Integrand size = 142, antiderivative size = 27 \[ \int \frac {e^{-\frac {-20 x-e^x x-2 x^2+2 x \log \left (\frac {5}{2}\right )}{-10-x+\log \left (\frac {5}{2}\right )}} \left (400-720 x-156 x^2-8 x^3+\left (-80+152 x+16 x^2\right ) \log \left (\frac {5}{2}\right )+(4-8 x) \log ^2\left (\frac {5}{2}\right )+e^x \left (-40 x-40 x^2-4 x^3+\left (4 x+4 x^2\right ) \log \left (\frac {5}{2}\right )\right )\right )}{1500+300 x+15 x^2+(-300-30 x) \log \left (\frac {5}{2}\right )+15 \log ^2\left (\frac {5}{2}\right )} \, dx=\frac {4}{15} e^{-x \left (2+\frac {e^x}{10+x-\log \left (\frac {5}{2}\right )}\right )} x \] Output:
4/15*x/exp((2+exp(x)/(10-ln(5/2)+x))*x)
\[ \int \frac {e^{-\frac {-20 x-e^x x-2 x^2+2 x \log \left (\frac {5}{2}\right )}{-10-x+\log \left (\frac {5}{2}\right )}} \left (400-720 x-156 x^2-8 x^3+\left (-80+152 x+16 x^2\right ) \log \left (\frac {5}{2}\right )+(4-8 x) \log ^2\left (\frac {5}{2}\right )+e^x \left (-40 x-40 x^2-4 x^3+\left (4 x+4 x^2\right ) \log \left (\frac {5}{2}\right )\right )\right )}{1500+300 x+15 x^2+(-300-30 x) \log \left (\frac {5}{2}\right )+15 \log ^2\left (\frac {5}{2}\right )} \, dx=\int \frac {e^{-\frac {-20 x-e^x x-2 x^2+2 x \log \left (\frac {5}{2}\right )}{-10-x+\log \left (\frac {5}{2}\right )}} \left (400-720 x-156 x^2-8 x^3+\left (-80+152 x+16 x^2\right ) \log \left (\frac {5}{2}\right )+(4-8 x) \log ^2\left (\frac {5}{2}\right )+e^x \left (-40 x-40 x^2-4 x^3+\left (4 x+4 x^2\right ) \log \left (\frac {5}{2}\right )\right )\right )}{1500+300 x+15 x^2+(-300-30 x) \log \left (\frac {5}{2}\right )+15 \log ^2\left (\frac {5}{2}\right )} \, dx \] Input:
Integrate[(400 - 720*x - 156*x^2 - 8*x^3 + (-80 + 152*x + 16*x^2)*Log[5/2] + (4 - 8*x)*Log[5/2]^2 + E^x*(-40*x - 40*x^2 - 4*x^3 + (4*x + 4*x^2)*Log[ 5/2]))/(E^((-20*x - E^x*x - 2*x^2 + 2*x*Log[5/2])/(-10 - x + Log[5/2]))*(1 500 + 300*x + 15*x^2 + (-300 - 30*x)*Log[5/2] + 15*Log[5/2]^2)),x]
Output:
Integrate[(400 - 720*x - 156*x^2 - 8*x^3 + (-80 + 152*x + 16*x^2)*Log[5/2] + (4 - 8*x)*Log[5/2]^2 + E^x*(-40*x - 40*x^2 - 4*x^3 + (4*x + 4*x^2)*Log[ 5/2]))/(E^((-20*x - E^x*x - 2*x^2 + 2*x*Log[5/2])/(-10 - x + Log[5/2]))*(1 500 + 300*x + 15*x^2 + (-300 - 30*x)*Log[5/2] + 15*Log[5/2]^2)), 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.
