Integrand size = 181, antiderivative size = 31 \[ \int \frac {7 x-2 x^2-3 x^3+e^{20} \left (5 x-x^2-2 x^3\right )+\left (-1+e^{20} (-1+x)+x\right ) \log (1-x)+\left (3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)\right ) \log \left (\frac {-3 x^2-2 e^{20} x^2+\left (x+e^{20} x\right ) \log (1-x)}{1+x+e^{20} (1+x)}\right )}{3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)} \, dx=x \log \left (\frac {x \left (-2 x+\frac {x}{-1-e^{20}}+\log (1-x)\right )}{1+x}\right ) \]
Time = 0.13 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.29 \[ \int \frac {7 x-2 x^2-3 x^3+e^{20} \left (5 x-x^2-2 x^3\right )+\left (-1+e^{20} (-1+x)+x\right ) \log (1-x)+\left (3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)\right ) \log \left (\frac {-3 x^2-2 e^{20} x^2+\left (x+e^{20} x\right ) \log (1-x)}{1+x+e^{20} (1+x)}\right )}{3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)} \, dx=x \log \left (\frac {x \left (-\left (\left (3+2 e^{20}\right ) x\right )+\left (1+e^{20}\right ) \log (1-x)\right )}{\left (1+e^{20}\right ) (1+x)}\right ) \]
Integrate[(7*x - 2*x^2 - 3*x^3 + E^20*(5*x - x^2 - 2*x^3) + (-1 + E^20*(-1 + x) + x)*Log[1 - x] + (3*x - 3*x^3 + E^20*(2*x - 2*x^3) + (-1 + x^2 + E^ 20*(-1 + x^2))*Log[1 - x])*Log[(-3*x^2 - 2*E^20*x^2 + (x + E^20*x)*Log[1 - x])/(1 + x + E^20*(1 + x))])/(3*x - 3*x^3 + E^20*(2*x - 2*x^3) + (-1 + x^ 2 + E^20*(-1 + x^2))*Log[1 - x]),x]
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {-3 x^3-2 x^2+e^{20} \left (-2 x^3-x^2+5 x\right )+\left (-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (x^2+e^{20} \left (x^2-1\right )-1\right ) \log (1-x)+3 x\right ) \log \left (\frac {-2 e^{20} x^2-3 x^2+\left (e^{20} x+x\right ) \log (1-x)}{x+e^{20} (x+1)+1}\right )+7 x+\left (e^{20} (x-1)+x-1\right ) \log (1-x)}{-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (x^2+e^{20} \left (x^2-1\right )-1\right ) \log (1-x)+3 x} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-3 x^3-2 x^2+e^{20} \left (-2 x^3-x^2+5 x\right )+\left (-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (x^2+e^{20} \left (x^2-1\right )-1\right ) \log (1-x)+3 x\right ) \log \left (\frac {-2 e^{20} x^2-3 x^2+\left (e^{20} x+x\right ) \log (1-x)}{x+e^{20} (x+1)+1}\right )+7 x+\left (e^{20} (x-1)+x-1\right ) \log (1-x)}{\left (1-x^2\right ) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}dx\) |
| \(\Big \downarrow \) 7276 |
| \(\displaystyle \int \left (\frac {3 x^3}{(x-1) (x+1) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}+\frac {2 x^2}{(x-1) (x+1) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}+\frac {e^{20} \left (-2 x^2-x+5\right ) x}{(1-x) (x+1) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}+\frac {7 x}{(1-x) (x+1) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}+\log \left (\frac {x \left (\left (1+e^{20}\right ) \log (1-x)-\left (3+2 e^{20}\right ) x\right )}{\left (1+e^{20}\right ) (x+1)}\right )+\frac {\left (-1-e^{20}\right ) \log (1-x)}{(x+1) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\left (3+2 e^{20}\right ) \int \frac {1}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)}dx+e^{20} \int \frac {1}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)}dx+2 \int \frac {1}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)}dx-\left (3+2 e^{20}\right ) \int \frac {1}{(-x-1) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}dx+2 e^{20} \int \frac {1}{(-x-1) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}dx+\frac {9}{2} \int \frac {1}{(-x-1) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}dx-\left (1+e^{20}\right ) \int \frac {1}{(1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}dx+e^{20} \int \frac {1}{(1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}dx+\frac {7}{2} \int \frac {1}{(1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}dx+\frac {5}{2} \int \frac {1}{(x-1) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}dx-\left (3+2 e^{20}\right ) \int \frac {x}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)}dx+2 e^{20} \int \frac {x}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)}dx+3 \int \frac {x}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)}dx+\frac {3}{2} \int \frac {1}{(x+1) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}dx-\left (1+e^{20}\right ) \int \frac {1}{\left (1+e^{20}\right ) \log (1-x)-3 \left (1+\frac {2 e^{20}}{3}\right ) x}dx+x \log \left (-\frac {x \left (\left (3+2 e^{20}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}{\left (1+e^{20}\right ) (x+1)}\right )\) |
Int[(7*x - 2*x^2 - 3*x^3 + E^20*(5*x - x^2 - 2*x^3) + (-1 + E^20*(-1 + x) + x)*Log[1 - x] + (3*x - 3*x^3 + E^20*(2*x - 2*x^3) + (-1 + x^2 + E^20*(-1 + x^2))*Log[1 - x])*Log[(-3*x^2 - 2*E^20*x^2 + (x + E^20*x)*Log[1 - x])/( 1 + x + E^20*(1 + x))])/(3*x - 3*x^3 + E^20*(2*x - 2*x^3) + (-1 + x^2 + E^ 20*(-1 + x^2))*Log[1 - x]),x]
3.26.82.3.1 Defintions of rubi rules used
Int[(u_)/((a_) + (b_.)*(x_)^(n_)), x_Symbol] :> With[{v = RationalFunctionE xpand[u/(a + b*x^n), x]}, Int[v, x] /; SumQ[v]] /; FreeQ[{a, b}, x] && IGtQ [n, 0]
Leaf count of result is larger than twice the leaf count of optimal. \(141\) vs. \(2(30)=60\).
Time = 4.83 (sec) , antiderivative size = 142, normalized size of antiderivative = 4.58
| method | result | size |
| parallelrisch | \(-\frac {-{\mathrm e}^{40} x \ln \left (\frac {\left (x \,{\mathrm e}^{20}+x \right ) \ln \left (1-x \right )-2 x^{2} {\mathrm e}^{20}-3 x^{2}}{x \,{\mathrm e}^{20}+{\mathrm e}^{20}+x +1}\right )-2 \ln \left (\frac {\left (x \,{\mathrm e}^{20}+x \right ) \ln \left (1-x \right )-2 x^{2} {\mathrm e}^{20}-3 x^{2}}{x \,{\mathrm e}^{20}+{\mathrm e}^{20}+x +1}\right ) {\mathrm e}^{20} x -\ln \left (\frac {\left (x \,{\mathrm e}^{20}+x \right ) \ln \left (1-x \right )-2 x^{2} {\mathrm e}^{20}-3 x^{2}}{x \,{\mathrm e}^{20}+{\mathrm e}^{20}+x +1}\right ) x}{\left ({\mathrm e}^{20}+1\right )^{2}}\) | \(142\) |
