\(\int \frac {490 x^2+35630 x^3+629520 x^4-665640 x^5+e^{2 x} (-56-4072 x-262148 x^2+266256 x^3)+(140 x^3+5020 x^4-5160 x^5+e^{2 x} (-16 x-2048 x^2+2064 x^3)) \log (1-x)+(10 x^4-10 x^5+e^{2 x} (-4 x^2+4 x^3)) \log ^2(1-x)}{e^{2 x} (-49 x^2-3563 x^3-62952 x^4+66564 x^5)+e^{2 x} (-14 x^3-502 x^4+516 x^5) \log (1-x)+e^{2 x} (-x^4+x^5) \log ^2(1-x)} \, dx\) [876]

Optimal result

Integrand size = 204, antiderivative size = 31 \[ \int \frac {490 x^2+35630 x^3+629520 x^4-665640 x^5+e^{2 x} \left (-56-4072 x-262148 x^2+266256 x^3\right )+\left (140 x^3+5020 x^4-5160 x^5+e^{2 x} \left (-16 x-2048 x^2+2064 x^3\right )\right ) \log (1-x)+\left (10 x^4-10 x^5+e^{2 x} \left (-4 x^2+4 x^3\right )\right ) \log ^2(1-x)}{e^{2 x} \left (-49 x^2-3563 x^3-62952 x^4+66564 x^5\right )+e^{2 x} \left (-14 x^3-502 x^4+516 x^5\right ) \log (1-x)+e^{2 x} \left (-x^4+x^5\right ) \log ^2(1-x)} \, dx=5 e^{-2 x}-\frac {4}{x+\frac {5}{258+\frac {2}{x}+\log (1-x)}} \] Output:

5/exp(x)^2-4/(x+5/(2/x+ln(1-x)+258))
                                                                                    
                                                                                    
 

Mathematica [A] (verified)

Time = 0.09 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.19 \[ \int \frac {490 x^2+35630 x^3+629520 x^4-665640 x^5+e^{2 x} \left (-56-4072 x-262148 x^2+266256 x^3\right )+\left (140 x^3+5020 x^4-5160 x^5+e^{2 x} \left (-16 x-2048 x^2+2064 x^3\right )\right ) \log (1-x)+\left (10 x^4-10 x^5+e^{2 x} \left (-4 x^2+4 x^3\right )\right ) \log ^2(1-x)}{e^{2 x} \left (-49 x^2-3563 x^3-62952 x^4+66564 x^5\right )+e^{2 x} \left (-14 x^3-502 x^4+516 x^5\right ) \log (1-x)+e^{2 x} \left (-x^4+x^5\right ) \log ^2(1-x)} \, dx=2 \left (\frac {5 e^{-2 x}}{2}-\frac {2}{x}+\frac {10}{x (7+258 x+x \log (1-x))}\right ) \] Input:

Integrate[(490*x^2 + 35630*x^3 + 629520*x^4 - 665640*x^5 + E^(2*x)*(-56 - 
4072*x - 262148*x^2 + 266256*x^3) + (140*x^3 + 5020*x^4 - 5160*x^5 + E^(2* 
x)*(-16*x - 2048*x^2 + 2064*x^3))*Log[1 - x] + (10*x^4 - 10*x^5 + E^(2*x)* 
(-4*x^2 + 4*x^3))*Log[1 - x]^2)/(E^(2*x)*(-49*x^2 - 3563*x^3 - 62952*x^4 + 
 66564*x^5) + E^(2*x)*(-14*x^3 - 502*x^4 + 516*x^5)*Log[1 - x] + E^(2*x)*( 
-x^4 + x^5)*Log[1 - x]^2),x]
 

Output:

2*(5/(2*E^(2*x)) - 2/x + 10/(x*(7 + 258*x + x*Log[1 - x])))
 

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.

