (e^x-x^2\right ) \log \left (-\frac {e^x-x^2}{2 x}\right )\right )}{e^x-x^2}dx\)

\(\Big \downarrow \) 25

\(\displaystyle -\frac {4}{81} \int \frac {e^{-4 x} x^3 \left (3 e^x \log \left (-\frac {e^x-x^2}{2 x}\right )+5 e^5\right )^3 \left (3 e^x x^2+5 e^5 (1-x) x^2+3 e^{2 x} (1-x)-5 e^{x+5} (1-x)-3 e^x \left (e^x-x^2\right ) \log \left (-\frac {e^x-x^2}{2 x}\right )\right )}{e^x-x^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -\frac {4}{81} \int \left (\frac {3 e^{-4 x} (x-2) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2+5 e^5\right )^3 x^7}{x^2-e^x}-81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) \left (x+\log \left (\frac {x^2-e^x}{2 x}\right )-1\right ) x^3-27 e^{-x} \log ^2\left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-6 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-5 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x+15 e^5 x+20 e^5 \log \left (\frac {x^2-e^x}{2 x}\right )-15 e^5\right ) x^3-27 e^{-2 x} \log \left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-6 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+15 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-30 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-25 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x+25 e^{10} x+50 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right )-25 e^{10}\right ) x^3-3 e^{-3 x} \left (27 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^7-54 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^6+135 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-270 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+225 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-450 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-375 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right ) x+125 e^{15} x+500 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right )-125 e^{15}\right ) x^3-e^{-4 x} \left (81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^9-162 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^8+405 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^7-810 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^6+675 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^5-1350 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^4+375 e^{15} x^3-750 e^{15} x^2-625 e^{20} x+625 e^{20}\right ) x^3\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -\frac {4}{81} \int \frac {e^{-4 x} x^3 \left (3 e^x \log \left (\frac {x^2-e^x}{2 x}\right )+5 e^5\right )^3 \left (3 e^x x^2-5 e^5 (x-1) x^2-3 e^{2 x} (x-1)+5 e^{x+5} (x-1)-3 e^x \left (e^x-x^2\right ) \log \left (\frac {x^2-e^x}{2 x}\right )\right )}{e^x-x^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -\frac {4}{81} \int \left (\frac {3 e^{-4 x} (x-2) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2+5 e^5\right )^3 x^7}{x^2-e^x}-81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) \left (x+\log \left (\frac {x^2-e^x}{2 x}\right )-1\right ) x^3-27 e^{-x} \log ^2\left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-6 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-5 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x+15 e^5 x+20 e^5 \log \left (\frac {x^2-e^x}{2 x}\right )-15 e^5\right ) x^3-27 e^{-2 x} \log \left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-6 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+15 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-30 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-25 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x+25 e^{10} x+50 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right )-25 e^{10}\right ) x^3-3 e^{-3 x} \left (27 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^7-54 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^6+135 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-270 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+225 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-450 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-375 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right ) x+125 e^{15} x+500 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right )-125 e^{15}\right ) x^3-e^{-4 x} \left (81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^9-162 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^8+405 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^7-810 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^6+675 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^5-1350 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^4+375 e^{15} x^3-750 e^{15} x^2-625 e^{20} x+625 e^{20}\right ) x^3\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -\frac {4}{81} \int \frac {e^{-4 x} x^3 \left (3 e^x \log \left (\frac {x^2-e^x}{2 x}\right )+5 e^5\right )^3 \left (3 e^x x^2-5 e^5 (x-1) x^2-3 e^{2 x} (x-1)+5 e^{x+5} (x-1)-3 e^x \left (e^x-x^2\right ) \log \left (\frac {x^2-e^x}{2 x}\right )\right )}{e^x-x^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -\frac {4}{81} \int \left (\frac {3 e^{-4 x} (x-2) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2+5 e^5\right )^3 x^7}{x^2-e^x}-81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) \left (x+\log \left (\frac {x^2-e^x}{2 x}\right )-1\right ) x^3-27 e^{-x} \log ^2\left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-6 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-5 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x+15 e^5 x+20 e^5 \log \left (\frac {x^2-e^x}{2 x}\right )-15 e^5\right ) x^3-27 e^{-2 x} \log \left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-6 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+15 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-30 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-25 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x+25 e^{10} x+50 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right )-25 e^{10}\right ) x^3-3 e^{-3 x} \left (27 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^7-54 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^6+135 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-270 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+225 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-450 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-375 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right ) x+125 e^{15} x+500 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right )-125 e^{15}\right ) x^3-e^{-4 x} \left (81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^9-162 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^8+405 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^7-810 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^6+675 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^5-1350 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^4+375 e^{15} x^3-750 e^{15} x^2-625 e^{20} x+625 e^{20}\right ) x^3\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -\frac {4}{81} \int \frac {e^{-4 x} x^3 \left (3 e^x \log \left (\frac {x^2-e^x}{2 x}\right )+5 e^5\right )^3 \left (3 e^x x^2-5 e^5 (x-1) x^2-3 e^{2 x} (x-1)+5 e^{x+5} (x-1)-3 e^x \left (e^x-x^2\right ) \log \left (\frac {x^2-e^x}{2 x}\right )\right )}{e^x-x^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -\frac {4}{81} \int \left (\frac {3 e^{-4 x} (x-2) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2+5 e^5\right )^3 x^7}{x^2-e^x}-81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) \left (x+\log \left (\frac {x^2-e^x}{2 x}\right )-1\right ) x^3-27 e^{-x} \log ^2\left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-6 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-5 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x+15 e^5 x+20 e^5 \log \left (\frac {x^2-e^x}{2 x}\right )-15 e^5\right ) x^3-27 e^{-2 x} \log \left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-6 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+15 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-30 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-25 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x+25 e^{10} x+50 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right )-25 e^{10}\right ) x^3-3 e^{-3 x} \left (27 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^7-54 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^6+135 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-270 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+225 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-450 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-375 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right ) x+125 e^{15} x+500 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right )-125 e^{15}\right ) x^3-e^{-4 x} \left (81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^9-162 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^8+405 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^7-810 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^6+675 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^5-1350 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^4+375 e^{15} x^3-750 e^{15} x^2-625 e^{20} x+625 e^{20}\right ) x^3\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -\frac {4}{81} \int \frac {e^{-4 x} x^3 \left (3 e^x \log \left (\frac {x^2-e^x}{2 x}\right )+5 e^5\right )^3 \left (3 e^x x^2-5 e^5 (x-1) x^2-3 e^{2 x} (x-1)+5 e^{x+5} (x-1)-3 e^x \left (e^x-x^2\right ) \log \left (\frac {x^2-e^x}{2 x}\right )\right )}{e^x-x^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -\frac {4}{81} \int \left (\frac {3 e^{-4 x} (x-2) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2+5 e^5\right )^3 x^7}{x^2-e^x}-81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) \left (x+\log \left (\frac {x^2-e^x}{2 x}\right )-1\right ) x^3-27 e^{-x} \log ^2\left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-6 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-5 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x+15 e^5 x+20 e^5 \log \left (\frac {x^2-e^x}{2 x}\right )-15 e^5\right ) x^3-27 e^{-2 x} \log \left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-6 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+15 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-30 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-25 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x+25 e^{10} x+50 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right )-25 e^{10}\right ) x^3-3 e^{-3 x} \left (27 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^7-54 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^6+135 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-270 