Integrand size = 317, antiderivative size = 30 \[ \int \frac {-132 x-e^{6 e^6} x-1800 x^3-9375 x^5-15625 x^7+e^{4 e^6} \left (-15 x-75 x^3\right )+e^x \left (2+5 x-100 x^2+25 x^3\right )+e^{2 e^6} \left (-76 x+e^x x-750 x^3-1875 x^5\right )+\left (76 x+3 e^{4 e^6} x-e^x x+750 x^3+1875 x^5+e^{2 e^6} \left (30 x+150 x^3\right )\right ) \log (x)+\left (-15 x-3 e^{2 e^6} x-75 x^3\right ) \log ^2(x)+x \log ^3(x)}{-125 x-e^{6 e^6} x-1875 x^3-9375 x^5-15625 x^7+e^{4 e^6} \left (-15 x-75 x^3\right )+e^{2 e^6} \left (-75 x-750 x^3-1875 x^5\right )+\left (75 x+3 e^{4 e^6} x+750 x^3+1875 x^5+e^{2 e^6} \left (30 x+150 x^3\right )\right ) \log (x)+\left (-15 x-3 e^{2 e^6} x-75 x^3\right ) \log ^2(x)+x \log ^3(x)} \, dx=x+\frac {-e^x+x}{\left (5+e^{2 e^6}+25 x^2-\log (x)\right )^2} \]
Time = 0.16 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.03 \[ \int \frac {-132 x-e^{6 e^6} x-1800 x^3-9375 x^5-15625 x^7+e^{4 e^6} \left (-15 x-75 x^3\right )+e^x \left (2+5 x-100 x^2+25 x^3\right )+e^{2 e^6} \left (-76 x+e^x x-750 x^3-1875 x^5\right )+\left (76 x+3 e^{4 e^6} x-e^x x+750 x^3+1875 x^5+e^{2 e^6} \left (30 x+150 x^3\right )\right ) \log (x)+\left (-15 x-3 e^{2 e^6} x-75 x^3\right ) \log ^2(x)+x \log ^3(x)}{-125 x-e^{6 e^6} x-1875 x^3-9375 x^5-15625 x^7+e^{4 e^6} \left (-15 x-75 x^3\right )+e^{2 e^6} \left (-75 x-750 x^3-1875 x^5\right )+\left (75 x+3 e^{4 e^6} x+750 x^3+1875 x^5+e^{2 e^6} \left (30 x+150 x^3\right )\right ) \log (x)+\left (-15 x-3 e^{2 e^6} x-75 x^3\right ) \log ^2(x)+x \log ^3(x)} \, dx=x-\frac {e^x-x}{\left (-5-e^{2 e^6}-25 x^2+\log (x)\right )^2} \]
Integrate[(-132*x - E^(6*E^6)*x - 1800*x^3 - 9375*x^5 - 15625*x^7 + E^(4*E ^6)*(-15*x - 75*x^3) + E^x*(2 + 5*x - 100*x^2 + 25*x^3) + E^(2*E^6)*(-76*x + E^x*x - 750*x^3 - 1875*x^5) + (76*x + 3*E^(4*E^6)*x - E^x*x + 750*x^3 + 1875*x^5 + E^(2*E^6)*(30*x + 150*x^3))*Log[x] + (-15*x - 3*E^(2*E^6)*x - 75*x^3)*Log[x]^2 + x*Log[x]^3)/(-125*x - E^(6*E^6)*x - 1875*x^3 - 9375*x^5 - 15625*x^7 + E^(4*E^6)*(-15*x - 75*x^3) + E^(2*E^6)*(-75*x - 750*x^3 - 1 875*x^5) + (75*x + 3*E^(4*E^6)*x + 750*x^3 + 1875*x^5 + E^(2*E^6)*(30*x + 150*x^3))*Log[x] + (-15*x - 3*E^(2*E^6)*x - 75*x^3)*Log[x]^2 + x*Log[x]^3) ,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.
