Integrand size = 336, antiderivative size = 32 \[ \int \frac {-4 x^2+2 x^3+\left (8 x-8 x^2+2 x^3\right ) \log (1-x)+\left (-4+6 x-2 x^2\right ) \log ^2(1-x)+e^{10-2 e^x} \left (-4 x^2+2 x^3+e^x \left (-4 x^3+4 x^4\right )+\left (4 x-2 x^2+e^x \left (8 x^2-8 x^3\right )\right ) \log (1-x)+e^x \left (-4 x+4 x^2\right ) \log ^2(1-x)\right )+\left (4 x^2-2 x^3+\left (-4 x+2 x^2\right ) \log (1-x)\right ) \log \left (x^2\right )}{-x^4+x^5+e^{30-6 e^x} \left (-x+x^2\right )+\left (3 x^3-3 x^4\right ) \log \left (x^2\right )+\left (-3 x^2+3 x^3\right ) \log ^2\left (x^2\right )+\left (x-x^2\right ) \log ^3\left (x^2\right )+e^{20-4 e^x} \left (-3 x^2+3 x^3+\left (3 x-3 x^2\right ) \log \left (x^2\right )\right )+e^{10-2 e^x} \left (-3 x^3+3 x^4+\left (6 x^2-6 x^3\right ) \log \left (x^2\right )+\left (-3 x+3 x^2\right ) \log ^2\left (x^2\right )\right )} \, dx=\frac {(-x+\log (1-x))^2}{\left (e^{10-2 e^x}+x-\log \left (x^2\right )\right )^2} \] Output:
(ln(1-x)-x)^2/(x+exp(5-exp(x))^2-ln(x^2))^2
Time = 0.21 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.50 \[ \int \frac {-4 x^2+2 x^3+\left (8 x-8 x^2+2 x^3\right ) \log (1-x)+\left (-4+6 x-2 x^2\right ) \log ^2(1-x)+e^{10-2 e^x} \left (-4 x^2+2 x^3+e^x \left (-4 x^3+4 x^4\right )+\left (4 x-2 x^2+e^x \left (8 x^2-8 x^3\right )\right ) \log (1-x)+e^x \left (-4 x+4 x^2\right ) \log ^2(1-x)\right )+\left (4 x^2-2 x^3+\left (-4 x+2 x^2\right ) \log (1-x)\right ) \log \left (x^2\right )}{-x^4+x^5+e^{30-6 e^x} \left (-x+x^2\right )+\left (3 x^3-3 x^4\right ) \log \left (x^2\right )+\left (-3 x^2+3 x^3\right ) \log ^2\left (x^2\right )+\left (x-x^2\right ) \log ^3\left (x^2\right )+e^{20-4 e^x} \left (-3 x^2+3 x^3+\left (3 x-3 x^2\right ) \log \left (x^2\right )\right )+e^{10-2 e^x} \left (-3 x^3+3 x^4+\left (6 x^2-6 x^3\right ) \log \left (x^2\right )+\left (-3 x+3 x^2\right ) \log ^2\left (x^2\right )\right )} \, dx=\frac {e^{4 e^x} (x-\log (1-x))^2}{\left (e^{10}+e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )\right )^2} \] Input:
Integrate[(-4*x^2 + 2*x^3 + (8*x - 8*x^2 + 2*x^3)*Log[1 - x] + (-4 + 6*x - 2*x^2)*Log[1 - x]^2 + E^(10 - 2*E^x)*(-4*x^2 + 2*x^3 + E^x*(-4*x^3 + 4*x^ 4) + (4*x - 2*x^2 + E^x*(8*x^2 - 8*x^3))*Log[1 - x] + E^x*(-4*x + 4*x^2)*L og[1 - x]^2) + (4*x^2 - 2*x^3 + (-4*x + 2*x^2)*Log[1 - x])*Log[x^2])/(-x^4 + x^5 + E^(30 - 6*E^x)*(-x + x^2) + (3*x^3 - 3*x^4)*Log[x^2] + (-3*x^2 + 3*x^3)*Log[x^2]^2 + (x - x^2)*Log[x^2]^3 + E^(20 - 4*E^x)*(-3*x^2 + 3*x^3 + (3*x - 3*x^2)*Log[x^2]) + E^(10 - 2*E^x)*(-3*x^3 + 3*x^4 + (6*x^2 - 6*x^ 3)*Log[x^2] + (-3*x + 3*x^2)*Log[x^2]^2)),x]
Output:
(E^(4*E^x)*(x - Log[1 - x])^2)/(E^10 + E^(2*E^x)*x - E^(2*E^x)*Log[x^2])^2
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.