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+225 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-450 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-375 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right ) x+125 e^{15} x+500 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right )-125 e^{15}\right ) x^3-e^{-4 x} \left (81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^9-162 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^8+405 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^7-810 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^6+675 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^5-1350 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^4+375 e^{15} x^3-750 e^{15} x^2-625 e^{20} x+625 e^{20}\right ) x^3\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -\frac {4}{81} \int \frac {e^{-4 x} x^3 \left (3 e^x \log \left (\frac {x^2-e^x}{2 x}\right )+5 e^5\right )^3 \left (3 e^x x^2-5 e^5 (x-1) x^2-3 e^{2 x} (x-1)+5 e^{x+5} (x-1)-3 e^x \left (e^x-x^2\right ) \log \left (\frac {x^2-e^x}{2 x}\right )\right )}{e^x-x^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -\frac {4}{81} \int \left (\frac {3 e^{-4 x} (x-2) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2+5 e^5\right )^3 x^7}{x^2-e^x}-81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) \left (x+\log \left (\frac {x^2-e^x}{2 x}\right )-1\right ) x^3-27 e^{-x} \log ^2\left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-6 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-5 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x+15 e^5 x+20 e^5 \log \left (\frac {x^2-e^x}{2 x}\right )-15 e^5\right ) x^3-27 e^{-2 x} \log \left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-6 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+15 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-30 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-25 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x+25 e^{10} x+50 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right )-25 e^{10}\right ) x^3-3 e^{-3 x} \left (27 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^7-54 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^6+135 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-270 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+225 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-450 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-375 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right ) x+125 e^{15} x+500 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right )-125 e^{15}\right ) x^3-e^{-4 x} \left (81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^9-162 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^8+405 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^7-810 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^6+675 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^5-1350 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^4+375 e^{15} x^3-750 e^{15} x^2-625 e^{20} x+625 e^{20}\right ) x^3\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -\frac {4}{81} \int \frac {e^{-4 x} x^3 \left (3 e^x \log \left (\frac {x^2-e^x}{2 x}\right )+5 e^5\right )^3 \left (3 e^x x^2-5 e^5 (x-1) x^2-3 e^{2 x} (x-1)+5 e^{x+5} (x-1)-3 e^x \left (e^x-x^2\right ) \log \left (\frac {x^2-e^x}{2 x}\right )\right )}{e^x-x^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -\frac {4}{81} \int \left (\frac {3 e^{-4 x} (x-2) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2+5 e^5\right )^3 x^7}{x^2-e^x}-81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) \left (x+\log \left (\frac {x^2-e^x}{2 x}\right )-1\right ) x^3-27 e^{-x} \log ^2\left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-6 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-5 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x+15 e^5 x+20 e^5 \log \left (\frac {x^2-e^x}{2 x}\right )-15 e^5\right ) x^3-27 e^{-2 x} \log \left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-6 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+15 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-30 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-25 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x+25 e^{10} x+50 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right )-25 e^{10}\right ) x^3-3 e^{-3 x} \left (27 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^7-54 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^6+135 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-270 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+225 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-450 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-375 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right ) x+125 e^{15} x+500 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right )-125 e^{15}\right ) x^3-e^{-4 x} \left (81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^9-162 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^8+405 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^7-810 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^6+675 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^5-1350 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^4+375 e^{15} x^3-750 e^{15} x^2-625 e^{20} x+625 e^{20}\right ) x^3\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -\frac {4}{81} \int \frac {e^{-4 x} x^3 \left (3 e^x \log \left (\frac {x^2-e^x}{2 x}\right )+5 e^5\right )^3 \left (3 e^x x^2-5 e^5 (x-1) x^2-3 e^{2 x} (x-1)+5 e^{x+5} (x-1)-3 e^x \left (e^x-x^2\right ) \log \left (\frac {x^2-e^x}{2 x}\right )\right )}{e^x-x^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -\frac {4}{81} \int \left (\frac {3 e^{-4 x} (x-2) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2+5 e^5\right )^3 x^7}{x^2-e^x}-81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) \left (x+\log \left (\frac {x^2-e^x}{2 x}\right )-1\right ) x^3-27 e^{-x} \log ^2\left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-6 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-5 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x+15 e^5 x+20 e^5 \log \left (\frac {x^2-e^x}{2 x}\right )-15 e^5\right ) x^3-27 e^{-2 x} \log \left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-6 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+15 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-30 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-25 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x+25 e^{10} x+50 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right )-25 e^{10}\right ) x^3-3 e^{-3 x} \left (27 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^7-54 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^6+135 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-270 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+225 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-450 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-375 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right ) x+125 e^{15} x+500 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right )-125 e^{15}\right ) x^3-e^{-4 x} \left (81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^9-162 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^8+405 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^7-810 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^6+675 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^5-1350 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^4+375 e^{15} x^3-750 e^{15} x^2-625 e^{20} x+625 e^{20}\right ) x^3\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -\frac {4}{81} \int \frac {e^{-4 x} x^3 \left (3 e^x \log \left (\frac {x^2-e^x}{2 x}\right )+5 e^5\right )^3 \left (3 e^x x^2-5 e^5 (x-1) x^2-3 e^{2 x} (x-1)+5 e^{x+5} (x-1)-3 e^x \left (e^x-x^2\right ) \log \left (\frac {x^2-e^x}{2 x}\right )\right )}{e^x-x^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -\frac {4}{81} \int \left (\frac {3 e^{-4 x} (x-2) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2+5 e^5\right )^3 x^7}{x^2-e^x}-81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) \left (x+\log \left (\frac {x^2-e^x}{2 x}\right )-1\right ) x^3-27 e^{-x} \log ^2\left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-6 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-5 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x+15 e^5 x+20 e^5 \log \left (\frac {x^2-e^x}{2 x}\right )-15 e^5\right ) x^3-27 e^{-2 x} \log \left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-6 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+15 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-30 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-25 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x+25 e^{10} x+50 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right )-25 e^{10}\right ) x^3-3 e^{-3 x} \left (27 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^7-54 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^6+135 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-270 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+225 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-450 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-375 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right ) x+125 e^{15} x+500 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right )-125 e^{15}\right ) x^3-e^{-4 x} \left (81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^9-162 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^8+405 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^7-810 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^6+675 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^5-1350 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^4+375 e^{15} x^3-750 e^{15} x^2-625 e^{20} x+625 e^{20}\right ) x^3\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -\frac {4}{81} \int \frac {e^{-4 x} x^3 \left (3 e^x \log \left (\frac {x^2-e^x}{2 x}\right )+5 e^5\right )^3 \left (3 e^x x^2-5 e^5 (x-1) x^2-3 e^{2 x} (x-1)+5 e^{x+5} (x-1)-3 e^x \left (e^x-x^2\right ) \log \left (\frac {x^2-e^x}{2 x}\right )\right )}{e^x-x^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -\frac {4}{81} \int \left (\frac {3 e^{-4 x} (x-2) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2+5 e^5\right )^3 x^7}{x^2-e^x}-81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) \left (x+\log \left (\frac {x^2-e^x}{2 x}\right )-1\right ) x^3-27 e^{-x} \log ^2\left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-6 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-5 