| \(\displaystyle \int \frac {-15625 x^7-9375 x^5-1800 x^3+e^{4 e^6} \left (-75 x^3-15 x\right )+\left (-75 x^3-3 e^{2 e^6} x-15 x\right ) \log ^2(x)+e^{2 e^6} \left (-1875 x^5-750 x^3+e^x x-76 x\right )+\left (1875 x^5+750 x^3+e^{2 e^6} \left (150 x^3+30 x\right )-e^x x+3 e^{4 e^6} x+76 x\right ) \log (x)+e^x \left (25 x^3-100 x^2+5 x+2\right )-e^{6 e^6} x-132 x+x \log ^3(x)}{-15625 x^7-9375 x^5-1875 x^3+e^{4 e^6} \left (-75 x^3-15 x\right )+\left (-75 x^3-3 e^{2 e^6} x-15 x\right ) \log ^2(x)+e^{2 e^6} \left (-1875 x^5-750 x^3-75 x\right )+\left (1875 x^5+750 x^3+e^{2 e^6} \left (150 x^3+30 x\right )+3 e^{4 e^6} x+75 x\right ) \log (x)-e^{6 e^6} x-125 x+x \log ^3(x)} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {-15625 x^7-9375 x^5-1800 x^3+e^{4 e^6} \left (-75 x^3-15 x\right )+\left (-75 x^3-3 e^{2 e^6} x-15 x\right ) \log ^2(x)+e^{2 e^6} \left (-1875 x^5-750 x^3+e^x x-76 x\right )+\left (1875 x^5+750 x^3+e^{2 e^6} \left (150 x^3+30 x\right )-e^x x+3 e^{4 e^6} x+76 x\right ) \log (x)+e^x \left (25 x^3-100 x^2+5 x+2\right )-e^{6 e^6} x-132 x+x \log ^3(x)}{-15625 x^7-9375 x^5-1875 x^3+e^{4 e^6} \left (-75 x^3-15 x\right )+\left (-75 x^3-3 e^{2 e^6} x-15 x\right ) \log ^2(x)+e^{2 e^6} \left (-1875 x^5-750 x^3-75 x\right )+\left (1875 x^5+750 x^3+e^{2 e^6} \left (150 x^3+30 x\right )+3 e^{4 e^6} x+75 x\right ) \log (x)+\left (-125-e^{6 e^6}\right ) x+x \log ^3(x)}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {-15625 x^7-9375 x^5-1800 x^3+e^{4 e^6} \left (-75 x^3-15 x\right )+\left (-75 x^3-3 e^{2 e^6} x-15 x\right ) \log ^2(x)+e^{2 e^6} \left (-1875 x^5-750 x^3+e^x x-76 x\right )+\left (1875 x^5+750 x^3+e^{2 e^6} \left (150 x^3+30 x\right )-e^x x+3 e^{4 e^6} x+76 x\right ) \log (x)+e^x \left (25 x^3-100 x^2+5 x+2\right )+\left (-132-e^{6 e^6}\right ) x+x \log ^3(x)}{-15625 x^7-9375 x^5-1875 x^3+e^{4 e^6} \left (-75 x^3-15 x\right )+\left (-75 x^3-3 e^{2 e^6} x-15 x\right ) \log ^2(x)+e^{2 e^6} \left (-1875 x^5-750 x^3-75 x\right )+\left (1875 x^5+750 x^3+e^{2 e^6} \left (150 x^3+30 x\right )+3 e^{4 e^6} x+75 x\right ) \log (x)+\left (-125-e^{6 e^6}\right ) x+x \log ^3(x)}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {15625 x^7+9375 x^5+1800 x^3-e^{4 e^6} \left (-75 x^3-15 x\right )-\left (-75 x^3-3 e^{2 e^6} x-15 x\right ) \log ^2(x)-e^{2 e^6} \left (-1875 x^5-750 x^3+e^x x-76 x\right )-\left (1875 x^5+750 x^3+e^{2 e^6} \left (150 x^3+30 x\right )-e^x x+3 e^{4 e^6} x+76 x\right ) \log (x)-e^x \left (25 x^3-100 x^2+5 x+2\right )-\left (-132-e^{6 e^6}\right ) x-x \log ^3(x)}{x \left (25 x^2-\log (x)+5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {\log ^3(x)}{\left (-25 