| \(\displaystyle \int \frac {2 x^3-4 x^2+\left (-2 x^2+6 x-4\right ) \log ^2(1-x)+\left (2 x^3-8 x^2+8 x\right ) \log (1-x)+\left (-2 x^3+4 x^2+\left (2 x^2-4 x\right ) \log (1-x)\right ) \log \left (x^2\right )+e^{10-2 e^x} \left (2 x^3-4 x^2+e^x \left (4 x^2-4 x\right ) \log ^2(1-x)+e^x \left (4 x^4-4 x^3\right )+\left (-2 x^2+e^x \left (8 x^2-8 x^3\right )+4 x\right ) \log (1-x)\right )}{x^5-x^4+e^{30-6 e^x} \left (x^2-x\right )+\left (x-x^2\right ) \log ^3\left (x^2\right )+\left (3 x^3-3 x^2\right ) \log ^2\left (x^2\right )+e^{20-4 e^x} \left (3 x^3-3 x^2+\left (3 x-3 x^2\right ) \log \left (x^2\right )\right )+e^{10-2 e^x} \left (3 x^4-3 x^3+\left (3 x^2-3 x\right ) \log ^2\left (x^2\right )+\left (6 x^2-6 x^3\right ) \log \left (x^2\right )\right )+\left (3 x^3-3 x^4\right ) \log \left (x^2\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 e^{4 e^x} (x-\log (1-x)) \left (-x \left (-e^{2 e^x} (x-2) \log \left (x^2\right )+e^{2 e^x} (x-2)+e^{10} (x-2)+2 e^{x+10} (x-1) x\right )-\left ((x-1) \left (e^{2 e^x} (x-2)-2 e^{x+10} x\right ) \log (1-x)\right )\right )}{(1-x) x \left (-e^{2 e^x} \log \left (x^2\right )+e^{2 e^x} x+e^{10}\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int -\frac {e^{4 e^x} (x-\log (1-x)) \left ((1-x) \left (e^{2 e^x} (2-x)+2 e^{x+10} x\right ) \log (1-x)-x \left (e^{2 e^x} (2-x)-e^{2 e^x} \log \left (x^2\right ) (2-x)+e^{10} (2-x)+2 e^{x+10} (1-x) x\right )\right )}{(1-x) x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -2 \int \frac {e^{4 e^x} (x-\log (1-x)) \left ((1-x) \left (e^{2 e^x} (2-x)+2 e^{x+10} x\right ) \log (1-x)-x \left (e^{2 e^x} (2-x)-e^{2 e^x} \log \left (x^2\right ) (2-x)+e^{10} (2-x)+2 e^{x+10} (1-x) x\right )\right )}{(1-x) x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (-\frac {2 e^{x+4 e^x+10} (x-\log (1-x))^2}{\left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) \log (1-x) (x-\log (1-x))}{x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}+\frac {e^{6 e^x} (x-2) \log \left (x^2\right ) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{10+4 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {e^{4 e^x} (x-\log (1-x)) \left ((x-1) \left (e^{2 e^x} (x-2)-2 e^{x+10} x\right ) \log (1-x)+x \left (e^{2 e^x} (x-2)-e^{2 e^x} \log \left (x^2\right ) (x-2)+e^{10} (x-2)+2 e^{x+10} (x-1) x\right )\right )}{(1-x) x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (-\frac {2 e^{x+4 e^x+10} (x-\log (1-x))^2}{\left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) \log (1-x) (x-\log (1-x))}{x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}+\frac {e^{6 e^x} (x-2) \log \left (x^2\right ) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{10+4 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {e^{4 e^x} (x-\log (1-x)) \left ((x-1) \left (e^{2 e^x} (x-2)-2 e^{x+10} x\right ) \log (1-x)+x \left (e^{2 e^x} (x-2)-e^{2 e^x} \log \left (x^2\right ) (x-2)+e^{10} (x-2)+2 e^{x+10} (x-1) x\right )\right )}{(1-x) x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (-\frac {2 e^{x+4 e^x+10} (x-\log (1-x))^2}{\left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) \log (1-x) (x-\log (1-x))}{x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}+\frac {e^{6 e^x} (x-2) \log \left (x^2\right ) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{10+4 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {e^{4 e^x} (x-\log (1-x)) \left ((x-1) \left (e^{2 e^x} (x-2)-2 e^{x+10} x\right ) \log (1-x)+x \left (e^{2 e^x} (x-2)-e^{2 e^x} \log \left (x^2\right ) (x-2)+e^{10} (x-2)+2 e^{x+10} (x-1) x\right )\right )}{(1-x) x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (-\frac {2 e^{x+4 e^x+10} (x-\log (1-x))^2}{\left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) \log (1-x) (x-\log (1-x))}{x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}+\frac {e^{6 e^x} (x-2) \log \left (x^2\right ) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{10+4 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {e^{4 e^x} (x-\log (1-x)) \left ((x-1) \left (e^{2 e^x} (x-2)-2 e^{x+10} x\right ) \log (1-x)+x \left (e^{2 e^x} (x-2)-e^{2 e^x} \log \left (x^2\right ) (x-2)+e^{10} (x-2)+2 e^{x+10} (x-1) x\right )\right )}{(1-x) x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (-\frac {2 e^{x+4 e^x+10} (x-\log (1-x))^2}{\left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) \log (1-x) (x-\log (1-x))}{x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}+\frac {e^{6 e^x} (x-2) \log \left (x^2\right ) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{10+4 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {e^{4 e^x} (x-\log (1-x)) \left ((x-1) \left (e^{2 e^x} (x-2)-2 e^{x+10} x\right ) \log (1-x)+x \left (e^{2 e^x} (x-2)-e^{2 e^x} \log \left (x^2\right ) (x-2)+e^{10} (x-2)+2 e^{x+10} (x-1) x\right )\right )}{(1-x) x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (-\frac {2 e^{x+4 e^x+10} (x-\log (1-x))^2}{\left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) \log (1-x) (x-\log (1-x))}{x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}+\frac {e^{6 e^x} (x-2) \log \left (x^2\right ) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{10+4 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {e^{4 e^x} (x-\log (1-x)) \left ((x-1) \left (e^{2 e^x} (x-2)-2 e^{x+10} x\right ) \log (1-x)+x \left (e^{2 e^x} (x-2)-e^{2 e^x} \log \left (x^2\right ) (x-2)+e^{10} (x-2)+2 e^{x+10} (x-1) x\right )\right )}{(1-x) x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (-\frac {2 e^{x+4 e^x+10} (x-\log (1-x))^2}{\left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) \log (1-x) (x-\log (1-x))}{x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}+\frac {e^{6 e^x} (x-2) \log \left (x^2\right ) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{10+4 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {e^{4 e^x} (x-\log (1-x)) \left ((x-1) \left (e^{2 e^x} (x-2)-2 e^{x+10} x\right ) \log (1-x)+x \left (e^{2 e^x} (x-2)-e^{2 e^x} \log \left (x^2\right ) (x-2)+e^{10} (x-2)+2 e^{x+10} (x-1) x\right )\right )}{(1-x) x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (-\frac {2 e^{x+4 e^x+10} (x-\log (1-x))^2}{\left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) \log (1-x) (x-\log (1-x))}{x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}+\frac {e^{6 e^x} (x-2) \log \left (x^2\right ) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{10+4 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {e^{4 e^x} (x-\log (1-x)) \left ((x-1) \left (e^{2 e^x} (x-2)-2 e^{x+10} x\right ) \log (1-x)+x \left (e^{2 e^x} (x-2)-e^{2 e^x} \log \left (x^2\right ) (x-2)+e^{10} (x-2)+2 e^{x+10} (x-1) x\right )\right )}{(1-x) x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (-\frac {2 e^{x+4 e^x+10} (x-\log (1-x))^2}{\left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) \log (1-x) (x-\log (1-x))}{x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}+\frac {e^{6 e^x} (x-2) \log \left (x^2\right ) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{10+4 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {e^{4 e^x} (x-\log (1-x)) \left ((x-1) \left (e^{2 e^x} (x-2)-2 e^{x+10} x\right ) \log (1-x)+x \left (e^{2 e^x} (x-2)-e^{2 e^x} \log \left (x^2\right ) (x-2)+e^{10} (x-2)+2 e^{x+10} (x-1) x\right )\right )}{(1-x) x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (-\frac {2 e^{x+4 e^x+10} (x-\log (1-x))^2}{\left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) \log (1-x) (x-\log (1-x))}{x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}+\frac {e^{6 e^x} (x-2) \log \left (x^2\right ) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{10+4 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {e^{4 e^x} (x-\log (1-x)) \left ((x-1) \left (e^{2 e^x} (x-2)-2 e^{x+10} x\right ) \log (1-x)+x \left (e^{2 e^x} (x-2)-e^{2 e^x} \log \left (x^2\right ) (x-2)+e^{10} (x-2)+2 e^{x+10} (x-1) x\right )\right )}{(1-x) x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (-\frac {2 e^{x+4 e^x+10} (x-\log (1-x))^2}{\left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) \log (1-x) (x-\log (1-x))}{x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}+\frac {e^{6 e^x} (x-2) \log \left (x^2\right ) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{10+4 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {e^{4 e^x} (x-\log (1-x)) \left ((x-1) \left (e^{2 e^x} (x-2)-2 e^{x+10} x\right ) \log (1-x)+x \left (e^{2 e^x} (x-2)-e^{2 e^x} \log \left (x^2\right ) (x-2)+e^{10} (x-2)+2 e^{x+10} (x-1) x\right )\right )}{(1-x) x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (-\frac {2 e^{x+4 e^x+10} (x-\log (1-x))^2}{\left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) \log (1-x) (x-\log (1-x))}{x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}+\frac {e^{6 e^x} (x-2) \log \left (x^2\right ) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{10+4 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {e^{4 e^x} (x-\log (1-x)) \left ((x-1) \left (e^{2 e^x} (x-2)-2 e^{x+10} x\right ) \log (1-x)+x \left (e^{2 e^x} (x-2)-e^{2 e^x} \log \left (x^2\right ) (x-2)+e^{10} (x-2)+2 e^{x+10} (x-1) x\right )\right )}{(1-x) x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (-\frac {2 e^{x+4 e^x+10} (x-\log (1-x))^2}{\left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) \log (1-x) (x-\log (1-x))}{x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}+\frac {e^{6 e^x} (x-2) \log \left (x^2\right ) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{10+4 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {e^{4 e^x} (x-\log (1-x)) \left ((x-1) \left (e^{2 e^x} (x-2)-2 e^{x+10} x\right ) \log (1-x)+x \left (e^{2 e^x} (x-2)-e^{2 e^x} \log \left (x^2\right ) (x-2)+e^{10} (x-2)+2 e^{x+10} (x-1) x\right )\right )}{(1-x) x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (-\frac {2 e^{x+4 e^x+10} (x-\log (1-x))^2}{\left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) \log (1-x) (x-\log (1-x))}{x \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}+\frac {e^{6 e^x} (x-2) \log \left (x^2\right ) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{6 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}-\frac {e^{10+4 e^x} (x-2) (x-\log (1-x))}{(x-1) \left (e^{2 e^x} x-e^{2 e^x} \log \left (x^2\right )+e^{10}\right )^3}\right )dx\) |
Input:
Int[(-4*x^2 + 2*x^3 + (8*x - 8*x^2 + 2*x^3)*Log[1 - x] + (-4 + 6*x - 2*x^2 )*Log[1 - x]^2 + E^(10 - 2*E^x)*(-4*x^2 + 2*x^3 + E^x*(-4*x^3 + 4*x^4) + ( 4*x - 2*x^2 + E^x*(8*x^2 - 8*x^3))*Log[1 - x] + E^x*(-4*x + 4*x^2)*Log[1 - x]^2) + (4*x^2 - 2*x^3 + (-4*x + 2*x^2)*Log[1 - x])*Log[x^2])/(-x^4 + x^5 + E^(30 - 6*E^x)*(-x + x^2) + (3*x^3 - 3*x^4)*Log[x^2] + (-3*x^2 + 3*x^3) *Log[x^2]^2 + (x - x^2)*Log[x^2]^3 + E^(20 - 4*E^x)*(-3*x^2 + 3*x^3 + (3*x - 3*x^2)*Log[x^2]) + E^(10 - 2*E^x)*(-3*x^3 + 3*x^4 + (6*x^2 - 6*x^3)*Log [x^2] + (-3*x + 3*x^2)*Log[x^2]^2)),x]
Output:
$Aborted
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.22 (sec) , antiderivative size = 92, normalized size of antiderivative = 2.88
\[\frac {4 x^{2}-8 x \ln \left (1-x \right )+4 \ln \left (1-x \right )^{2}}{\left (2 \,{\mathrm e}^{-2 \,{\mathrm e}^{x}+10}+i \pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )-2 i \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}-4 \ln \left (x \right )+2 x +i \pi \operatorname {csgn}\left (i x^{2}\right )^{3}\right )^{2}}\]
Input:
int((((4*x^2-4*x)*exp(x)*ln(1-x)^2+((-8*x^3+8*x^2)*exp(x)-2*x^2+4*x)*ln(1- x)+(4*x^4-4*x^3)*exp(x)+2*x^3-4*x^2)*exp(5-exp(x))^2+((2*x^2-4*x)*ln(1-x)- 2*x^3+4*x^2)*ln(x^2)+(-2*x^2+6*x-4)*ln(1-x)^2+(2*x^3-8*x^2+8*x)*ln(1-x)+2* x^3-4*x^2)/((x^2-x)*exp(5-exp(x))^6+((-3*x^2+3*x)*ln(x^2)+3*x^3-3*x^2)*exp (5-exp(x))^4+((3*x^2-3*x)*ln(x^2)^2+(-6*x^3+6*x^2)*ln(x^2)+3*x^4-3*x^3)*ex p(5-exp(x))^2+(-x^2+x)*ln(x^2)^3+(3*x^3-3*x^2)*ln(x^2)^2+(-3*x^4+3*x^3)*ln (x^2)+x^5-x^4),x)
Output:
4*(x^2-2*x*ln(1-x)+ln(1-x)^2)/(2*exp(-2*exp(x)+10)+I*Pi*csgn(I*x)^2*csgn(I *x^2)-2*I*Pi*csgn(I*x)*csgn(I*x^2)^2-4*ln(x)+2*x+I*Pi*csgn(I*x^2)^3)^2
Leaf count of result is larger than twice the leaf count of optimal. 65 vs. \(2 (30) = 60\).