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x+15 e^5 x+20 e^5 \log \left (\frac {x^2-e^x}{2 x}\right )-15 e^5\right ) x^3-27 e^{-2 x} \log \left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-6 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+15 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-30 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-25 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x+25 e^{10} x+50 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right )-25 e^{10}\right ) x^3-3 e^{-3 x} \left (27 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^7-54 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^6+135 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-270 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+225 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-450 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-375 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right ) x+125 e^{15} x+500 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right )-125 e^{15}\right ) x^3-e^{-4 x} \left (81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^9-162 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^8+405 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^7-810 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^6+675 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^5-1350 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^4+375 e^{15} x^3-750 e^{15} x^2-625 e^{20} x+625 e^{20}\right ) x^3\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -\frac {4}{81} \int \frac {e^{-4 x} x^3 \left (3 e^x \log \left (\frac {x^2-e^x}{2 x}\right )+5 e^5\right )^3 \left (3 e^x x^2-5 e^5 (x-1) x^2-3 e^{2 x} (x-1)+5 e^{x+5} (x-1)-3 e^x \left (e^x-x^2\right ) \log \left (\frac {x^2-e^x}{2 x}\right )\right )}{e^x-x^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -\frac {4}{81} \int \left (\frac {3 e^{-4 x} (x-2) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2+5 e^5\right )^3 x^7}{x^2-e^x}-81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) \left (x+\log \left (\frac {x^2-e^x}{2 x}\right )-1\right ) x^3-27 e^{-x} \log ^2\left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-6 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-5 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x+15 e^5 x+20 e^5 \log \left (\frac {x^2-e^x}{2 x}\right )-15 e^5\right ) x^3-27 e^{-2 x} \log \left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-6 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+15 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-30 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-25 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x+25 e^{10} x+50 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right )-25 e^{10}\right ) x^3-3 e^{-3 x} \left (27 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^7-54 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^6+135 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-270 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+225 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-450 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-375 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right ) x+125 e^{15} x+500 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right )-125 e^{15}\right ) x^3-e^{-4 x} \left (81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^9-162 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^8+405 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^7-810 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^6+675 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^5-1350 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^4+375 e^{15} x^3-750 e^{15} x^2-625 e^{20} x+625 e^{20}\right ) x^3\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -\frac {4}{81} \int \frac {e^{-4 x} x^3 \left (3 e^x \log \left (\frac {x^2-e^x}{2 x}\right )+5 e^5\right )^3 \left (3 e^x x^2-5 e^5 (x-1) x^2-3 e^{2 x} (x-1)+5 e^{x+5} (x-1)-3 e^x \left (e^x-x^2\right ) \log \left (\frac {x^2-e^x}{2 x}\right )\right )}{e^x-x^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -\frac {4}{81} \int \left (\frac {3 e^{-4 x} (x-2) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2+5 e^5\right )^3 x^7}{x^2-e^x}-81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) \left (x+\log \left (\frac {x^2-e^x}{2 x}\right )-1\right ) x^3-27 e^{-x} \log ^2\left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-6 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-5 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x+15 e^5 x+20 e^5 \log \left (\frac {x^2-e^x}{2 x}\right )-15 e^5\right ) x^3-27 e^{-2 x} \log \left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-6 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+15 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-30 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-25 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x+25 e^{10} x+50 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right )-25 e^{10}\right ) x^3-3 e^{-3 x} \left (27 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^7-54 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^6+135 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-270 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+225 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-450 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-375 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right ) x+125 e^{15} x+500 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right )-125 e^{15}\right ) x^3-e^{-4 x} \left (81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^9-162 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^8+405 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^7-810 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^6+675 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^5-1350 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^4+375 e^{15} x^3-750 e^{15} x^2-625 e^{20} x+625 e^{20}\right ) x^3\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -\frac {4}{81} \int \frac {e^{-4 x} x^3 \left (3 e^x \log \left (\frac {x^2-e^x}{2 x}\right )+5 e^5\right )^3 \left (3 e^x x^2-5 e^5 (x-1) x^2-3 e^{2 x} (x-1)+5 e^{x+5} (x-1)-3 e^x \left (e^x-x^2\right ) \log \left (\frac {x^2-e^x}{2 x}\right )\right )}{e^x-x^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -\frac {4}{81} \int \left (\frac {3 e^{-4 x} (x-2) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2+5 e^5\right )^3 x^7}{x^2-e^x}-81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) \left (x+\log \left (\frac {x^2-e^x}{2 x}\right )-1\right ) x^3-27 e^{-x} \log ^2\left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-6 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-5 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x+15 e^5 x+20 e^5 \log \left (\frac {x^2-e^x}{2 x}\right )-15 e^5\right ) x^3-27 e^{-2 x} \log \left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-6 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+15 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-30 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-25 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x+25 e^{10} x+50 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right )-25 e^{10}\right ) x^3-3 e^{-3 x} \left (27 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^7-54 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^6+135 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-270 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+225 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-450 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-375 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right ) x+125 e^{15} x+500 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right )-125 e^{15}\right ) x^3-e^{-4 x} \left (81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^9-162 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^8+405 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^7-810 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^6+675 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^5-1350 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^4+375 e^{15} x^3-750 e^{15} x^2-625 e^{20} x+625 e^{20}\right ) x^3\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -\frac {4}{81} \int \frac {e^{-4 x} x^3 \left (3 e^x \log \left (\frac {x^2-e^x}{2 x}\right )+5 e^5\right )^3 \left (3 e^x x^2-5 e^5 (x-1) x^2-3 e^{2 x} (x-1)+5 e^{x+5} (x-1)-3 e^x \left (e^x-x^2\right ) \log \left (\frac {x^2-e^x}{2 x}\right )\right )}{e^x-x^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -\frac {4}{81} \int \left (\frac {3 e^{-4 x} (x-2) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2+5 e^5\right )^3 x^7}{x^2-e^x}-81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) \left (x+\log \left (\frac {x^2-e^x}{2 x}\right )-1\right ) x^3-27 e^{-x} \log ^2\left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-6 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-5 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x+15 e^5 x+20 e^5 \log \left (\frac {x^2-e^x}{2 x}\right )-15 e^5\right ) x^3-27 e^{-2 x} \log \left (\frac {x^2-e^x}{2 x}\right ) \left (3 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-6 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+15 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-30 e^5 \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-25 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x+25 e^{10} x+50 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right )-25 e^{10}\right ) x^3-3 e^{-3 x} \left (27 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^7-54 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^6+135 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^5-270 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^4+225 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^3-450 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^2-375 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right ) x+125 e^{15} x+500 e^{15} \log \left (\frac {x^2-e^x}{2 x}\right )-125 e^{15}\right ) x^3-e^{-4 x} \left (81 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^9-162 \log ^3\left (\frac {x^2-e^x}{2 x}\right ) x^8+405 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^7-810 e^5 \log ^2\left (\frac {x^2-e^x}{2 x}\right ) x^6+675 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^5-1350 e^{10} \log \left (\frac {x^2-e^x}{2 x}\right ) x^4+375 e^{15} x^3-750 e^{15} x^2-625 e^{20} x+625 e^{20}\right ) x^3\right )dx\)