x^2+\log (x)-5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}+\frac {3 \left (25 x^2+e^{2 e^6}+5\right ) \log ^2(x)}{\left (25 x^2-\log (x)+5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}+\frac {1800 \left (1+\frac {5 e^{2 e^6}}{12}\right ) x^2}{\left (25 x^2-\log (x)+5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}+\frac {750 x^2 \log (x)}{\left (-25 x^2+\log (x)-5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}+\frac {30 e^{2 e^6} \left (-5 x^2-1\right ) \log (x)}{\left (25 x^2-\log (x)+5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}+\frac {15 e^{4 e^6} \left (5 x^2+1\right )}{\left (25 x^2-\log (x)+5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}+\frac {76 e^{2 e^6} \left (1+\frac {1}{76} e^{-2 e^6} \left (132+e^{6 e^6}\right )\right )}{\left (25 x^2-\log (x)+5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}+\frac {76 \left (1+\frac {3 e^{4 e^6}}{76}\right ) \log (x)}{\left (-25 x^2+\log (x)-5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}+\frac {15625 x^6}{\left (25 x^2-\log (x)+5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}+\frac {9375 \left (1+\frac {e^{2 e^6}}{5}\right ) x^4}{\left (25 x^2-\log (x)+5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}+\frac {1875 x^4 \log (x)}{\left (-25 x^2+\log (x)-5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}+\frac {e^x \left (-25 x^3+100 x^2-5 \left (1+\frac {e^{2 e^6}}{5}\right ) x+x \log (x)-2\right )}{x \left (25 x^2-\log (x)+5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle x+\left (132+76 e^{2 e^6}+e^{6 e^6}\right ) \int \frac {1}{\left (25 x^2-\log (x)+5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}dx+2 \left (5+e^{2 e^6}\right )^3 \int \frac {1}{\left (25 x^2-\log (x)+5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}dx+15 e^{4 e^6} \int \frac {1}{\left (25 x^2-\log (x)+5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}dx+150 \left (12+5 e^{2 e^6}\right ) \int \frac {x^2}{\left (25 x^2-\log (x)+5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}dx-150 e^{2 e^6} \left (10+e^{2 e^6}\right ) \int \frac {x^2}{\left (25 x^2-\log (x)+5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}dx+225 \left (5+e^{2 e^6}\right )^2 \int \frac {x^2}{\left (25 x^2-\log (x)+5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}dx-750 \left (5+e^{2 e^6}\right ) \int \frac {x^2}{\left (25 x^2-\log (x)+5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}dx+75 e^{4 e^6} \int \frac {x^2}{\left (25 x^2-\log (x)+5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}dx+3750 \left (5+e^{2 e^6}\right ) \int \frac {x^4}{\left (25 x^2-\log (x)+5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}dx+62500 \int \frac {x^6}{\left (25 x^2-\log (x)+5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}dx+\left (76+3 e^{4 e^6}\right ) \int \frac {1}{\left (25 x^2-\log (x)+5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^2}dx-3 \left (5+e^{2 e^6}\right )^2 \int \frac {1}{\left (25 x^2-\log (x)+5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^2}dx+30 e^{2 e^6} \int \frac {1}{\left (25 x^2-\log (x)+5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^2}dx-150 \left (5+e^{2 e^6}\right ) \int \frac {x^2}{\left (25 x^2-\log (x)+5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^2}dx+150 e^{2 e^6} \int \frac {x^2}{\left (25 x^2-\log (x)+5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^2}dx+750 \int \frac {x^2}{\left (25 x^2-\log (x)+5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^2}dx+3 \left (5+e^{2 e^6}\right ) \int \frac {1}{25 x^2-\log (x)+5 \left (1+\frac {e^{2 e^6}}{5}\right )}dx+75 \int \frac {x^2}{25 x^2-\log (x)+5 \left (1+\frac {e^{2 e^6}}{5}\right )}dx+\left (5+e^{2 e^6}\right ) \left (76+3 e^{4 e^6}\right ) \int \frac {1}{\left (-25 x^2+\log (x)-5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}dx+30 e^{2 e^6} \left (5+e^{2 e^6}\right ) \int \frac {1}{\left (-25 x^2+\log (x)-5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}dx+25 \left (76+3 e^{4 e^6}\right ) \int \frac {x^2}{\left (-25 x^2+\log (x)-5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}dx+75 \left (5+e^{2 e^6}\right )^2 \int \frac {x^2}{\left (-25 x^2+\log (x)-5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}dx+3750 e^{2 e^6} \int \frac {x^4}{\left (-25 x^2+\log (x)-5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}dx+18750 \int \frac {x^4}{\left (-25 x^2+\log (x)-5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}dx+62500 \int \frac {x^6}{\left (-25 x^2+\log (x)-5 \left (1+\frac {e^{2 e^6}}{5}\right )\right )^3}dx+3 \left (5+e^{2 e^6}\right ) \int \frac {1}{-25 x^2+\log (x)-5 \left (1+\frac {e^{2 e^6}}{5}\right )}dx+75 \int \frac {x^2}{-25 x^2+\log (x)-5 \left (1+\frac {e^{2 e^6}}{5}\right )}dx-\frac {e^x \left (25 x^3-\log (x) x+\left (5+e^{2 e^6}\right ) x\right )}{\left (25 x^2-\log (x)+e^{2 e^6}+5\right )^3 x}\) |
Int[(-132*x - E^(6*E^6)*x - 1800*x^3 - 9375*x^5 - 15625*x^7 + E^(4*E^6)*(- 15*x - 75*x^3) + E^x*(2 + 5*x - 100*x^2 + 25*x^3) + E^(2*E^6)*(-76*x + E^x *x - 750*x^3 - 1875*x^5) + (76*x + 3*E^(4*E^6)*x - E^x*x + 750*x^3 + 1875* x^5 + E^(2*E^6)*(30*x + 150*x^3))*Log[x] + (-15*x - 3*E^(2*E^6)*x - 75*x^3 )*Log[x]^2 + x*Log[x]^3)/(-125*x - E^(6*E^6)*x - 1875*x^3 - 9375*x^5 - 156 25*x^7 + E^(4*E^6)*(-15*x - 75*x^3) + E^(2*E^6)*(-75*x - 750*x^3 - 1875*x^ 5) + (75*x + 3*E^(4*E^6)*x + 750*x^3 + 1875*x^5 + E^(2*E^6)*(30*x + 150*x^ 3))*Log[x] + (-15*x - 3*E^(2*E^6)*x - 75*x^3)*Log[x]^2 + x*Log[x]^3),x]