Time = 0.08 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.03 \[ \int \frac {-4 x^2+2 x^3+\left (8 x-8 x^2+2 x^3\right ) \log (1-x)+\left (-4+6 x-2 x^2\right ) \log ^2(1-x)+e^{10-2 e^x} \left (-4 x^2+2 x^3+e^x \left (-4 x^3+4 x^4\right )+\left (4 x-2 x^2+e^x \left (8 x^2-8 x^3\right )\right ) \log (1-x)+e^x \left (-4 x+4 x^2\right ) \log ^2(1-x)\right )+\left (4 x^2-2 x^3+\left (-4 x+2 x^2\right ) \log (1-x)\right ) \log \left (x^2\right )}{-x^4+x^5+e^{30-6 e^x} \left (-x+x^2\right )+\left (3 x^3-3 x^4\right ) \log \left (x^2\right )+\left (-3 x^2+3 x^3\right ) \log ^2\left (x^2\right )+\left (x-x^2\right ) \log ^3\left (x^2\right )+e^{20-4 e^x} \left (-3 x^2+3 x^3+\left (3 x-3 x^2\right ) \log \left (x^2\right )\right )+e^{10-2 e^x} \left (-3 x^3+3 x^4+\left (6 x^2-6 x^3\right ) \log \left (x^2\right )+\left (-3 x+3 x^2\right ) \log ^2\left (x^2\right )\right )} \, dx=\frac {x^{2} - 2 \, x \log \left (-x + 1\right ) + \log \left (-x + 1\right )^{2}}{x^{2} + 2 \, {\left (x - \log \left (x^{2}\right )\right )} e^{\left (-2 \, e^{x} + 10\right )} - 2 \, x \log \left (x^{2}\right ) + \log \left (x^{2}\right )^{2} + e^{\left (-4 \, e^{x} + 20\right )}} \] Input:
integrate((((4*x^2-4*x)*exp(x)*log(1-x)^2+((-8*x^3+8*x^2)*exp(x)-2*x^2+4*x )*log(1-x)+(4*x^4-4*x^3)*exp(x)+2*x^3-4*x^2)*exp(5-exp(x))^2+((2*x^2-4*x)* log(1-x)-2*x^3+4*x^2)*log(x^2)+(-2*x^2+6*x-4)*log(1-x)^2+(2*x^3-8*x^2+8*x) *log(1-x)+2*x^3-4*x^2)/((x^2-x)*exp(5-exp(x))^6+((-3*x^2+3*x)*log(x^2)+3*x ^3-3*x^2)*exp(5-exp(x))^4+((3*x^2-3*x)*log(x^2)^2+(-6*x^3+6*x^2)*log(x^2)+ 3*x^4-3*x^3)*exp(5-exp(x))^2+(-x^2+x)*log(x^2)^3+(3*x^3-3*x^2)*log(x^2)^2+ (-3*x^4+3*x^3)*log(x^2)+x^5-x^4),x, algorithm="fricas")
Output:
(x^2 - 2*x*log(-x + 1) + log(-x + 1)^2)/(x^2 + 2*(x - log(x^2))*e^(-2*e^x + 10) - 2*x*log(x^2) + log(x^2)^2 + e^(-4*e^x + 20))
Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (24) = 48\).
Time = 0.37 (sec) , antiderivative size = 63, normalized size of antiderivative = 1.97 \[ \int \frac {-4 x^2+2 x^3+\left (8 x-8 x^2+2 x^3\right ) \log (1-x)+\left (-4+6 x-2 x^2\right ) \log ^2(1-x)+e^{10-2 e^x} \left (-4 x^2+2 x^3+e^x \left (-4 x^3+4 x^4\right )+\left (4 x-2 x^2+e^x \left (8 x^2-8 x^3\right )\right ) \log (1-x)+e^x \left (-4 x+4 x^2\right ) \log ^2(1-x)\right )+\left (4 x^2-2 x^3+\left (-4 x+2 x^2\right ) \log (1-x)\right ) \log \left (x^2\right )}{-x^4+x^5+e^{30-6 e^x} \left (-x+x^2\right )+\left (3 x^3-3 x^4\right ) \log \left (x^2\right )+\left (-3 x^2+3 x^3\right ) \log ^2\left (x^2\right )+\left (x-x^2\right ) \log ^3\left (x^2\right )+e^{20-4 e^x} \left (-3 x^2+3 x^3+\left (3 x-3 x^2\right ) \log \left (x^2\right )\right )+e^{10-2 e^x} \left (-3 x^3+3 x^4+\left (6 x^2-6 x^3\right ) \log \left (x^2\right )+\left (-3 x+3 x^2\right ) \log ^2\left (x^2\right )\right )} \, dx=\frac {x^{2} - 2 x \log {\left (1 - x \right )} + \log {\left (1 - x \right )}^{2}}{x^{2} - 2 x \log {\left (x^{2} \right )} + \left (2 x - 2 \log {\left (x^{2} \right )}\right ) e^{10 - 2 e^{x}} + e^{20 - 4 e^{x}} + \log {\left (x^{2} \right )}^{2}} \] Input:
integrate((((4*x**2-4*x)*exp(x)*ln(1-x)**2+((-8*x**3+8*x**2)*exp(x)-2*x**2 +4*x)*ln(1-x)+(4*x**4-4*x**3)*exp(x)+2*x**3-4*x**2)*exp(5-exp(x))**2+((2*x **2-4*x)*ln(1-x)-2*x**3+4*x**2)*ln(x**2)+(-2*x**2+6*x-4)*ln(1-x)**2+(2*x** 3-8*x**2+8*x)*ln(1-x)+2*x**3-4*x**2)/((x**2-x)*exp(5-exp(x))**6+((-3*x**2+ 3*x)*ln(x**2)+3*x**3-3*x**2)*exp(5-exp(x))**4+((3*x**2-3*x)*ln(x**2)**2+(- 6*x**3+6*x**2)*ln(x**2)+3*x**4-3*x**3)*exp(5-exp(x))**2+(-x**2+x)*ln(x**2) **3+(3*x**3-3*x**2)*ln(x**2)**2+(-3*x**4+3*x**3)*ln(x**2)+x**5-x**4),x)
Output:
(x**2 - 2*x*log(1 - x) + log(1 - x)**2)/(x**2 - 2*x*log(x**2) + (2*x - 2*l og(x**2))*exp(10 - 2*exp(x)) + exp(20 - 4*exp(x)) + log(x**2)**2)
Leaf count of result is larger than twice the leaf count of optimal. 83 vs. \(2 (30) = 60\).