input

Int[(-1500*E^(15 - 3*x)*x^5 + E^(20 - 4*x)*(-2500*x^5 + 2500*x^6) + E^x*(E 
^(20 - 4*x)*(2500*x^3 - 2500*x^4) + E^(15 - 3*x)*(-1500*x^3 + 1500*x^4)) + 
 (-2700*E^(10 - 2*x)*x^5 + E^(15 - 3*x)*(-6000*x^5 + 4500*x^6) + E^x*(E^(1 
5 - 3*x)*(6000*x^3 - 4500*x^4) + E^(10 - 2*x)*(-2700*x^3 + 2700*x^4)))*Log 
[(-E^x + x^2)/(2*x)] + (-1620*E^(5 - x)*x^5 + E^(10 - 2*x)*(-5400*x^5 + 27 
00*x^6) + E^x*(E^(10 - 2*x)*(5400*x^3 - 2700*x^4) + E^(5 - x)*(-1620*x^3 + 
 1620*x^4)))*Log[(-E^x + x^2)/(2*x)]^2 + (-324*x^5 + E^(5 - x)*(-2160*x^5 
+ 540*x^6) + E^x*(-324*x^3 + 324*x^4 + E^(5 - x)*(2160*x^3 - 540*x^4)))*Lo 
g[(-E^x + x^2)/(2*x)]^3 + (324*E^x*x^3 - 324*x^5)*Log[(-E^x + x^2)/(2*x)]^ 
4)/(81*E^x - 81*x^2),x]
 

output

$Aborted
 

3.20.96.3.1 Defintions of rubi rules used

rule 25

Int[-(Fx_), x_Symbol] :> Simp[Identity[-1]   Int[Fx, x], x]
 

rule 27

Int[(a_)*(Fx_), x_Symbol] :> Simp[a   Int[Fx, x], x] /; FreeQ[a, x] &&  !Ma 
tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
 

rule 7239

Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl 
erIntegrandQ[v, u, x]]
 

rule 7293

Int[u_, x_Symbol] :> With[{v = ExpandIntegrand[u, x]}, Int[v, x] /; SumQ[v] 
]
 

3.20.96.4 Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(117\) vs. \(2(26)=52\).

Time = 11.34 (sec) , antiderivative size = 118, normalized size of antiderivative = 3.69

method	result	size
parallelrisch	\(\frac {625 \,{\mathrm e}^{-4 x +20} x^{4}}{81}+\frac {500 \ln \left (-\frac {{\mathrm e}^{x}-x^{2}}{2 x}\right ) {\mathrm e}^{15-3 x} x^{4}}{27}+\frac {50 \ln \left (-\frac {{\mathrm e}^{x}-x^{2}}{2 x}\right )^{2} {\mathrm e}^{-2 x +10} x^{4}}{3}+\frac {20 \ln \left (-\frac {{\mathrm e}^{x}-x^{2}}{2 x}\right )^{3} {\mathrm e}^{5-x} x^{4}}{3}+\ln \left (-\frac {{\mathrm e}^{x}-x^{2}}{2 x}\right )^{4} x^{4}\)	\(118\)
risch	\(\text {Expression too large to display}\)	\(11288\)