| risch | \(x \ln \left (\left (x -\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}+\frac {3 x}{2}-\frac {\ln \left (1-x \right )}{2}\right )-\ln \left (1+x \right ) x +x \ln \left (x \right )-\frac {i \pi x {\operatorname {csgn}\left (\frac {i x \left (\left (-x +\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}-\frac {3 x}{2}+\frac {\ln \left (1-x \right )}{2}\right )}{1+x}\right )}^{3}}{2}+\frac {i \pi x \,\operatorname {csgn}\left (i x \right ) {\operatorname {csgn}\left (\frac {i x \left (\left (-x +\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}-\frac {3 x}{2}+\frac {\ln \left (1-x \right )}{2}\right )}{1+x}\right )}^{2}}{2}-\frac {i \pi x \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (\frac {i \left (\left (-x +\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}-\frac {3 x}{2}+\frac {\ln \left (1-x \right )}{2}\right )}{1+x}\right ) \operatorname {csgn}\left (\frac {i x \left (\left (-x +\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}-\frac {3 x}{2}+\frac {\ln \left (1-x \right )}{2}\right )}{1+x}\right )}{2}-\frac {i \pi x \,\operatorname {csgn}\left (i \left (\left (-x +\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}-\frac {3 x}{2}+\frac {\ln \left (1-x \right )}{2}\right )\right ) {\operatorname {csgn}\left (\frac {i \left (\left (-x +\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}-\frac {3 x}{2}+\frac {\ln \left (1-x \right )}{2}\right )}{1+x}\right )}^{2}}{2}-\frac {i \pi x \,\operatorname {csgn}\left (\frac {i}{1+x}\right ) \operatorname {csgn}\left (i \left (\left (-x +\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}-\frac {3 x}{2}+\frac {\ln \left (1-x \right )}{2}\right )\right ) \operatorname {csgn}\left (\frac {i \left (\left (-x +\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}-\frac {3 x}{2}+\frac {\ln \left (1-x \right )}{2}\right )}{1+x}\right )}{2}-\frac {i \pi x \,\operatorname {csgn}\left (\frac {i \left (\left (-x +\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}-\frac {3 x}{2}+\frac {\ln \left (1-x \right )}{2}\right )}{1+x}\right ) {\operatorname {csgn}\left (\frac {i x \left (\left (-x +\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}-\frac {3 x}{2}+\frac {\ln \left (1-x \right )}{2}\right )}{1+x}\right )}^{2}}{2}+\frac {i \pi x \,\operatorname {csgn}\left (\frac {i}{1+x}\right ) {\operatorname {csgn}\left (\frac {i \left (\left (-x +\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}-\frac {3 x}{2}+\frac {\ln \left (1-x \right )}{2}\right )}{1+x}\right )}^{2}}{2}-i \pi x {\operatorname {csgn}\left (\frac {i x \left (\left (-x +\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}-\frac {3 x}{2}+\frac {\ln \left (1-x \right )}{2}\right )}{1+x}\right )}^{2}+\frac {i \pi x {\operatorname {csgn}\left (\frac {i \left (\left (-x +\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}-\frac {3 x}{2}+\frac {\ln \left (1-x \right )}{2}\right )}{1+x}\right )}^{3}}{2}+i x \pi -\ln \left ({\mathrm e}^{20}+1\right ) x +x \ln \left (2\right )\) | \(608\) |