\(\displaystyle \int \frac {-665640 x^5+629520 x^4+35630 x^3+490 x^2+e^{2 x} \left (266256 x^3-262148 x^2-4072 x-56\right )+\left (-10 x^5+10 x^4+e^{2 x} \left (4 x^3-4 x^2\right )\right ) \log ^2(1-x)+\left (-5160 x^5+5020 x^4+140 x^3+e^{2 x} \left (2064 x^3-2048 x^2-16 x\right )\right ) \log (1-x)}{e^{2 x} \left (x^5-x^4\right ) \log ^2(1-x)+e^{2 x} \left (516 x^5-502 x^4-14 x^3\right ) \log (1-x)+e^{2 x} \left (66564 x^5-62952 x^4-3563 x^3-49 x^2\right )} \, dx\)

\(\Big \downarrow \) 7292

\(\displaystyle \int \frac {e^{-2 x} \left (665640 x^5-629520 x^4-35630 x^3-490 x^2-e^{2 x} \left (266256 x^3-262148 x^2-4072 x-56\right )-\left (-10 x^5+10 x^4+e^{2 x} \left (4 x^3-4 x^2\right )\right ) \log ^2(1-x)-\left (-5160 x^5+5020 x^4+140 x^3+e^{2 x} \left (2064 x^3-2048 x^2-16 x\right )\right ) \log (1-x)\right )}{(1-x) x^2 (258 x+x \log (1-x)+7)^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {10 e^{-2 x} x^3 \log ^2(1-x)}{(x-1) (258 x+x \log (1-x)+7)^2}-\frac {5160 e^{-2 x} x^3 \log (1-x)}{(x-1) (258 x+x \log (1-x)+7)^2}-\frac {665640 e^{-2 x} x^3}{(x-1) (258 x+x \log (1-x)+7)^2}+\frac {10 e^{-2 x} x^2 \log ^2(1-x)}{(x-1) (258 x+x \log (1-x)+7)^2}+\frac {5020 e^{-2 x} x^2 \log (1-x)}{(x-1) (258 x+x \log (1-x)+7)^2}+\frac {629520 e^{-2 x} x^2}{(x-1) (258 x+x \log (1-x)+7)^2}+\frac {4 \left (66564 x^3+x^3 \log ^2(1-x)+516 x^3 \log (1-x)-65537 x^2-x^2 \log ^2(1-x)-512 x^2 \log (1-x)-1018 x-4 x \log (1-x)-14\right )}{(x-1) x^2 (258 x+x \log (1-x)+7)^2}+\frac {140 e^{-2 x} x \log (1-x)}{(x-1) (258 x+x \log (1-x)+7)^2}+\frac {35630 e^{-2 x} x}{(x-1) (258 x+x \log (1-x)+7)^2}+\frac {490 e^{-2 x}}{(x-1) (258 x+x \log (1-x)+7)^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {2 e^{-2 x} \left (5 (x-1) x^2 (258 x+7)^2-(x-1) x^2 \left (2 e^{2 x}-5 x^2\right ) \log ^2(1-x)-2 (x-1) x \left (e^{2 x} (516 x+4)-5 x^2 (258 x+7)\right ) \log (1-x)-2 e^{2 x} \left (66564 x^3-65537 x^2-1018 x-14\right )\right )}{(1-x) x^2 (258 x+x \log (1-x)+7)^2}dx\)

\(\Big \downarrow \) 27

\(\displaystyle 2 \int -\frac {e^{-2 x} \left (5 (1-x) x^2 (258 x+7)^2-(1-x) x^2 \left (2 e^{2 x}-5 x^2\right ) \log ^2(1-x)-2 e^{2 x} \left (-66564 x^3+65537 x^2+1018 x+14\right )-2 (1-x) x \left (4 e^{2 x} (129 x+1)-5 x^2 (258 x+7)\right ) \log (1-x)\right )}{(1-x) x^2 (\log (1-x) x+258 x+7)^2}dx\)

\(\Big \downarrow \) 25

\(\displaystyle -2 \int \frac {e^{-2 x} \left (5 (1-x) x^2 (258 x+7)^2-(1-x) x^2 \left (2 e^{2 x}-5 x^2\right ) \log ^2(1-x)-2 e^{2 x} \left (-66564 x^3+65537 x^2+1018 x+14\right )-2 (1-x) x \left (4 e^{2 x} (129 x+1)-5 x^2 (258 x+7)\right ) \log (1-x)\right )}{(1-x) x^2 (\log (1-x) x+258 x+7)^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -2 \int \left (5 e^{-2 x}-\frac {2 \left (\log ^2(1-x) x^3+516 \log (1-x) x^3+66564 x^3-\log ^2(1-x) x^2-512 \log (1-x) x^2-65537 x^2-4 \log (1-x) x-1018 x-14\right )}{(x-1) x^2 (\log (1-x) x+258 x+7)^2}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle -2 \left (-70 \int \frac {1}{x^2 (\log (1-x) x+258 x+7)^2}dx+20 \int \frac {1}{x^2 (\log (1-x) x+258 x+7)}dx+10 \int \frac {1}{(x-1) (\log (1-x) x+258 x+7)^2}dx-\frac {5 e^{-2 x}}{2}+\frac {2}{x}\right )\)