input

int(((324*exp(x)*x^3-324*x^5)*ln(1/2*(-exp(x)+x^2)/x)^4+(((-540*x^4+2160*x 
^3)*exp(5-x)+324*x^4-324*x^3)*exp(x)+(540*x^6-2160*x^5)*exp(5-x)-324*x^5)* 
ln(1/2*(-exp(x)+x^2)/x)^3+(((-2700*x^4+5400*x^3)*exp(5-x)^2+(1620*x^4-1620 
*x^3)*exp(5-x))*exp(x)+(2700*x^6-5400*x^5)*exp(5-x)^2-1620*x^5*exp(5-x))*l 
n(1/2*(-exp(x)+x^2)/x)^2+(((-4500*x^4+6000*x^3)*exp(5-x)^3+(2700*x^4-2700* 
x^3)*exp(5-x)^2)*exp(x)+(4500*x^6-6000*x^5)*exp(5-x)^3-2700*x^5*exp(5-x)^2 
)*ln(1/2*(-exp(x)+x^2)/x)+((-2500*x^4+2500*x^3)*exp(5-x)^4+(1500*x^4-1500* 
x^3)*exp(5-x)^3)*exp(x)+(2500*x^6-2500*x^5)*exp(5-x)^4-1500*x^5*exp(5-x)^3 
)/(81*exp(x)-81*x^2),x,method=_RETURNVERBOSE)
 

output

625/81*exp(5-x)^4*x^4+500/27*ln(-1/2*(exp(x)-x^2)/x)*exp(5-x)^3*x^4+50/3*l 
n(-1/2*(exp(x)-x^2)/x)^2*exp(5-x)^2*x^4+20/3*ln(-1/2*(exp(x)-x^2)/x)^3*exp 
(5-x)*x^4+ln(-1/2*(exp(x)-x^2)/x)^4*x^4
 

3.20.96.5 Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 116 vs. \(2 (29) = 58\).

Time = 0.25 (sec) , antiderivative size = 116, normalized size of antiderivative = 3.62 \[ \int \frac {-1500 e^{15-3 x} x^5+e^{20-4 x} \left (-2500 x^5+2500 x^6\right )+e^x \left (e^{20-4 x} \left (2500 x^3-2500 x^4\right )+e^{15-3 x} \left (-1500 x^3+1500 x^4\right )\right )+\left (-2700 e^{10-2 x} x^5+e^{15-3 x} \left (-6000 x^5+4500 x^6\right )+e^x \left (e^{15-3 x} \left (6000 x^3-4500 x^4\right )+e^{10-2 x} \left (-2700 x^3+2700 x^4\right )\right )\right ) \log \left (\frac {-e^x+x^2}{2 x}\right )+\left (-1620 e^{5-x} x^5+e^{10-2 x} \left (-5400 x^5+2700 x^6\right )+e^x \left (e^{10-2 x} \left (5400 x^3-2700 x^4\right )+e^{5-x} \left (-1620 x^3+1620 x^4\right )\right )\right ) \log ^2\left (\frac {-e^x+x^2}{2 x}\right )+\left (-324 x^5+e^{5-x} \left (-2160 x^5+540 x^6\right )+e^x \left (-324 x^3+324 x^4+e^{5-x} \left (2160 x^3-540 x^4\right )\right )\right ) \log ^3\left (\frac {-e^x+x^2}{2 x}\right )+\left (324 e^x x^3-324 x^5\right ) \log ^4\left (\frac {-e^x+x^2}{2 x}\right )}{81 e^x-81 x^2} \, dx=\frac {1}{81} \, {\left (81 \, x^{4} e^{\left (4 \, x\right )} \log \left (\frac {x^{2} - e^{x}}{2 \, x}\right )^{4} + 540 \, x^{4} e^{\left (3 \, x + 5\right )} \log \left (\frac {x^{2} - e^{x}}{2 \, x}\right )^{3} + 1350 \, x^{4} e^{\left (2 \, x + 10\right )} \log \left (\frac {x^{2} - e^{x}}{2 \, x}\right )^{2} + 1500 \, x^{4} e^{\left (x + 15\right )} \log \left (\frac {x^{2} - e^{x}}{2 \, x}\right ) + 625 \, x^{4} e^{20}\right )} e^{\left (-4 \, x\right )} \]

input

integrate(((324*exp(x)*x^3-324*x^5)*log(1/2*(-exp(x)+x^2)/x)^4+(((-540*x^4 
+2160*x^3)*exp(5-x)+324*x^4-324*x^3)*exp(x)+(540*x^6-2160*x^5)*exp(5-x)-32 
4*x^5)*log(1/2*(-exp(x)+x^2)/x)^3+(((-2700*x^4+5400*x^3)*exp(5-x)^2+(1620* 
x^4-1620*x^3)*exp(5-x))*exp(x)+(2700*x^6-5400*x^5)*exp(5-x)^2-1620*x^5*exp 
(5-x))*log(1/2*(-exp(x)+x^2)/x)^2+(((-4500*x^4+6000*x^3)*exp(5-x)^3+(2700* 
x^4-2700*x^3)*exp(5-x)^2)*exp(x)+(4500*x^6-6000*x^5)*exp(5-x)^3-2700*x^5*e 
xp(5-x)^2)*log(1/2*(-exp(x)+x^2)/x)+((-2500*x^4+2500*x^3)*exp(5-x)^4+(1500 
*x^4-1500*x^3)*exp(5-x)^3)*exp(x)+(2500*x^6-2500*x^5)*exp(5-x)^4-1500*x^5* 
exp(5-x)^3)/(81*exp(x)-81*x^2),x, algorithm=\
 

output

1/81*(81*x^4*e^(4*x)*log(1/2*(x^2 - e^x)/x)^4 + 540*x^4*e^(3*x + 5)*log(1/ 
2*(x^2 - e^x)/x)^3 + 1350*x^4*e^(2*x + 10)*log(1/2*(x^2 - e^x)/x)^2 + 1500 
*x^4*e^(x + 15)*log(1/2*(x^2 - e^x)/x) + 625*x^4*e^20)*e^(-4*x)
 