int(((((x^2-1)*exp(20)+x^2-1)*ln(1-x)+(-2*x^3+2*x)*exp(20)-3*x^3+3*x)*ln(( (x*exp(20)+x)*ln(1-x)-2*x^2*exp(20)-3*x^2)/((1+x)*exp(20)+x+1))+((-1+x)*ex p(20)+x-1)*ln(1-x)+(-2*x^3-x^2+5*x)*exp(20)-3*x^3-2*x^2+7*x)/(((x^2-1)*exp (20)+x^2-1)*ln(1-x)+(-2*x^3+2*x)*exp(20)-3*x^3+3*x),x,method=_RETURNVERBOS E)
-(-exp(20)^2*x*ln(((x*exp(20)+x)*ln(1-x)-2*x^2*exp(20)-3*x^2)/(x*exp(20)+e xp(20)+x+1))-2*ln(((x*exp(20)+x)*ln(1-x)-2*x^2*exp(20)-3*x^2)/(x*exp(20)+e xp(20)+x+1))*exp(20)*x-ln(((x*exp(20)+x)*ln(1-x)-2*x^2*exp(20)-3*x^2)/(x*e xp(20)+exp(20)+x+1))*x)/(exp(20)+1)^2
Time = 0.27 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.39 \[ \int \frac {7 x-2 x^2-3 x^3+e^{20} \left (5 x-x^2-2 x^3\right )+\left (-1+e^{20} (-1+x)+x\right ) \log (1-x)+\left (3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)\right ) \log \left (\frac {-3 x^2-2 e^{20} x^2+\left (x+e^{20} x\right ) \log (1-x)}{1+x+e^{20} (1+x)}\right )}{3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)} \, dx=x \log \left (-\frac {2 \, x^{2} e^{20} + 3 \, x^{2} - {\left (x e^{20} + x\right )} \log \left (-x + 1\right )}{{\left (x + 1\right )} e^{20} + x + 1}\right ) \]
integrate(((((x^2-1)*exp(20)+x^2-1)*log(1-x)+(-2*x^3+2*x)*exp(20)-3*x^3+3* x)*log(((x*exp(20)+x)*log(1-x)-2*x^2*exp(20)-3*x^2)/((1+x)*exp(20)+x+1))+( (-1+x)*exp(20)+x-1)*log(1-x)+(-2*x^3-x^2+5*x)*exp(20)-3*x^3-2*x^2+7*x)/((( x^2-1)*exp(20)+x^2-1)*log(1-x)+(-2*x^3+2*x)*exp(20)-3*x^3+3*x),x, algorith m=\
Time = 0.63 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.19 \[ \int \frac {7 x-2 x^2-3 x^3+e^{20} \left (5 x-x^2-2 x^3\right )+\left (-1+e^{20} (-1+x)+x\right ) \log (1-x)+\left (3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)\right ) \log \left (\frac {-3 x^2-2 e^{20} x^2+\left (x+e^{20} x\right ) \log (1-x)}{1+x+e^{20} (1+x)}\right )}{3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)} \, dx=x \log {\left (\frac {- 2 x^{2} e^{20} - 3 x^{2} + \left (x + x e^{20}\right ) \log {\left (1 - x \right )}}{x + \left (x + 1\right ) e^{20} + 1} \right )} \]
integrate(((((x**2-1)*exp(20)+x**2-1)*ln(1-x)+(-2*x**3+2*x)*exp(20)-3*x**3 +3*x)*ln(((x*exp(20)+x)*ln(1-x)-2*x**2*exp(20)-3*x**2)/((1+x)*exp(20)+x+1) )+((-1+x)*exp(20)+x-1)*ln(1-x)+(-2*x**3-x**2+5*x)*exp(20)-3*x**3-2*x**2+7* x)/(((x**2-1)*exp(20)+x**2-1)*ln(1-x)+(-2*x**3+2*x)*exp(20)-3*x**3+3*x),x)