| \(\displaystyle \int \frac {\left (-8 x^3-156 x^2+\left (16 x^2+152 x-80\right ) \log \left (\frac {5}{2}\right )+e^x \left (-4 x^3-40 x^2+\left (4 x^2+4 x\right ) \log \left (\frac {5}{2}\right )-40 x\right )-720 x+(4-8 x) \log ^2\left (\frac {5}{2}\right )+400\right ) \exp \left (-\frac {-2 x^2-e^x x-20 x+2 x \log \left (\frac {5}{2}\right )}{-x-10+\log \left (\frac {5}{2}\right )}\right )}{15 x^2+300 x+(-30 x-300) \log \left (\frac {5}{2}\right )+1500+15 \log ^2\left (\frac {5}{2}\right )} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (-8 x^3-156 x^2+\left (16 x^2+152 x-80\right ) \log \left (\frac {5}{2}\right )+e^x \left (-4 x^3-40 x^2+\left (4 x^2+4 x\right ) \log \left (\frac {5}{2}\right )-40 x\right )-720 x+(4-8 x) \log ^2\left (\frac {5}{2}\right )+400\right ) \exp \left (-\frac {-2 x^2-e^x x-20 x \left (1-\frac {1}{10} \log \left (\frac {5}{2}\right )\right )}{-x-10+\log \left (\frac {5}{2}\right )}\right )}{15 x^2+30 x \left (10-\log \left (\frac {5}{2}\right )\right )+15 \left (10-\log \left (\frac {5}{2}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7277 |
| \(\displaystyle 60 \int \frac {\exp \left (-\frac {2 x^2+e^x x+2 \left (10-\log \left (\frac {5}{2}\right )\right ) x}{x-\log \left (\frac {5}{2}\right )+10}\right ) \left (-2 x^3-39 x^2-180 x-e^x \left (x^3+10 x^2+10 x-\left (x^2+x\right ) \log \left (\frac {5}{2}\right )\right )+(1-2 x) \log ^2\left (\frac {5}{2}\right )-2 \left (-2 x^2-19 x+10\right ) \log \left (\frac {5}{2}\right )+100\right )}{225 \left (x-\log \left (\frac {5}{2}\right )+10\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {4}{15} \int \frac {\exp \left (-\frac {2 x^2+e^x x+2 \left (10-\log \left (\frac {5}{2}\right )\right ) x}{x-\log \left (\frac {5}{2}\right )+10}\right ) \left (-2 x^3-39 x^2-180 x-e^x \left (x^3+10 x^2+10 x-\left (x^2+x\right ) \log \left (\frac {5}{2}\right )\right )+(1-2 x) \log ^2\left (\frac {5}{2}\right )-2 \left (-2 x^2-19 x+10\right ) \log \left (\frac {5}{2}\right )+100\right )}{\left (x-\log \left (\frac {5}{2}\right )+10\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {4}{15} \int \left (-\frac {2 \exp \left (-\frac {2 x^2+e^x x+2 \left (10-\log \left (\frac {5}{2}\right )\right ) x}{x-\log \left (\frac {5}{2}\right )+10}\right ) x^3}{\left (x-\log \left (\frac {5}{2}\right )+10\right )^2}-\frac {39 \exp \left (-\frac {2 x^2+e^x x+2 \left (10-\log \left (\frac {5}{2}\right )\right ) x}{x-\log \left (\frac {5}{2}\right )+10}\right ) x^2}{\left (x-\log \left (\frac {5}{2}\right )+10\right )^2}+\frac {\exp \left (x-\frac {2 x^2+e^x x+2 \left (10-\log \left (\frac {5}{2}\right )\right ) x}{x-\log \left (\frac {5}{2}\right )+10}\right ) \left (-x^2-\left (10-\log \left (\frac {5}{2}\right )\right ) x+\log \left (\frac {5}{2}\right )-10\right ) x}{\left (x-\log \left (\frac {5}{2}\right )+10\right )^2}-\frac {180 \exp \left (-\frac {2 x^2+e^x x+2 \left (10-\log \left (\frac {5}{2}\right )\right ) x}{x-\log \left (\frac {5}{2}\right )+10}\right ) x}{\left (x-\log \left (\frac {5}{2}\right )+10\right )^2}+\frac {100 \exp \left (-\frac {2 x^2+e^x x+2 \left (10-\log \left (\frac {5}{2}\right )\right ) x}{x-\log \left (\frac {5}{2}\right )+10}\right )}{\left (x-\log \left (\frac {5}{2}\right )+10\right )^2}-\frac {\exp \left (-\frac {2 x^2+e^x x+2 \left (10-\log \left (\frac {5}{2}\right )\right ) x}{x-\log \left (\frac {5}{2}\right )+10}\right ) (2 x-1) \log ^2\left (\frac {5}{2}\right )}{\left (x-\log \left (\frac {5}{2}\right )+10\right )^2}+\frac {2 \exp \left (-\frac {2 x^2+e^x x+2 \left (10-\log \left (\frac {5}{2}\right )\right ) x}{x-\log \left (\frac {5}{2}\right )+10}\right ) (x+10) (2 x-1) \log \left (\frac {5}{2}\right )}{\left (x-\log \left (\frac {5}{2}\right )+10\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {4}{15} \int \frac {\exp \left (-\frac {x \left (2 x+e^x+20 \left (1-\frac {1}{10} \log \left (\frac {5}{2}\right )\right )\right )}{x-\log \left (\frac {5}{2}\right )+10}\right ) \left (-\left (\left (2+e^x\right ) x^3\right )+\left (-39+e^x \left (-10+\log \left (\frac {5}{2}\right )\right )+4 \log \left (\frac {5}{2}\right )\right ) x^2+\left (18+e^x-2 \log \left (\frac {5}{2}\right )\right ) \left (-10+\log \left (\frac {5}{2}\right )\right ) x+\left (-10+\log \left (\frac {5}{2}\right )\right )^2\right )}{\left (x-\log \left (\frac {5}{2}\right )+10\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {4}{15} \int \left (-\frac {2 \exp \left (-\frac {x \left (2 x+e^x+20 \left (1-\frac {1}{10} \log \left (\frac {5}{2}\right )\right )\right )}{x-\log \left (\frac {5}{2}\right )+10}\right ) x^3}{\left (x-\log \left (\frac {5}{2}\right )+10\right )^2}-\frac {39 \exp \left (-\frac {x \left (2 x+e^x+20 \left (1-\frac {1}{10} \log \left (\frac {5}{2}\right )\right )\right )}{x-\log \left (\frac {5}{2}\right )+10}\right ) \left (1-\frac {4}{39} \log \left (\frac {5}{2}\right )\right ) x^2}{\left (x-\log \left (\frac {5}{2}\right )+10\right )^2}+\frac {\exp \left (x-\frac {x \left (2 x+e^x+20 \left (1-\frac {1}{10} \log \left (\frac {5}{2}\right )\right )\right )}{x-\log \left (\frac {5}{2}\right )+10}\right ) \left (-x^2-\left (10-\log \left (\frac {5}{2}\right )\right ) x+\log \left (\frac {5}{2}\right )-10\right ) x}{\left (x-\log \left (\frac {5}{2}\right )+10\right )^2}+\frac {18 \exp \left (-\frac {x \left (2 x+e^x+20 \left (1-\frac {1}{10} \log \left (\frac {5}{2}\right )\right )\right )}{x-\log \left (\frac {5}{2}\right )+10}\right ) \left (1-\frac {1}{9} \log \left (\frac {5}{2}\right )\right ) \left (-10+\log \left (\frac {5}{2}\right )\right ) x}{\left (x-\log \left (\frac {5}{2}\right )+10\right )^2}+\frac {\exp \left (-\frac {x \left (2 x+e^x+20 \left (1-\frac {1}{10} \log \left (\frac {5}{2}\right )\right )\right )}{x-\log \left (\frac {5}{2}\right )+10}\right ) \left (-10+\log \left (\frac {5}{2}\right )\right )^2}{\left (x-\log \left (\frac {5}{2}\right )+10\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {4}{15} \left (\left (10-\log \left (\frac {5}{2}\right )\right ) \int e^{-\frac {x \left (x+e^x+10 \left (1-\frac {1}{10} \log \left (\frac {5}{2}\right )\right )\right )}{x-\log \left (\frac {5}{2}\right )+10}}dx+4 \left (10-\log \left (\frac {5}{2}\right )\right ) \int e^{-\frac {x \left (2 x+e^x+20 \left (1-\frac {1}{10} \log \left (\frac {5}{2}\right )\right )\right )}{x-\log \left (\frac {5}{2}\right )+10}}dx-\left (39-4 \log \left (\frac {5}{2}\right )\right ) \int e^{-\frac {x \left (2 x+e^x+20 \left (1-\frac {1}{10} \log \left (\frac {5}{2}\right )\right )\right )}{x-\log \left (\frac {5}{2}\right )+10}}dx-\int e^{-\frac {x \left (x+e^x+10 \left (1-\frac {1}{10} \log \left (\frac {5}{2}\right )\right )\right )}{x-\log \left (\frac {5}{2}\right )+10}} xdx-2 \int e^{-\frac {x \left (2 x+e^x+20 \left (1-\frac {1}{10} \log \left (\frac {5}{2}\right )\right )\right )}{x-\log \left (\frac {5}{2}\right )+10}} xdx+\left (10-\log \left (\frac {5}{2}\right )\right )^2 \int \frac {e^{-\frac {x \left (x+e^x+10 \left (1-\frac {1}{10} \log \left (\frac {5}{2}\right )\right )\right )}{x-\log \left (\frac {5}{2}\right )+10}}}{\left (x-\log \left (\frac {5}{2}\right )+10\right )^2}dx+2 \left (10-\log \left (\frac {5}{2}\right )\right )^3 \int \frac {e^{-\frac {x \left (2 x+e^x+20 \left (1-\frac {1}{10} \log \left (\frac {5}{2}\right )\right )\right )}{x-\log \left (\frac {5}{2}\right )+10}}}{\left (x-\log \left (\frac {5}{2}\right )+10\right )^2}dx+2 \left (9-\log \left (\frac {5}{2}\right )\right ) \left (10-\log \left (\frac {5}{2}\right )\right )^2 \int \frac {e^{-\frac {x \left (2 x+e^x+20 \left (1-\frac {1}{10} \log \left (\frac {5}{2}\right )\right )\right )}{x-\log \left (\frac {5}{2}\right )+10}}}{\left (x-\log \left (\frac {5}{2}\right )+10\right )^2}dx-\left (39-4 \log \left (\frac {5}{2}\right )\right ) \left (10-\log \left (\frac {5}{2}\right )\right )^2 \int \frac {e^{-\frac {x \left (2 x+e^x+20 \left (1-\frac {1}{10} \log \left (\frac {5}{2}\right )\right )\right )}{x-\log \left (\frac {5}{2}\right )+10}}}{\left (x-\log \left (\frac {5}{2}\right )+10\right )^2}dx+\left (10-\log \left (\frac {5}{2}\right )\right )^2 \int \frac {e^{-\frac {x \left (2 x+e^x+20 \left (1-\frac {1}{10} \log \left (\frac {5}{2}\right )\right )\right )}{x-\log \left (\frac {5}{2}\right )+10}}}{\left (x-\log \left (\frac {5}{2}\right )+10\right )^2}dx-\left (10-\log \left (\frac {5}{2}\right )\right ) \left (11-\log \left (\frac {5}{2}\right )\right ) \int \frac {e^{-\frac {x \left (x+e^x+10 \left (1-\frac {1}{10} \log \left (\frac {5}{2}\right )\right )\right )}{x-\log \left (\frac {5}{2}\right )+10}}}{x-\log \left (\frac {5}{2}\right )+10}dx-6 \left (10-\log \left (\frac {5}{2}\right )\right )^2 \int \frac {e^{-\frac {x \left (2 x+e^x+20 \left (1-\frac {1}{10} \log \left (\frac {5}{2}\right )\right )\right )}{x-\log \left (\frac {5}{2}\right )+10}}}{x-\log \left (\frac {5}{2}\right )+10}dx-2 \left (9-\log \left (\frac {5}{2}\right )\right ) \left (10-\log \left (\frac {5}{2}\right )\right ) \int \frac {e^{-\frac {x \left (2 x+e^x+20 \left (1-\frac {1}{10} \log \left (\frac {5}{2}\right )\right )\right )}{x-\log \left (\frac {5}{2}\right )+10}}}{x-\log \left (\frac {5}{2}\right )+10}dx+2 \left (39-4 \log \left (\frac {5}{2}\right )\right ) \left (10-\log \left (\frac {5}{2}\right )\right ) \int \frac {e^{-\frac {x \left (2 x+e^x+20 \left (1-\frac {1}{10} \log \left (\frac {5}{2}\right )\right )\right )}{x-\log \left (\frac {5}{2}\right )+10}}}{x-\log \left (\frac {5}{2}\right )+10}dx\right )\) |
Input:
Int[(400 - 720*x - 156*x^2 - 8*x^3 + (-80 + 152*x + 16*x^2)*Log[5/2] + (4 - 8*x)*Log[5/2]^2 + E^x*(-40*x - 40*x^2 - 4*x^3 + (4*x + 4*x^2)*Log[5/2])) /(E^((-20*x - E^x*x - 2*x^2 + 2*x*Log[5/2])/(-10 - x + Log[5/2]))*(1500 + 300*x + 15*x^2 + (-300 - 30*x)*Log[5/2] + 15*Log[5/2]^2)),x]
Output:
$Aborted
Time = 1.26 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.26
| method | result | size |
| risch | \(\frac {4 x \,{\mathrm e}^{-\frac {x \left ({\mathrm e}^{x}-2 \ln \left (5\right )+2 \ln \left (2\right )+2 x +20\right )}{-\ln \left (5\right )+\ln \left (2\right )+x +10}}}{15}\) | \(34\) |
| parallelrisch | \(\frac {\left (4 x \ln \left (\frac {5}{2}\right )-4 x^{2}-40 x \right ) {\mathrm e}^{\frac {x \left ({\mathrm e}^{x}-2 \ln \left (\frac {5}{2}\right )+2 x +20\right )}{\ln \left (\frac {5}{2}\right )-x -10}}}{15 \ln \left (\frac {5}{2}\right )-15 x -150}\) | \(52\) |
| norman | \(\frac {\left (\left (-\frac {8}{3}+\frac {4 \ln \left (5\right )}{15}-\frac {4 \ln \left (2\right )}{15}\right ) x -\frac {4 x^{2}}{15}\right ) {\mathrm e}^{-\frac {-{\mathrm e}^{x} x +2 x \ln \left (\frac {5}{2}\right )-2 x^{2}-20 x}{\ln \left (\frac {5}{2}\right )-x -10}}}{\ln \left (\frac {5}{2}\right )-x -10}\) | \(61\) |