3.20.96.6 Sympy [F(-1)]

Timed out. \[ \int \frac {-1500 e^{15-3 x} x^5+e^{20-4 x} \left (-2500 x^5+2500 x^6\right )+e^x \left (e^{20-4 x} \left (2500 x^3-2500 x^4\right )+e^{15-3 x} \left (-1500 x^3+1500 x^4\right )\right )+\left (-2700 e^{10-2 x} x^5+e^{15-3 x} \left (-6000 x^5+4500 x^6\right )+e^x \left (e^{15-3 x} \left (6000 x^3-4500 x^4\right )+e^{10-2 x} \left (-2700 x^3+2700 x^4\right )\right )\right ) \log \left (\frac {-e^x+x^2}{2 x}\right )+\left (-1620 e^{5-x} x^5+e^{10-2 x} \left (-5400 x^5+2700 x^6\right )+e^x \left (e^{10-2 x} \left (5400 x^3-2700 x^4\right )+e^{5-x} \left (-1620 x^3+1620 x^4\right )\right )\right ) \log ^2\left (\frac {-e^x+x^2}{2 x}\right )+\left (-324 x^5+e^{5-x} \left (-2160 x^5+540 x^6\right )+e^x \left (-324 x^3+324 x^4+e^{5-x} \left (2160 x^3-540 x^4\right )\right )\right ) \log ^3\left (\frac {-e^x+x^2}{2 x}\right )+\left (324 e^x x^3-324 x^5\right ) \log ^4\left (\frac {-e^x+x^2}{2 x}\right )}{81 e^x-81 x^2} \, dx=\text {Timed out} \]

input

integrate(((324*exp(x)*x**3-324*x**5)*ln(1/2*(-exp(x)+x**2)/x)**4+(((-540* 
x**4+2160*x**3)*exp(5-x)+324*x**4-324*x**3)*exp(x)+(540*x**6-2160*x**5)*ex 
p(5-x)-324*x**5)*ln(1/2*(-exp(x)+x**2)/x)**3+(((-2700*x**4+5400*x**3)*exp( 
5-x)**2+(1620*x**4-1620*x**3)*exp(5-x))*exp(x)+(2700*x**6-5400*x**5)*exp(5 
-x)**2-1620*x**5*exp(5-x))*ln(1/2*(-exp(x)+x**2)/x)**2+(((-4500*x**4+6000* 
x**3)*exp(5-x)**3+(2700*x**4-2700*x**3)*exp(5-x)**2)*exp(x)+(4500*x**6-600 
0*x**5)*exp(5-x)**3-2700*x**5*exp(5-x)**2)*ln(1/2*(-exp(x)+x**2)/x)+((-250 
0*x**4+2500*x**3)*exp(5-x)**4+(1500*x**4-1500*x**3)*exp(5-x)**3)*exp(x)+(2 
500*x**6-2500*x**5)*exp(5-x)**4-1500*x**5*exp(5-x)**3)/(81*exp(x)-81*x**2) 
,x)
 

output

Timed out
 

3.20.96.7 Maxima [F(-1)]

Timed out. \[ \int \frac {-1500 e^{15-3 x} x^5+e^{20-4 x} \left (-2500 x^5+2500 x^6\right )+e^x \left (e^{20-4 x} \left (2500 x^3-2500 x^4\right )+e^{15-3 x} \left (-1500 x^3+1500 x^4\right )\right )+\left (-2700 e^{10-2 x} x^5+e^{15-3 x} \left (-6000 x^5+4500 x^6\right )+e^x \left (e^{15-3 x} \left (6000 x^3-4500 x^4\right )+e^{10-2 x} \left (-2700 x^3+2700 x^4\right )\right )\right ) \log \left (\frac {-e^x+x^2}{2 x}\right )+\left (-1620 e^{5-x} x^5+e^{10-2 x} \left (-5400 x^5+2700 x^6\right )+e^x \left (e^{10-2 x} \left (5400 x^3-2700 x^4\right )+e^{5-x} \left (-1620 x^3+1620 x^4\right )\right )\right ) \log ^2\left (\frac {-e^x+x^2}{2 x}\right )+\left (-324 x^5+e^{5-x} \left (-2160 x^5+540 x^6\right )+e^x \left (-324 x^3+324 x^4+e^{5-x} \left (2160 x^3-540 x^4\right )\right )\right ) \log ^3\left (\frac {-e^x+x^2}{2 x}\right )+\left (324 e^x x^3-324 x^5\right ) \log ^4\left (\frac {-e^x+x^2}{2 x}\right )}{81 e^x-81 x^2} \, dx=\text {Timed out} \]

input

integrate(((324*exp(x)*x^3-324*x^5)*log(1/2*(-exp(x)+x^2)/x)^4+(((-540*x^4 
+2160*x^3)*exp(5-x)+324*x^4-324*x^3)*exp(x)+(540*x^6-2160*x^5)*exp(5-x)-32 
4*x^5)*log(1/2*(-exp(x)+x^2)/x)^3+(((-2700*x^4+5400*x^3)*exp(5-x)^2+(1620* 
x^4-1620*x^3)*exp(5-x))*exp(x)+(2700*x^6-5400*x^5)*exp(5-x)^2-1620*x^5*exp 
(5-x))*log(1/2*(-exp(x)+x^2)/x)^2+(((-4500*x^4+6000*x^3)*exp(5-x)^3+(2700* 
x^4-2700*x^3)*exp(5-x)^2)*exp(x)+(4500*x^6-6000*x^5)*exp(5-x)^3-2700*x^5*e 
xp(5-x)^2)*log(1/2*(-exp(x)+x^2)/x)+((-2500*x^4+2500*x^3)*exp(5-x)^4+(1500 
*x^4-1500*x^3)*exp(5-x)^3)*exp(x)+(2500*x^6-2500*x^5)*exp(5-x)^4-1500*x^5* 
exp(5-x)^3)/(81*exp(x)-81*x^2),x, algorithm=\
 

output

Timed out
 

3.20.96.8 Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 672 vs. \(2 (29) = 58\).