Time = 0.33 (sec) , antiderivative size = 60, normalized size of antiderivative = 1.94 \[ \int \frac {7 x-2 x^2-3 x^3+e^{20} \left (5 x-x^2-2 x^3\right )+\left (-1+e^{20} (-1+x)+x\right ) \log (1-x)+\left (3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)\right ) \log \left (\frac {-3 x^2-2 e^{20} x^2+\left (x+e^{20} x\right ) \log (1-x)}{1+x+e^{20} (1+x)}\right )}{3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)} \, dx=-x {\left (\log \left (-e^{16} + e^{12} - e^{8} + e^{4} - 1\right ) + \log \left (e^{4} + 1\right )\right )} + x \log \left (x {\left (2 \, e^{20} + 3\right )} - {\left (e^{20} + 1\right )} \log \left (-x + 1\right )\right ) - x \log \left (x + 1\right ) + x \log \left (x\right ) \]
integrate(((((x^2-1)*exp(20)+x^2-1)*log(1-x)+(-2*x^3+2*x)*exp(20)-3*x^3+3* x)*log(((x*exp(20)+x)*log(1-x)-2*x^2*exp(20)-3*x^2)/((1+x)*exp(20)+x+1))+( (-1+x)*exp(20)+x-1)*log(1-x)+(-2*x^3-x^2+5*x)*exp(20)-3*x^3-2*x^2+7*x)/((( x^2-1)*exp(20)+x^2-1)*log(1-x)+(-2*x^3+2*x)*exp(20)-3*x^3+3*x),x, algorith m=\
-x*(log(-e^16 + e^12 - e^8 + e^4 - 1) + log(e^4 + 1)) + x*log(x*(2*e^20 + 3) - (e^20 + 1)*log(-x + 1)) - x*log(x + 1) + x*log(x)
Time = 0.61 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.55 \[ \int \frac {7 x-2 x^2-3 x^3+e^{20} \left (5 x-x^2-2 x^3\right )+\left (-1+e^{20} (-1+x)+x\right ) \log (1-x)+\left (3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)\right ) \log \left (\frac {-3 x^2-2 e^{20} x^2+\left (x+e^{20} x\right ) \log (1-x)}{1+x+e^{20} (1+x)}\right )}{3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)} \, dx=x \log \left (-2 \, x^{2} e^{20} + x e^{20} \log \left (-x + 1\right ) - 3 \, x^{2} + x \log \left (-x + 1\right )\right ) - x \log \left (x e^{20} + x + e^{20} + 1\right ) \]
integrate(((((x^2-1)*exp(20)+x^2-1)*log(1-x)+(-2*x^3+2*x)*exp(20)-3*x^3+3* x)*log(((x*exp(20)+x)*log(1-x)-2*x^2*exp(20)-3*x^2)/((1+x)*exp(20)+x+1))+( (-1+x)*exp(20)+x-1)*log(1-x)+(-2*x^3-x^2+5*x)*exp(20)-3*x^3-2*x^2+7*x)/((( x^2-1)*exp(20)+x^2-1)*log(1-x)+(-2*x^3+2*x)*exp(20)-3*x^3+3*x),x, algorith m=\
x*log(-2*x^2*e^20 + x*e^20*log(-x + 1) - 3*x^2 + x*log(-x + 1)) - x*log(x* e^20 + x + e^20 + 1)
Time = 11.58 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.39 \[ \int \frac {7 x-2 x^2-3 x^3+e^{20} \left (5 x-x^2-2 x^3\right )+\left (-1+e^{20} (-1+x)+x\right ) \log (1-x)+\left (3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)\right ) \log \left (\frac {-3 x^2-2 e^{20} x^2+\left (x+e^{20} x\right ) \log (1-x)}{1+x+e^{20} (1+x)}\right )}{3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)} \, dx=x\,\ln \left (-\frac {2\,x^2\,{\mathrm {e}}^{20}-\ln \left (1-x\right )\,\left (x+x\,{\mathrm {e}}^{20}\right )+3\,x^2}{x+{\mathrm {e}}^{20}\,\left (x+1\right )+1}\right ) \]
int((7*x - exp(20)*(x^2 - 5*x + 2*x^3) + log(-(2*x^2*exp(20) - log(1 - x)* (x + x*exp(20)) + 3*x^2)/(x + exp(20)*(x + 1) + 1))*(3*x + exp(20)*(2*x - 2*x^3) + log(1 - x)*(x^2 + exp(20)*(x^2 - 1) - 1) - 3*x^3) + log(1 - x)*(x + exp(20)*(x - 1) - 1) - 2*x^2 - 3*x^3)/(3*x + exp(20)*(2*x - 2*x^3) + lo g(1 - x)*(x^2 + exp(20)*(x^2 - 1) - 1) - 3*x^3),x)