Input:
int((((4*x^2+4*x)*ln(5/2)-4*x^3-40*x^2-40*x)*exp(x)+(-8*x+4)*ln(5/2)^2+(16 *x^2+152*x-80)*ln(5/2)-8*x^3-156*x^2-720*x+400)/(15*ln(5/2)^2+(-30*x-300)* ln(5/2)+15*x^2+300*x+1500)/exp((-exp(x)*x+2*x*ln(5/2)-2*x^2-20*x)/(ln(5/2) -x-10)),x,method=_RETURNVERBOSE)
Output:
4/15*x*exp(-x*(exp(x)-2*ln(5)+2*ln(2)+2*x+20)/(-ln(5)+ln(2)+x+10))
Time = 0.11 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.22 \[ \int \frac {e^{-\frac {-20 x-e^x x-2 x^2+2 x \log \left (\frac {5}{2}\right )}{-10-x+\log \left (\frac {5}{2}\right )}} \left (400-720 x-156 x^2-8 x^3+\left (-80+152 x+16 x^2\right ) \log \left (\frac {5}{2}\right )+(4-8 x) \log ^2\left (\frac {5}{2}\right )+e^x \left (-40 x-40 x^2-4 x^3+\left (4 x+4 x^2\right ) \log \left (\frac {5}{2}\right )\right )\right )}{1500+300 x+15 x^2+(-300-30 x) \log \left (\frac {5}{2}\right )+15 \log ^2\left (\frac {5}{2}\right )} \, dx=\frac {4}{15} \, x e^{\left (-\frac {2 \, x^{2} + x e^{x} - 2 \, x \log \left (\frac {5}{2}\right ) + 20 \, x}{x - \log \left (\frac {5}{2}\right ) + 10}\right )} \] Input:
integrate((((4*x^2+4*x)*log(5/2)-4*x^3-40*x^2-40*x)*exp(x)+(-8*x+4)*log(5/ 2)^2+(16*x^2+152*x-80)*log(5/2)-8*x^3-156*x^2-720*x+400)/(15*log(5/2)^2+(- 30*x-300)*log(5/2)+15*x^2+300*x+1500)/exp((-exp(x)*x+2*x*log(5/2)-2*x^2-20 *x)/(log(5/2)-x-10)),x, algorithm="fricas")
Output:
4/15*x*e^(-(2*x^2 + x*e^x - 2*x*log(5/2) + 20*x)/(x - log(5/2) + 10))
Time = 47.77 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.33 \[ \int \frac {e^{-\frac {-20 x-e^x x-2 x^2+2 x \log \left (\frac {5}{2}\right )}{-10-x+\log \left (\frac {5}{2}\right )}} \left (400-720 x-156 x^2-8 x^3+\left (-80+152 x+16 x^2\right ) \log \left (\frac {5}{2}\right )+(4-8 x) \log ^2\left (\frac {5}{2}\right )+e^x \left (-40 x-40 x^2-4 x^3+\left (4 x+4 x^2\right ) \log \left (\frac {5}{2}\right )\right )\right )}{1500+300 x+15 x^2+(-300-30 x) \log \left (\frac {5}{2}\right )+15 \log ^2\left (\frac {5}{2}\right )} \, dx=\frac {4 x e^{- \frac {- 2 x^{2} - x e^{x} - 20 x + 2 x \log {\left (\frac {5}{2} \right )}}{- x - 10 + \log {\left (\frac {5}{2} \right )}}}}{15} \] Input:
integrate((((4*x**2+4*x)*ln(5/2)-4*x**3-40*x**2-40*x)*exp(x)+(-8*x+4)*ln(5 /2)**2+(16*x**2+152*x-80)*ln(5/2)-8*x**3-156*x**2-720*x+400)/(15*ln(5/2)** 2+(-30*x-300)*ln(5/2)+15*x**2+300*x+1500)/exp((-exp(x)*x+2*x*ln(5/2)-2*x** 2-20*x)/(ln(5/2)-x-10)),x)
Output:
4*x*exp(-(-2*x**2 - x*exp(x) - 20*x + 2*x*log(5/2))/(-x - 10 + log(5/2)))/ 15
Leaf count of result is larger than twice the leaf count of optimal. 60 vs. \(2 (21) = 42\).