Time = 0.74 (sec) , antiderivative size = 83, normalized size of antiderivative = 2.59 \[ \int \frac {-4 x^2+2 x^3+\left (8 x-8 x^2+2 x^3\right ) \log (1-x)+\left (-4+6 x-2 x^2\right ) \log ^2(1-x)+e^{10-2 e^x} \left (-4 x^2+2 x^3+e^x \left (-4 x^3+4 x^4\right )+\left (4 x-2 x^2+e^x \left (8 x^2-8 x^3\right )\right ) \log (1-x)+e^x \left (-4 x+4 x^2\right ) \log ^2(1-x)\right )+\left (4 x^2-2 x^3+\left (-4 x+2 x^2\right ) \log (1-x)\right ) \log \left (x^2\right )}{-x^4+x^5+e^{30-6 e^x} \left (-x+x^2\right )+\left (3 x^3-3 x^4\right ) \log \left (x^2\right )+\left (-3 x^2+3 x^3\right ) \log ^2\left (x^2\right )+\left (x-x^2\right ) \log ^3\left (x^2\right )+e^{20-4 e^x} \left (-3 x^2+3 x^3+\left (3 x-3 x^2\right ) \log \left (x^2\right )\right )+e^{10-2 e^x} \left (-3 x^3+3 x^4+\left (6 x^2-6 x^3\right ) \log \left (x^2\right )+\left (-3 x+3 x^2\right ) \log ^2\left (x^2\right )\right )} \, dx=\frac {x^{2} e^{\left (4 \, e^{x}\right )} - 2 \, x e^{\left (4 \, e^{x}\right )} \log \left (-x + 1\right ) + e^{\left (4 \, e^{x}\right )} \log \left (-x + 1\right )^{2}}{{\left (x^{2} - 4 \, x \log \left (x\right ) + 4 \, \log \left (x\right )^{2}\right )} e^{\left (4 \, e^{x}\right )} + 2 \, {\left (x e^{10} - 2 \, e^{10} \log \left (x\right )\right )} e^{\left (2 \, e^{x}\right )} + e^{20}} \] Input:
integrate((((4*x^2-4*x)*exp(x)*log(1-x)^2+((-8*x^3+8*x^2)*exp(x)-2*x^2+4*x )*log(1-x)+(4*x^4-4*x^3)*exp(x)+2*x^3-4*x^2)*exp(5-exp(x))^2+((2*x^2-4*x)* log(1-x)-2*x^3+4*x^2)*log(x^2)+(-2*x^2+6*x-4)*log(1-x)^2+(2*x^3-8*x^2+8*x) *log(1-x)+2*x^3-4*x^2)/((x^2-x)*exp(5-exp(x))^6+((-3*x^2+3*x)*log(x^2)+3*x ^3-3*x^2)*exp(5-exp(x))^4+((3*x^2-3*x)*log(x^2)^2+(-6*x^3+6*x^2)*log(x^2)+ 3*x^4-3*x^3)*exp(5-exp(x))^2+(-x^2+x)*log(x^2)^3+(3*x^3-3*x^2)*log(x^2)^2+ (-3*x^4+3*x^3)*log(x^2)+x^5-x^4),x, algorithm="maxima")
Output:
(x^2*e^(4*e^x) - 2*x*e^(4*e^x)*log(-x + 1) + e^(4*e^x)*log(-x + 1)^2)/((x^ 2 - 4*x*log(x) + 4*log(x)^2)*e^(4*e^x) + 2*(x*e^10 - 2*e^10*log(x))*e^(2*e ^x) + e^20)
Timed out. \[ \int \frac {-4 x^2+2 x^3+\left (8 x-8 x^2+2 x^3\right ) \log (1-x)+\left (-4+6 x-2 x^2\right ) \log ^2(1-x)+e^{10-2 e^x} \left (-4 x^2+2 x^3+e^x \left (-4 x^3+4 x^4\right )+\left (4 x-2 x^2+e^x \left (8 x^2-8 x^3\right )\right ) \log (1-x)+e^x \left (-4 x+4 x^2\right ) \log ^2(1-x)\right )+\left (4 x^2-2 x^3+\left (-4 x+2 x^2\right ) \log (1-x)\right ) \log \left (x^2\right )}{-x^4+x^5+e^{30-6 e^x} \left (-x+x^2\right )+\left (3 x^3-3 x^4\right ) \log \left (x^2\right )+\left (-3 x^2+3 x^3\right ) \log ^2\left (x^2\right )+\left (x-x^2\right ) \log ^3\left (x^2\right )+e^{20-4 e^x} \left (-3 x^2+3 x^3+\left (3 x-3 x^2\right ) \log \left (x^2\right )\right )+e^{10-2 e^x} \left (-3 x^3+3 x^4+\left (6 x^2-6 x^3\right ) \log \left (x^2\right )+\left (-3 x+3 x^2\right ) \log ^2\left (x^2\right )\right )} \, dx=\text {Timed out} \] Input:
integrate((((4*x^2-4*x)*exp(x)*log(1-x)^2+((-8*x^3+8*x^2)*exp(x)-2*x^2+4*x )*log(1-x)+(4*x^4-4*x^3)*exp(x)+2*x^3-4*x^2)*exp(5-exp(x))^2+((2*x^2-4*x)* log(1-x)-2*x^3+4*x^2)*log(x^2)+(-2*x^2+6*x-4)*log(1-x)^2+(2*x^3-8*x^2+8*x) *log(1-x)+2*x^3-4*x^2)/((x^2-x)*exp(5-exp(x))^6+((-3*x^2+3*x)*log(x^2)+3*x ^3-3*x^2)*exp(5-exp(x))^4+((3*x^2-3*x)*log(x^2)^2+(-6*x^3+6*x^2)*log(x^2)+ 3*x^4-3*x^3)*exp(5-exp(x))^2+(-x^2+x)*log(x^2)^3+(3*x^3-3*x^2)*log(x^2)^2+ (-3*x^4+3*x^3)*log(x^2)+x^5-x^4),x, algorithm="giac")
Output:
Timed out
Timed out. \[ \int \frac {-4 x^2+2 x^3+\left (8 x-8 x^2+2 x^3\right ) \log (1-x)+\left (-4+6 x-2 x^2\right ) \log ^2(1-x)+e^{10-2 e^x} \left (-4 x^2+2 x^3+e^x \left (-4 x^3+4 x^4\right )+\left (4 x-2 x^2+e^x \left (8 x^2-8 x^3\right )\right ) \log (1-x)+e^x \left (-4 x+4 x^2\right ) \log ^2(1-x)\right )+\left (4 x^2-2 x^3+\left (-4 x+2 x^2\right ) \log (1-x)\right ) \log \left (x^2\right )}{-x^4+x^5+e^{30-6 e^x} \left (-x+x^2\right )+\left (3 x^3-3 x^4\right ) \log \left (x^2\right )+\left (-3 x^2+3 x^3\right ) \log ^2\left (x^2\right )+\left (x-x^2\right ) \log ^3\left (x^2\right )+e^{20-4 e^x} \left (-3 x^2+3 x^3+\left (3 x-3 x^2\right ) \log \left (x^2\right )\right )+e^{10-2 e^x} \left (-3 x^3+3 x^4+\left (6 x^2-6 x^3\right ) \log \left (x^2\right )+\left (-3 x+3 x^2\right ) \log ^2\left (x^2\right )\right )} \, dx=\int \frac {{\mathrm {e}}^{10-2\,{\mathrm {e}}^x}\,\left ({\mathrm {e}}^x\,\left (4\,x^3-4\,x^4\right )-\ln \left (1-x\right )\,\left (4\,x+{\mathrm {e}}^x\,\left (8\,x^2-8\,x^3\right )-2\,x^2\right )+4\,x^2-2\,x^3+{\mathrm {e}}^x\,{\ln \left (1-x\right )}^2\,\left (4\,x-4\,x^2\right )\right )-\ln \left (1-x\right )\,\left (2\,x^3-8\,x^2+8\,x\right )+{\ln \left (1-x\right )}^2\,\left (2\,x^2-6\,x+4\right )+4\,x^2-2\,x^3+\ln \left (x^2\right )\,\left (\ln \left (1-x\right )\,\left (4\,x-2\,x^2\right )-4\,x^2+2\,x^3\right )}{{\mathrm {e}}^{10-2\,{\mathrm {e}}^x}\,\left ({\ln \left (x^2\right )}^2\,\left (3\,x-3\,x^2\right )-\ln \left (x^2\right )\,\left (6\,x^2-6\,x^3\right )+3\,x^3-3\,x^4\right )-{\ln \left (x^2\right )}^3\,\left (x-x^2\right )-{\mathrm {e}}^{20-4\,{\mathrm {e}}^x}\,\left (\ln \left (x^2\right )\,\left (3\,x-3\,x^2\right )-3\,x^2+3\,x^3\right )+{\mathrm {e}}^{30-6\,{\mathrm {e}}^x}\,\left (x-x^2\right )-\ln \left (x^2\right )\,\left (3\,x^3-3\,x^4\right )+{\ln \left (x^2\right )}^2\,\left (3\,x^2-3\,x^3\right )+x^4-x^5} \,d x \] Input:
int((exp(10 - 2*exp(x))*(exp(x)*(4*x^3 - 4*x^4) - log(1 - x)*(4*x + exp(x) *(8*x^2 - 8*x^3) - 2*x^2) + 4*x^2 - 2*x^3 + exp(x)*log(1 - x)^2*(4*x - 4*x ^2)) - log(1 - x)*(8*x - 8*x^2 + 2*x^3) + log(1 - x)^2*(2*x^2 - 6*x + 4) + 4*x^2 - 2*x^3 + log(x^2)*(log(1 - x)*(4*x - 2*x^2) - 4*x^2 + 2*x^3))/(exp (10 - 2*exp(x))*(log(x^2)^2*(3*x - 3*x^2) - log(x^2)*(6*x^2 - 6*x^3) + 3*x ^3 - 3*x^4) - log(x^2)^3*(x - x^2) - exp(20 - 4*exp(x))*(log(x^2)*(3*x - 3 *x^2) - 3*x^2 + 3*x^3) + exp(30 - 6*exp(x))*(x - x^2) - log(x^2)*(3*x^3 - 3*x^4) + log(x^2)^2*(3*x^2 - 3*x^3) + x^4 - x^5),x)