Time = 3.04 (sec) , antiderivative size = 672, normalized size of antiderivative = 21.00 \[ \int \frac {-1500 e^{15-3 x} x^5+e^{20-4 x} \left (-2500 x^5+2500 x^6\right )+e^x \left (e^{20-4 x} \left (2500 x^3-2500 x^4\right )+e^{15-3 x} \left (-1500 x^3+1500 x^4\right )\right )+\left (-2700 e^{10-2 x} x^5+e^{15-3 x} \left (-6000 x^5+4500 x^6\right )+e^x \left (e^{15-3 x} \left (6000 x^3-4500 x^4\right )+e^{10-2 x} \left (-2700 x^3+2700 x^4\right )\right )\right ) \log \left (\frac {-e^x+x^2}{2 x}\right )+\left (-1620 e^{5-x} x^5+e^{10-2 x} \left (-5400 x^5+2700 x^6\right )+e^x \left (e^{10-2 x} \left (5400 x^3-2700 x^4\right )+e^{5-x} \left (-1620 x^3+1620 x^4\right )\right )\right ) \log ^2\left (\frac {-e^x+x^2}{2 x}\right )+\left (-324 x^5+e^{5-x} \left (-2160 x^5+540 x^6\right )+e^x \left (-324 x^3+324 x^4+e^{5-x} \left (2160 x^3-540 x^4\right )\right )\right ) \log ^3\left (\frac {-e^x+x^2}{2 x}\right )+\left (324 e^x x^3-324 x^5\right ) \log ^4\left (\frac {-e^x+x^2}{2 x}\right )}{81 e^x-81 x^2} \, dx =\text {Too large to display} \]

input

integrate(((324*exp(x)*x^3-324*x^5)*log(1/2*(-exp(x)+x^2)/x)^4+(((-540*x^4 
+2160*x^3)*exp(5-x)+324*x^4-324*x^3)*exp(x)+(540*x^6-2160*x^5)*exp(5-x)-32 
4*x^5)*log(1/2*(-exp(x)+x^2)/x)^3+(((-2700*x^4+5400*x^3)*exp(5-x)^2+(1620* 
x^4-1620*x^3)*exp(5-x))*exp(x)+(2700*x^6-5400*x^5)*exp(5-x)^2-1620*x^5*exp 
(5-x))*log(1/2*(-exp(x)+x^2)/x)^2+(((-4500*x^4+6000*x^3)*exp(5-x)^3+(2700* 
x^4-2700*x^3)*exp(5-x)^2)*exp(x)+(4500*x^6-6000*x^5)*exp(5-x)^3-2700*x^5*e 
xp(5-x)^2)*log(1/2*(-exp(x)+x^2)/x)+((-2500*x^4+2500*x^3)*exp(5-x)^4+(1500 
*x^4-1500*x^3)*exp(5-x)^3)*exp(x)+(2500*x^6-2500*x^5)*exp(5-x)^4-1500*x^5* 
exp(5-x)^3)/(81*exp(x)-81*x^2),x, algorithm=\
 

output

1/81*(81*x^4*e^(4*x)*log(2)^4 - 324*x^4*e^(4*x)*log(2)^3*log(x^2 - e^x) + 
486*x^4*e^(4*x)*log(2)^2*log(x^2 - e^x)^2 - 324*x^4*e^(4*x)*log(2)*log(x^2 
 - e^x)^3 + 81*x^4*e^(4*x)*log(x^2 - e^x)^4 + 324*x^4*e^(4*x)*log(2)^3*log 
(x) - 972*x^4*e^(4*x)*log(2)^2*log(x^2 - e^x)*log(x) + 972*x^4*e^(4*x)*log 
(2)*log(x^2 - e^x)^2*log(x) - 324*x^4*e^(4*x)*log(x^2 - e^x)^3*log(x) + 48 
6*x^4*e^(4*x)*log(2)^2*log(x)^2 - 972*x^4*e^(4*x)*log(2)*log(x^2 - e^x)*lo 
g(x)^2 + 486*x^4*e^(4*x)*log(x^2 - e^x)^2*log(x)^2 + 324*x^4*e^(4*x)*log(2 
)*log(x)^3 - 324*x^4*e^(4*x)*log(x^2 - e^x)*log(x)^3 + 81*x^4*e^(4*x)*log( 
x)^4 - 540*x^4*e^(3*x + 5)*log(2)^3 + 1620*x^4*e^(3*x + 5)*log(2)^2*log(x^ 
2 - e^x) - 1620*x^4*e^(3*x + 5)*log(2)*log(x^2 - e^x)^2 + 540*x^4*e^(3*x + 
 5)*log(x^2 - e^x)^3 - 1620*x^4*e^(3*x + 5)*log(2)^2*log(x) + 3240*x^4*e^( 
3*x + 5)*log(2)*log(x^2 - e^x)*log(x) - 1620*x^4*e^(3*x + 5)*log(x^2 - e^x 
)^2*log(x) - 1620*x^4*e^(3*x + 5)*log(2)*log(x)^2 + 1620*x^4*e^(3*x + 5)*l 
og(x^2 - e^x)*log(x)^2 - 540*x^4*e^(3*x + 5)*log(x)^3 + 1350*x^4*e^(2*x + 
10)*log(2)^2 - 2700*x^4*e^(2*x + 10)*log(2)*log(x^2 - e^x) + 1350*x^4*e^(2 
*x + 10)*log(x^2 - e^x)^2 + 2700*x^4*e^(2*x + 10)*log(2)*log(x) - 2700*x^4 
*e^(2*x + 10)*log(x^2 - e^x)*log(x) + 1350*x^4*e^(2*x + 10)*log(x)^2 - 150 
0*x^4*e^(x + 15)*log(2) + 1500*x^4*e^(x + 15)*log(x^2 - e^x) - 1500*x^4*e^ 
(x + 15)*log(x) + 625*x^4*e^20)*e^(-4*x)
 