Input:

Int[(490*x^2 + 35630*x^3 + 629520*x^4 - 665640*x^5 + E^(2*x)*(-56 - 4072*x 
 - 262148*x^2 + 266256*x^3) + (140*x^3 + 5020*x^4 - 5160*x^5 + E^(2*x)*(-1 
6*x - 2048*x^2 + 2064*x^3))*Log[1 - x] + (10*x^4 - 10*x^5 + E^(2*x)*(-4*x^ 
2 + 4*x^3))*Log[1 - x]^2)/(E^(2*x)*(-49*x^2 - 3563*x^3 - 62952*x^4 + 66564 
*x^5) + E^(2*x)*(-14*x^3 - 502*x^4 + 516*x^5)*Log[1 - x] + E^(2*x)*(-x^4 + 
 x^5)*Log[1 - x]^2),x]
 

Output:

$Aborted
 

Maple [A] (verified)

Time = 0.35 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.29

\[\frac {\left (-4 \,{\mathrm e}^{2 x}+5 x \right ) {\mathrm e}^{-2 x}}{x}+\frac {20}{x \left (x \ln \left (1-x \right )+258 x +7\right )}\]

Input:

int((((4*x^3-4*x^2)*exp(x)^2-10*x^5+10*x^4)*ln(1-x)^2+((2064*x^3-2048*x^2- 
16*x)*exp(x)^2-5160*x^5+5020*x^4+140*x^3)*ln(1-x)+(266256*x^3-262148*x^2-4 
072*x-56)*exp(x)^2-665640*x^5+629520*x^4+35630*x^3+490*x^2)/((x^5-x^4)*exp 
(x)^2*ln(1-x)^2+(516*x^5-502*x^4-14*x^3)*exp(x)^2*ln(1-x)+(66564*x^5-62952 
*x^4-3563*x^3-49*x^2)*exp(x)^2),x)
 

Output:

(-4*exp(2*x)+5*x)/x*exp(-2*x)+20/x/(x*ln(1-x)+258*x+7)
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 72 vs. \(2 (30) = 60\).

Time = 0.08 (sec) , antiderivative size = 72, normalized size of antiderivative = 2.32 \[ \int \frac {490 x^2+35630 x^3+629520 x^4-665640 x^5+e^{2 x} \left (-56-4072 x-262148 x^2+266256 x^3\right )+\left (140 x^3+5020 x^4-5160 x^5+e^{2 x} \left (-16 x-2048 x^2+2064 x^3\right )\right ) \log (1-x)+\left (10 x^4-10 x^5+e^{2 x} \left (-4 x^2+4 x^3\right )\right ) \log ^2(1-x)}{e^{2 x} \left (-49 x^2-3563 x^3-62952 x^4+66564 x^5\right )+e^{2 x} \left (-14 x^3-502 x^4+516 x^5\right ) \log (1-x)+e^{2 x} \left (-x^4+x^5\right ) \log ^2(1-x)} \, dx=\frac {1290 \, x^{2} - 8 \, {\left (129 \, x + 1\right )} e^{\left (2 \, x\right )} + {\left (5 \, x^{2} - 4 \, x e^{\left (2 \, x\right )}\right )} \log \left (-x + 1\right ) + 35 \, x}{x^{2} e^{\left (2 \, x\right )} \log \left (-x + 1\right ) + {\left (258 \, x^{2} + 7 \, x\right )} e^{\left (2 \, x\right )}} \] Input:

integrate((((4*x^3-4*x^2)*exp(x)^2-10*x^5+10*x^4)*log(1-x)^2+((2064*x^3-20 
48*x^2-16*x)*exp(x)^2-5160*x^5+5020*x^4+140*x^3)*log(1-x)+(266256*x^3-2621 
48*x^2-4072*x-56)*exp(x)^2-665640*x^5+629520*x^4+35630*x^3+490*x^2)/((x^5- 
x^4)*exp(x)^2*log(1-x)^2+(516*x^5-502*x^4-14*x^3)*exp(x)^2*log(1-x)+(66564 
*x^5-62952*x^4-3563*x^3-49*x^2)*exp(x)^2),x, algorithm="fricas")
 

Output:

(1290*x^2 - 8*(129*x + 1)*e^(2*x) + (5*x^2 - 4*x*e^(2*x))*log(-x + 1) + 35 
*x)/(x^2*e^(2*x)*log(-x + 1) + (258*x^2 + 7*x)*e^(2*x))
 

Sympy [A] (verification not implemented)

Time = 0.22 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.87 \[ \int \frac {490 x^2+35630 x^3+629520 x^4-665640 x^5+e^{2 x} \left (-56-4072 x-262148 x^2+266256 x^3\right )+\left (140 x^3+5020 x^4-5160 x^5+e^{2 x} \left (-16 x-2048 x^2+2064 x^3\right )\right ) \log (1-x)+\left (10 x^4-10 x^5+e^{2 x} \left (-4 x^2+4 x^3\right )\right ) \log ^2(1-x)}{e^{2 x} \left (-49 x^2-3563 x^3-62952 x^4+66564 x^5\right )+e^{2 x} \left (-14 x^3-502 x^4+516 x^5\right ) \log (1-x)+e^{2 x} \left (-x^4+x^5\right ) \log ^2(1-x)} \, dx=5 e^{- 2 x} + \frac {20}{x^{2} \log {\left (1 - x \right )} + 258 x^{2} + 7 x} - \frac {4}{x} \] Input:

integrate((((4*x**3-4*x**2)*exp(x)**2-10*x**5+10*x**4)*ln(1-x)**2+((2064*x 
**3-2048*x**2-16*x)*exp(x)**2-5160*x**5+5020*x**4+140*x**3)*ln(1-x)+(26625 
6*x**3-262148*x**2-4072*x-56)*exp(x)**2-665640*x**5+629520*x**4+35630*x**3 
+490*x**2)/((x**5-x**4)*exp(x)**2*ln(1-x)**2+(516*x**5-502*x**4-14*x**3)*e 
xp(x)**2*ln(1-x)+(66564*x**5-62952*x**4-3563*x**3-49*x**2)*exp(x)**2),x)
 

Output:

5*exp(-2*x) + 20/(x**2*log(1 - x) + 258*x**2 + 7*x) - 4/x
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 72 vs. \(2 (30) = 60\).

Time = 0.14 (sec) , antiderivative size = 72, normalized size of antiderivative = 2.32 \[ \int \frac {490 x^2+35630 x^3+629520 x^4-665640 x^5+e^{2 x} \left (-56-4072 x-262148 x^2+266256 x^3\right )+\left (140 x^3+5020 x^4-5160 x^5+e^{2 x} \left (-16 x-2048 x^2+2064 x^3\right )\right ) \log (1-x)+\left (10 x^4-10 x^5+e^{2 x} \left (-4 x^2+4 x^3\right )\right ) \log ^2(1-x)}{e^{2 x} \left (-49 x^2-3563 x^3-62952 x^4+66564 x^5\right )+e^{2 x} \left (-14 x^3-502 x^4+516 x^5\right ) \log (1-x)+e^{2 x} \left (-x^4+x^5\right ) \log ^2(1-x)} \, dx=\frac {1290 \, x^{2} - 8 \, {\left (129 \, x + 1\right )} e^{\left (2 \, x\right )} + {\left (5 \, x^{2} - 4 \, x e^{\left (2 \, x\right )}\right )} \log \left (-x + 1\right ) + 35 \, x}{x^{2} e^{\left (2 \, x\right )} \log \left (-x + 1\right ) + {\left (258 \, x^{2} + 7 \, x\right )} e^{\left (2 \, x\right )}} \] Input:

integrate((((4*x^3-4*x^2)*exp(x)^2-10*x^5+10*x^4)*log(1-x)^2+((2064*x^3-20 
48*x^2-16*x)*exp(x)^2-5160*x^5+5020*x^4+140*x^3)*log(1-x)+(266256*x^3-2621 
48*x^2-4072*x-56)*exp(x)^2-665640*x^5+629520*x^4+35630*x^3+490*x^2)/((x^5- 
x^4)*exp(x)^2*log(1-x)^2+(516*x^5-502*x^4-14*x^3)*exp(x)^2*log(1-x)+(66564 
*x^5-62952*x^4-3563*x^3-49*x^2)*exp(x)^2),x, algorithm="maxima")
 

Output:

(1290*x^2 - 8*(129*x + 1)*e^(2*x) + (5*x^2 - 4*x*e^(2*x))*log(-x + 1) + 35 
*x)/(x^2*e^(2*x)*log(-x + 1) + (258*x^2 + 7*x)*e^(2*x))
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 177 vs. \(2 (30) = 60\).