Output:
int((exp(10 - 2*exp(x))*(exp(x)*(4*x^3 - 4*x^4) - log(1 - x)*(4*x + exp(x) *(8*x^2 - 8*x^3) - 2*x^2) + 4*x^2 - 2*x^3 + exp(x)*log(1 - x)^2*(4*x - 4*x ^2)) - log(1 - x)*(8*x - 8*x^2 + 2*x^3) + log(1 - x)^2*(2*x^2 - 6*x + 4) + 4*x^2 - 2*x^3 + log(x^2)*(log(1 - x)*(4*x - 2*x^2) - 4*x^2 + 2*x^3))/(exp (10 - 2*exp(x))*(log(x^2)^2*(3*x - 3*x^2) - log(x^2)*(6*x^2 - 6*x^3) + 3*x ^3 - 3*x^4) - log(x^2)^3*(x - x^2) - exp(20 - 4*exp(x))*(log(x^2)*(3*x - 3 *x^2) - 3*x^2 + 3*x^3) + exp(30 - 6*exp(x))*(x - x^2) - log(x^2)*(3*x^3 - 3*x^4) + log(x^2)^2*(3*x^2 - 3*x^3) + x^4 - x^5), x)
Time = 0.31 (sec) , antiderivative size = 103, normalized size of antiderivative = 3.22 \[ \int \frac {-4 x^2+2 x^3+\left (8 x-8 x^2+2 x^3\right ) \log (1-x)+\left (-4+6 x-2 x^2\right ) \log ^2(1-x)+e^{10-2 e^x} \left (-4 x^2+2 x^3+e^x \left (-4 x^3+4 x^4\right )+\left (4 x-2 x^2+e^x \left (8 x^2-8 x^3\right )\right ) \log (1-x)+e^x \left (-4 x+4 x^2\right ) \log ^2(1-x)\right )+\left (4 x^2-2 x^3+\left (-4 x+2 x^2\right ) \log (1-x)\right ) \log \left (x^2\right )}{-x^4+x^5+e^{30-6 e^x} \left (-x+x^2\right )+\left (3 x^3-3 x^4\right ) \log \left (x^2\right )+\left (-3 x^2+3 x^3\right ) \log ^2\left (x^2\right )+\left (x-x^2\right ) \log ^3\left (x^2\right )+e^{20-4 e^x} \left (-3 x^2+3 x^3+\left (3 x-3 x^2\right ) \log \left (x^2\right )\right )+e^{10-2 e^x} \left (-3 x^3+3 x^4+\left (6 x^2-6 x^3\right ) \log \left (x^2\right )+\left (-3 x+3 x^2\right ) \log ^2\left (x^2\right )\right )} \, dx=\frac {e^{4 e^{x}} \left (\mathrm {log}\left (1-x \right )^{2}-2 \,\mathrm {log}\left (1-x \right ) x +x^{2}\right )}{e^{4 e^{x}} \mathrm {log}\left (x^{2}\right )^{2}-2 e^{4 e^{x}} \mathrm {log}\left (x^{2}\right ) x +e^{4 e^{x}} x^{2}-2 e^{2 e^{x}} \mathrm {log}\left (x^{2}\right ) e^{10}+2 e^{2 e^{x}} e^{10} x +e^{20}} \] Input:
int((((4*x^2-4*x)*exp(x)*log(1-x)^2+((-8*x^3+8*x^2)*exp(x)-2*x^2+4*x)*log( 1-x)+(4*x^4-4*x^3)*exp(x)+2*x^3-4*x^2)*exp(5-exp(x))^2+((2*x^2-4*x)*log(1- x)-2*x^3+4*x^2)*log(x^2)+(-2*x^2+6*x-4)*log(1-x)^2+(2*x^3-8*x^2+8*x)*log(1 -x)+2*x^3-4*x^2)/((x^2-x)*exp(5-exp(x))^6+((-3*x^2+3*x)*log(x^2)+3*x^3-3*x ^2)*exp(5-exp(x))^4+((3*x^2-3*x)*log(x^2)^2+(-6*x^3+6*x^2)*log(x^2)+3*x^4- 3*x^3)*exp(5-exp(x))^2+(-x^2+x)*log(x^2)^3+(3*x^3-3*x^2)*log(x^2)^2+(-3*x^ 4+3*x^3)*log(x^2)+x^5-x^4),x)
Output:
(e**(4*e**x)*(log( - x + 1)**2 - 2*log( - x + 1)*x + x**2))/(e**(4*e**x)*l og(x**2)**2 - 2*e**(4*e**x)*log(x**2)*x + e**(4*e**x)*x**2 - 2*e**(2*e**x) *log(x**2)*e**10 + 2*e**(2*e**x)*e**10*x + e**20)