3.20.96.9 Mupad [F(-1)]

Timed out. \[ \int \frac {-1500 e^{15-3 x} x^5+e^{20-4 x} \left (-2500 x^5+2500 x^6\right )+e^x \left (e^{20-4 x} \left (2500 x^3-2500 x^4\right )+e^{15-3 x} \left (-1500 x^3+1500 x^4\right )\right )+\left (-2700 e^{10-2 x} x^5+e^{15-3 x} \left (-6000 x^5+4500 x^6\right )+e^x \left (e^{15-3 x} \left (6000 x^3-4500 x^4\right )+e^{10-2 x} \left (-2700 x^3+2700 x^4\right )\right )\right ) \log \left (\frac {-e^x+x^2}{2 x}\right )+\left (-1620 e^{5-x} x^5+e^{10-2 x} \left (-5400 x^5+2700 x^6\right )+e^x \left (e^{10-2 x} \left (5400 x^3-2700 x^4\right )+e^{5-x} \left (-1620 x^3+1620 x^4\right )\right )\right ) \log ^2\left (\frac {-e^x+x^2}{2 x}\right )+\left (-324 x^5+e^{5-x} \left (-2160 x^5+540 x^6\right )+e^x \left (-324 x^3+324 x^4+e^{5-x} \left (2160 x^3-540 x^4\right )\right )\right ) \log ^3\left (\frac {-e^x+x^2}{2 x}\right )+\left (324 e^x x^3-324 x^5\right ) \log ^4\left (\frac {-e^x+x^2}{2 x}\right )}{81 e^x-81 x^2} \, dx=\int -\frac {{\mathrm {e}}^x\,\left ({\mathrm {e}}^{15-3\,x}\,\left (1500\,x^3-1500\,x^4\right )-{\mathrm {e}}^{20-4\,x}\,\left (2500\,x^3-2500\,x^4\right )\right )+{\ln \left (-\frac {\frac {{\mathrm {e}}^x}{2}-\frac {x^2}{2}}{x}\right )}^2\,\left ({\mathrm {e}}^x\,\left ({\mathrm {e}}^{5-x}\,\left (1620\,x^3-1620\,x^4\right )-{\mathrm {e}}^{10-2\,x}\,\left (5400\,x^3-2700\,x^4\right )\right )+{\mathrm {e}}^{10-2\,x}\,\left (5400\,x^5-2700\,x^6\right )+1620\,x^5\,{\mathrm {e}}^{5-x}\right )+{\ln \left (-\frac {\frac {{\mathrm {e}}^x}{2}-\frac {x^2}{2}}{x}\right )}^3\,\left ({\mathrm {e}}^{5-x}\,\left (2160\,x^5-540\,x^6\right )-{\mathrm {e}}^x\,\left ({\mathrm {e}}^{5-x}\,\left (2160\,x^3-540\,x^4\right )-324\,x^3+324\,x^4\right )+324\,x^5\right )+{\mathrm {e}}^{20-4\,x}\,\left (2500\,x^5-2500\,x^6\right )+1500\,x^5\,{\mathrm {e}}^{15-3\,x}-{\ln \left (-\frac {\frac {{\mathrm {e}}^x}{2}-\frac {x^2}{2}}{x}\right )}^4\,\left (324\,x^3\,{\mathrm {e}}^x-324\,x^5\right )+\ln \left (-\frac {\frac {{\mathrm {e}}^x}{2}-\frac {x^2}{2}}{x}\right )\,\left ({\mathrm {e}}^x\,\left ({\mathrm {e}}^{10-2\,x}\,\left (2700\,x^3-2700\,x^4\right )-{\mathrm {e}}^{15-3\,x}\,\left (6000\,x^3-4500\,x^4\right )\right )+{\mathrm {e}}^{15-3\,x}\,\left (6000\,x^5-4500\,x^6\right )+2700\,x^5\,{\mathrm {e}}^{10-2\,x}\right )}{81\,{\mathrm {e}}^x-81\,x^2} \,d x \]

input

int(-(exp(x)*(exp(15 - 3*x)*(1500*x^3 - 1500*x^4) - exp(20 - 4*x)*(2500*x^ 
3 - 2500*x^4)) + log(-(exp(x)/2 - x^2/2)/x)^2*(exp(x)*(exp(5 - x)*(1620*x^ 
3 - 1620*x^4) - exp(10 - 2*x)*(5400*x^3 - 2700*x^4)) + exp(10 - 2*x)*(5400 
*x^5 - 2700*x^6) + 1620*x^5*exp(5 - x)) + log(-(exp(x)/2 - x^2/2)/x)^3*(ex 
p(5 - x)*(2160*x^5 - 540*x^6) - exp(x)*(exp(5 - x)*(2160*x^3 - 540*x^4) - 
324*x^3 + 324*x^4) + 324*x^5) + exp(20 - 4*x)*(2500*x^5 - 2500*x^6) + 1500 
*x^5*exp(15 - 3*x) - log(-(exp(x)/2 - x^2/2)/x)^4*(324*x^3*exp(x) - 324*x^ 
5) + log(-(exp(x)/2 - x^2/2)/x)*(exp(x)*(exp(10 - 2*x)*(2700*x^3 - 2700*x^ 
4) - exp(15 - 3*x)*(6000*x^3 - 4500*x^4)) + exp(15 - 3*x)*(6000*x^5 - 4500 
*x^6) + 2700*x^5*exp(10 - 2*x)))/(81*exp(x) - 81*x^2),x)
 

output

int(-(exp(x)*(exp(15 - 3*x)*(1500*x^3 - 1500*x^4) - exp(20 - 4*x)*(2500*x^ 
3 - 2500*x^4)) + log(-(exp(x)/2 - x^2/2)/x)^2*(exp(x)*(exp(5 - x)*(1620*x^ 
3 - 1620*x^4) - exp(10 - 2*x)*(5400*x^3 - 2700*x^4)) + exp(10 - 2*x)*(5400 
*x^5 - 2700*x^6) + 1620*x^5*exp(5 - x)) + log(-(exp(x)/2 - x^2/2)/x)^3*(ex 
p(5 - x)*(2160*x^5 - 540*x^6) - exp(x)*(exp(5 - x)*(2160*x^3 - 540*x^4) - 
324*x^3 + 324*x^4) + 324*x^5) + exp(20 - 4*x)*(2500*x^5 - 2500*x^6) + 1500 
*x^5*exp(15 - 3*x) - log(-(exp(x)/2 - x^2/2)/x)^4*(324*x^3*exp(x) - 324*x^ 
5) + log(-(exp(x)/2 - x^2/2)/x)*(exp(x)*(exp(10 - 2*x)*(2700*x^3 - 2700*x^ 
4) - exp(15 - 3*x)*(6000*x^3 - 4500*x^4)) + exp(15 - 3*x)*(6000*x^5 - 4500 
*x^6) + 2700*x^5*exp(10 - 2*x)))/(81*exp(x) - 81*x^2), x)