Time = 0.22 (sec) , antiderivative size = 177, normalized size of antiderivative = 5.71 \[ \int \frac {490 x^2+35630 x^3+629520 x^4-665640 x^5+e^{2 x} \left (-56-4072 x-262148 x^2+266256 x^3\right )+\left (140 x^3+5020 x^4-5160 x^5+e^{2 x} \left (-16 x-2048 x^2+2064 x^3\right )\right ) \log (1-x)+\left (10 x^4-10 x^5+e^{2 x} \left (-4 x^2+4 x^3\right )\right ) \log ^2(1-x)}{e^{2 x} \left (-49 x^2-3563 x^3-62952 x^4+66564 x^5\right )+e^{2 x} \left (-14 x^3-502 x^4+516 x^5\right ) \log (1-x)+e^{2 x} \left (-x^4+x^5\right ) \log ^2(1-x)} \, dx=\frac {5 \, {\left (x - 1\right )}^{2} e^{\left (-2 \, x + 2\right )} \log \left (-x + 1\right ) + 1290 \, {\left (x - 1\right )}^{2} e^{\left (-2 \, x + 2\right )} - 4 \, {\left (x - 1\right )} e^{2} \log \left (-x + 1\right ) + 10 \, {\left (x - 1\right )} e^{\left (-2 \, x + 2\right )} \log \left (-x + 1\right ) - 1032 \, {\left (x - 1\right )} e^{2} + 2615 \, {\left (x - 1\right )} e^{\left (-2 \, x + 2\right )} - 4 \, e^{2} \log \left (-x + 1\right ) + 5 \, e^{\left (-2 \, x + 2\right )} \log \left (-x + 1\right ) - 1040 \, e^{2} + 1325 \, e^{\left (-2 \, x + 2\right )}}{{\left (x - 1\right )}^{2} e^{2} \log \left (-x + 1\right ) + 258 \, {\left (x - 1\right )}^{2} e^{2} + 2 \, {\left (x - 1\right )} e^{2} \log \left (-x + 1\right ) + 523 \, {\left (x - 1\right )} e^{2} + e^{2} \log \left (-x + 1\right ) + 265 \, e^{2}} \] Input:

integrate((((4*x^3-4*x^2)*exp(x)^2-10*x^5+10*x^4)*log(1-x)^2+((2064*x^3-20 
48*x^2-16*x)*exp(x)^2-5160*x^5+5020*x^4+140*x^3)*log(1-x)+(266256*x^3-2621 
48*x^2-4072*x-56)*exp(x)^2-665640*x^5+629520*x^4+35630*x^3+490*x^2)/((x^5- 
x^4)*exp(x)^2*log(1-x)^2+(516*x^5-502*x^4-14*x^3)*exp(x)^2*log(1-x)+(66564 
*x^5-62952*x^4-3563*x^3-49*x^2)*exp(x)^2),x, algorithm="giac")
 

Output:

(5*(x - 1)^2*e^(-2*x + 2)*log(-x + 1) + 1290*(x - 1)^2*e^(-2*x + 2) - 4*(x 
 - 1)*e^2*log(-x + 1) + 10*(x - 1)*e^(-2*x + 2)*log(-x + 1) - 1032*(x - 1) 
*e^2 + 2615*(x - 1)*e^(-2*x + 2) - 4*e^2*log(-x + 1) + 5*e^(-2*x + 2)*log( 
-x + 1) - 1040*e^2 + 1325*e^(-2*x + 2))/((x - 1)^2*e^2*log(-x + 1) + 258*( 
x - 1)^2*e^2 + 2*(x - 1)*e^2*log(-x + 1) + 523*(x - 1)*e^2 + e^2*log(-x + 
1) + 265*e^2)
 

Mupad [B] (verification not implemented)