3.4.38.3.1 Defintions of rubi rules used
Int[(u_.)*((v_.) + (a_.)*(Fx_) + (b_.)*(Fx_))^(p_.), x_Symbol] :> Int[u*(v + (a + b)*Fx)^p, x] /; FreeQ[{a, b}, x] && !FreeQ[Fx, x]
Time = 6.37 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.93
| method | result | size |
| risch | \(x +\frac {x -{\mathrm e}^{x}}{\left (25 x^{2}+{\mathrm e}^{2 \,{\mathrm e}^{6}}-\ln \left (x \right )+5\right )^{2}}\) | \(28\) |
| parallelrisch | \(-\frac {-26 x -10 x \,{\mathrm e}^{2 \,{\mathrm e}^{6}}-x \,{\mathrm e}^{4 \,{\mathrm e}^{6}}-x \ln \left (x \right )^{2}+10 x \ln \left (x \right )-250 x^{3}+{\mathrm e}^{x}-625 x^{5}+50 x^{3} \ln \left (x \right )+2 \ln \left (x \right ) {\mathrm e}^{2 \,{\mathrm e}^{6}} x -50 \,{\mathrm e}^{2 \,{\mathrm e}^{6}} x^{3}}{{\mathrm e}^{4 \,{\mathrm e}^{6}}+50 \,{\mathrm e}^{2 \,{\mathrm e}^{6}} x^{2}+625 x^{4}-2 \ln \left (x \right ) {\mathrm e}^{2 \,{\mathrm e}^{6}}-50 x^{2} \ln \left (x \right )+10 \,{\mathrm e}^{2 \,{\mathrm e}^{6}}+250 x^{2}+\ln \left (x \right )^{2}-10 \ln \left (x \right )+25}\) | \(150\) |
int((x*ln(x)^3+(-3*x*exp(exp(3)^2)^2-75*x^3-15*x)*ln(x)^2+(3*x*exp(exp(3)^ 2)^4+(150*x^3+30*x)*exp(exp(3)^2)^2-exp(x)*x+1875*x^5+750*x^3+76*x)*ln(x)- x*exp(exp(3)^2)^6+(-75*x^3-15*x)*exp(exp(3)^2)^4+(exp(x)*x-1875*x^5-750*x^ 3-76*x)*exp(exp(3)^2)^2+(25*x^3-100*x^2+5*x+2)*exp(x)-15625*x^7-9375*x^5-1 800*x^3-132*x)/(x*ln(x)^3+(-3*x*exp(exp(3)^2)^2-75*x^3-15*x)*ln(x)^2+(3*x* exp(exp(3)^2)^4+(150*x^3+30*x)*exp(exp(3)^2)^2+1875*x^5+750*x^3+75*x)*ln(x )-x*exp(exp(3)^2)^6+(-75*x^3-15*x)*exp(exp(3)^2)^4+(-1875*x^5-750*x^3-75*x )*exp(exp(3)^2)^2-15625*x^7-9375*x^5-1875*x^3-125*x),x,method=_RETURNVERBO SE)
Leaf count of result is larger than twice the leaf count of optimal. 119 vs. \(2 (27) = 54\).
Time = 0.24 (sec) , antiderivative size = 119, normalized size of antiderivative = 3.97 \[ \int \frac {-132 x-e^{6 e^6} x-1800 x^3-9375 x^5-15625 x^7+e^{4 e^6} \left (-15 x-75 x^3\right )+e^x \left (2+5 x-100 x^2+25 x^3\right )+e^{2 e^6} \left (-76 x+e^x x-750 x^3-1875 x^5\right )+\left (76 x+3 e^{4 e^6} x-e^x x+750 x^3+1875 x^5+e^{2 e^6} \left (30 x+150 x^3\right )\right ) \log (x)+\left (-15 x-3 e^{2 e^6} x-75 x^3\right ) \log ^2(x)+x \log ^3(x)}{-125 x-e^{6 e^6} x-1875 x^3-9375 x^5-15625 x^7+e^{4 e^6} \left (-15 x-75 x^3\right )+e^{2 e^6} \left (-75 x-750 x^3-1875 x^5\right )+\left (75 x+3 e^{4 e^6} x+750 x^3+1875 x^5+e^{2 e^6} \left (30 x+150 x^3\right )\right ) \log (x)+\left (-15 x-3 e^{2 e^6} x-75 