Time = 0.34 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.22 \[ \int \frac {e^{-\frac {-20 x-e^x x-2 x^2+2 x \log \left (\frac {5}{2}\right )}{-10-x+\log \left (\frac {5}{2}\right )}} \left (400-720 x-156 x^2-8 x^3+\left (-80+152 x+16 x^2\right ) \log \left (\frac {5}{2}\right )+(4-8 x) \log ^2\left (\frac {5}{2}\right )+e^x \left (-40 x-40 x^2-4 x^3+\left (4 x+4 x^2\right ) \log \left (\frac {5}{2}\right )\right )\right )}{1500+300 x+15 x^2+(-300-30 x) \log \left (\frac {5}{2}\right )+15 \log ^2\left (\frac {5}{2}\right )} \, dx=\frac {4}{15} \, x e^{\left (-2 \, x - \frac {e^{x} \log \left (5\right )}{x - \log \left (5\right ) + \log \left (2\right ) + 10} + \frac {e^{x} \log \left (2\right )}{x - \log \left (5\right ) + \log \left (2\right ) + 10} + \frac {10 \, e^{x}}{x - \log \left (5\right ) + \log \left (2\right ) + 10} - e^{x}\right )} \] Input:
integrate((((4*x^2+4*x)*log(5/2)-4*x^3-40*x^2-40*x)*exp(x)+(-8*x+4)*log(5/ 2)^2+(16*x^2+152*x-80)*log(5/2)-8*x^3-156*x^2-720*x+400)/(15*log(5/2)^2+(- 30*x-300)*log(5/2)+15*x^2+300*x+1500)/exp((-exp(x)*x+2*x*log(5/2)-2*x^2-20 *x)/(log(5/2)-x-10)),x, algorithm="maxima")
Output:
4/15*x*e^(-2*x - e^x*log(5)/(x - log(5) + log(2) + 10) + e^x*log(2)/(x - l og(5) + log(2) + 10) + 10*e^x/(x - log(5) + log(2) + 10) - e^x)
\[ \int \frac {e^{-\frac {-20 x-e^x x-2 x^2+2 x \log \left (\frac {5}{2}\right )}{-10-x+\log \left (\frac {5}{2}\right )}} \left (400-720 x-156 x^2-8 x^3+\left (-80+152 x+16 x^2\right ) \log \left (\frac {5}{2}\right )+(4-8 x) \log ^2\left (\frac {5}{2}\right )+e^x \left (-40 x-40 x^2-4 x^3+\left (4 x+4 x^2\right ) \log \left (\frac {5}{2}\right )\right )\right )}{1500+300 x+15 x^2+(-300-30 x) \log \left (\frac {5}{2}\right )+15 \log ^2\left (\frac {5}{2}\right )} \, dx=\int { -\frac {4 \, {\left (2 \, x^{3} + {\left (2 \, x - 1\right )} \log \left (\frac {5}{2}\right )^{2} + 39 \, x^{2} + {\left (x^{3} + 10 \, x^{2} - {\left (x^{2} + x\right )} \log \left (\frac {5}{2}\right ) + 10 \, x\right )} e^{x} - 2 \, {\left (2 \, x^{2} + 19 \, x - 10\right )} \log \left (\frac {5}{2}\right ) + 180 \, x - 100\right )} e^{\left (-\frac {2 \, x^{2} + x e^{x} - 2 \, x \log \left (\frac {5}{2}\right ) + 20 \, x}{x - \log \left (\frac {5}{2}\right ) + 10}\right )}}{15 \, {\left (x^{2} - 2 \, {\left (x + 10\right )} \log \left (\frac {5}{2}\right ) + \log \left (\frac {5}{2}\right )^{2} + 20 \, x + 100\right )}} \,d x } \] Input:
integrate((((4*x^2+4*x)*log(5/2)-4*x^3-40*x^2-40*x)*exp(x)+(-8*x+4)*log(5/ 2)^2+(16*x^2+152*x-80)*log(5/2)-8*x^3-156*x^2-720*x+400)/(15*log(5/2)^2+(- 30*x-300)*log(5/2)+15*x^2+300*x+1500)/exp((-exp(x)*x+2*x*log(5/2)-2*x^2-20 *x)/(log(5/2)-x-10)),x, algorithm="giac")
Output:
integrate(-4/15*(2*x^3 + (2*x - 1)*log(5/2)^2 + 39*x^2 + (x^3 + 10*x^2 - ( x^2 + x)*log(5/2) + 10*x)*e^x - 2*(2*x^2 + 19*x - 10)*log(5/2) + 180*x - 1 00)*e^(-(2*x^2 + x*e^x - 2*x*log(5/2) + 20*x)/(x - log(5/2) + 10))/(x^2 - 2*(x + 10)*log(5/2) + log(5/2)^2 + 20*x + 100), x)
Timed out. \[ \int \frac {e^{-\frac {-20 x-e^x x-2 x^2+2 x \log \left (\frac {5}{2}\right )}{-10-x+\log \left (\frac {5}{2}\right )}} \left (400-720 x-156 x^2-8 x^3+\left (-80+152 x+16 x^2\right ) \log \left (\frac {5}{2}\right )+(4-8 x) \log ^2\left (\frac {5}{2}\right )+e^x \left (-40 x-40 x^2-4 x^3+\left (4 x+4 x^2\right ) \log \left (\frac {5}{2}\right )\right )\right )}{1500+300 x+15 x^2+(-300-30 x) \log \left (\frac {5}{2}\right )+15 \log ^2\left (\frac {5}{2}\right )} \, dx=\text {Hanged} \] Input:
int(-(exp(-(20*x - 2*x*log(5/2) + x*exp(x) + 2*x^2)/(x - log(5/2) + 10))*( 720*x + exp(x)*(40*x - log(5/2)*(4*x + 4*x^2) + 40*x^2 + 4*x^3) - log(5/2) *(152*x + 16*x^2 - 80) + log(5/2)^2*(8*x - 4) + 156*x^2 + 8*x^3 - 400))/(3 00*x - log(5/2)*(30*x + 300) + 15*log(5/2)^2 + 15*x^2 + 1500),x)
Output:
\text{Hanged}
Time = 0.16 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.96 \[ \int \frac {e^{-\frac {-20 x-e^x x-2 x^2+2 x \log \left (\frac {5}{2}\right )}{-10-x+\log \left (\frac {5}{2}\right )}} \left (400-720 x-156 x^2-8 x^3+\left (-80+152 x+16 x^2\right ) \log \left (\frac {5}{2}\right )+(4-8 x) \log ^2\left (\frac {5}{2}\right )+e^x \left (-40 x-40 x^2-4 x^3+\left (4 x+4 x^2\right ) \log \left (\frac {5}{2}\right )\right )\right )}{1500+300 x+15 x^2+(-300-30 x) \log \left (\frac {5}{2}\right )+15 \log ^2\left (\frac {5}{2}\right )} \, dx=\frac {4 e^{\frac {e^{x} x}{\mathrm {log}\left (\frac {5}{2}\right )-x -10}} x}{15 e^{2 x}} \] Input:
int((((4*x^2+4*x)*log(5/2)-4*x^3-40*x^2-40*x)*exp(x)+(-8*x+4)*log(5/2)^2+( 16*x^2+152*x-80)*log(5/2)-8*x^3-156*x^2-720*x+400)/(15*log(5/2)^2+(-30*x-3 00)*log(5/2)+15*x^2+300*x+1500)/exp((-exp(x)*x+2*x*log(5/2)-2*x^2-20*x)/(l og(5/2)-x-10)),x)
Output:
(4*e**((e**x*x)/(log(5/2) - x - 10))*x)/(15*e**(2*x))