Time = 0.69 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.03 \[ \int \frac {490 x^2+35630 x^3+629520 x^4-665640 x^5+e^{2 x} \left (-56-4072 x-262148 x^2+266256 x^3\right )+\left (140 x^3+5020 x^4-5160 x^5+e^{2 x} \left (-16 x-2048 x^2+2064 x^3\right )\right ) \log (1-x)+\left (10 x^4-10 x^5+e^{2 x} \left (-4 x^2+4 x^3\right )\right ) \log ^2(1-x)}{e^{2 x} \left (-49 x^2-3563 x^3-62952 x^4+66564 x^5\right )+e^{2 x} \left (-14 x^3-502 x^4+516 x^5\right ) \log (1-x)+e^{2 x} \left (-x^4+x^5\right ) \log ^2(1-x)} \, dx=5\,{\mathrm {e}}^{-2\,x}+\frac {20}{x\,\left (258\,x+x\,\ln \left (1-x\right )+7\right )}-\frac {4}{x} \] Input:

int((exp(2*x)*(4072*x + 262148*x^2 - 266256*x^3 + 56) + log(1 - x)*(exp(2* 
x)*(16*x + 2048*x^2 - 2064*x^3) - 140*x^3 - 5020*x^4 + 5160*x^5) + log(1 - 
 x)^2*(exp(2*x)*(4*x^2 - 4*x^3) - 10*x^4 + 10*x^5) - 490*x^2 - 35630*x^3 - 
 629520*x^4 + 665640*x^5)/(exp(2*x)*(49*x^2 + 3563*x^3 + 62952*x^4 - 66564 
*x^5) + exp(2*x)*log(1 - x)^2*(x^4 - x^5) + exp(2*x)*log(1 - x)*(14*x^3 + 
502*x^4 - 516*x^5)),x)
 

Output:

5*exp(-2*x) + 20/(x*(258*x + x*log(1 - x) + 7)) - 4/x
 

Reduce [B] (verification not implemented)

Time = 0.34 (sec) , antiderivative size = 144, normalized size of antiderivative = 4.65 \[ \int \frac {490 x^2+35630 x^3+629520 x^4-665640 x^5+e^{2 x} \left (-56-4072 x-262148 x^2+266256 x^3\right )+\left (140 x^3+5020 x^4-5160 x^5+e^{2 x} \left (-16 x-2048 x^2+2064 x^3\right )\right ) \log (1-x)+\left (10 x^4-10 x^5+e^{2 x} \left (-4 x^2+4 x^3\right )\right ) \log ^2(1-x)}{e^{2 x} \left (-49 x^2-3563 x^3-62952 x^4+66564 x^5\right )+e^{2 x} \left (-14 x^3-502 x^4+516 x^5\right ) \log (1-x)+e^{2 x} \left (-x^4+x^5\right ) \log ^2(1-x)} \, dx=\frac {4 e^{2 x} \mathrm {log}\left (1-x \right )^{2} x^{2}-4 e^{2 x} \mathrm {log}\left (1-x \right ) \mathrm {log}\left (x -1\right ) x^{2}+2064 e^{2 x} \mathrm {log}\left (1-x \right ) x^{2}-1032 e^{2 x} \mathrm {log}\left (x -1\right ) x^{2}-28 e^{2 x} \mathrm {log}\left (x -1\right ) x +266256 e^{2 x} x^{2}-56 e^{2 x}+35 \,\mathrm {log}\left (1-x \right ) x^{2}+9030 x^{2}+245 x}{7 e^{2 x} x \left (\mathrm {log}\left (1-x \right ) x +258 x +7\right )} \] Input:

int((((4*x^3-4*x^2)*exp(x)^2-10*x^5+10*x^4)*log(1-x)^2+((2064*x^3-2048*x^2 
-16*x)*exp(x)^2-5160*x^5+5020*x^4+140*x^3)*log(1-x)+(266256*x^3-262148*x^2 
-4072*x-56)*exp(x)^2-665640*x^5+629520*x^4+35630*x^3+490*x^2)/((x^5-x^4)*e 
xp(x)^2*log(1-x)^2+(516*x^5-502*x^4-14*x^3)*exp(x)^2*log(1-x)+(66564*x^5-6 
2952*x^4-3563*x^3-49*x^2)*exp(x)^2),x)
 

Output:

(4*e**(2*x)*log( - x + 1)**2*x**2 - 4*e**(2*x)*log( - x + 1)*log(x - 1)*x* 
*2 + 2064*e**(2*x)*log( - x + 1)*x**2 - 1032*e**(2*x)*log(x - 1)*x**2 - 28 
*e**(2*x)*log(x - 1)*x + 266256*e**(2*x)*x**2 - 56*e**(2*x) + 35*log( - x 
+ 1)*x**2 + 9030*x**2 + 245*x)/(7*e**(2*x)*x*(log( - x + 1)*x + 258*x + 7) 
)