x^3\right ) \log ^2(x)+x \log ^3(x)} \, dx=\frac {625 \, x^{5} + 250 \, x^{3} + x \log \left (x\right )^{2} + x e^{\left (4 \, e^{6}\right )} + 10 \, {\left (5 \, x^{3} + x\right )} e^{\left (2 \, e^{6}\right )} - 2 \, {\left (25 \, x^{3} + x e^{\left (2 \, e^{6}\right )} + 5 \, x\right )} \log \left (x\right ) + 26 \, x - e^{x}}{625 \, x^{4} + 250 \, x^{2} + 10 \, {\left (5 \, x^{2} + 1\right )} e^{\left (2 \, e^{6}\right )} - 2 \, {\left (25 \, x^{2} + e^{\left (2 \, e^{6}\right )} + 5\right )} \log \left (x\right ) + \log \left (x\right )^{2} + e^{\left (4 \, e^{6}\right )} + 25} \]
integrate((x*log(x)^3+(-3*x*exp(exp(3)^2)^2-75*x^3-15*x)*log(x)^2+(3*x*exp (exp(3)^2)^4+(150*x^3+30*x)*exp(exp(3)^2)^2-exp(x)*x+1875*x^5+750*x^3+76*x )*log(x)-x*exp(exp(3)^2)^6+(-75*x^3-15*x)*exp(exp(3)^2)^4+(exp(x)*x-1875*x ^5-750*x^3-76*x)*exp(exp(3)^2)^2+(25*x^3-100*x^2+5*x+2)*exp(x)-15625*x^7-9 375*x^5-1800*x^3-132*x)/(x*log(x)^3+(-3*x*exp(exp(3)^2)^2-75*x^3-15*x)*log (x)^2+(3*x*exp(exp(3)^2)^4+(150*x^3+30*x)*exp(exp(3)^2)^2+1875*x^5+750*x^3 +75*x)*log(x)-x*exp(exp(3)^2)^6+(-75*x^3-15*x)*exp(exp(3)^2)^4+(-1875*x^5- 750*x^3-75*x)*exp(exp(3)^2)^2-15625*x^7-9375*x^5-1875*x^3-125*x),x, algori thm=\
(625*x^5 + 250*x^3 + x*log(x)^2 + x*e^(4*e^6) + 10*(5*x^3 + x)*e^(2*e^6) - 2*(25*x^3 + x*e^(2*e^6) + 5*x)*log(x) + 26*x - e^x)/(625*x^4 + 250*x^2 + 10*(5*x^2 + 1)*e^(2*e^6) - 2*(25*x^2 + e^(2*e^6) + 5)*log(x) + log(x)^2 + e^(4*e^6) + 25)
Leaf count of result is larger than twice the leaf count of optimal. 139 vs. \(2 (24) = 48\).
Time = 0.28 (sec) , antiderivative size = 139, normalized size of antiderivative = 4.63 \[ \int \frac {-132 x-e^{6 e^6} x-1800 x^3-9375 x^5-15625 x^7+e^{4 e^6} \left (-15 x-75 x^3\right )+e^x \left (2+5 x-100 x^2+25 x^3\right )+e^{2 e^6} \left (-76 x+e^x x-750 x^3-1875 x^5\right )+\left (76 x+3 e^{4 e^6} x-e^x x+750 x^3+1875 x^5+e^{2 e^6} \left (30 x+150 x^3\right )\right ) \log (x)+\left (-15 x-3 e^{2 e^6} x-75 x^3\right ) \log ^2(x)+x \log ^3(x)}{-125 x-e^{6 e^6} x-1875 x^3-9375 x^5-15625 x^7+e^{4 e^6} \left (-15 x-75 x^3\right )+e^{2 e^6} \left (-75 x-750 x^3-1875 x^5\right )+\left (75 x+3 e^{4 e^6} x+750 x^3+1875 x^5+e^{2 e^6} \left (30 x+150 x^3\right )\right ) \log (x)+\left (-15 x-3 e^{2 e^6} x-75 x^3\right ) \log ^2(x)+x \log ^3(x)} \, dx=x + \frac {x}{625 x^{4} + 250 x^{2} + 50 x^{2} e^{2 e^{6}} + \left (- 50 x^{2} - 10 - 2 e^{2 e^{6}}\right ) \log {\left (x \right )} + \log {\left (x \right )}^{2} + 25 + 10 e^{2 e^{6}} + e^{4 e^{6}}} - \frac {e^{x}}{625 x^{4} - 50 x^{2} \log {\left (x \right )} + 250 x^{2} + 50 x^{2} e^{2 e^{6}} + \log {\left (x \right )}^{2} - 10 \log {\left (x \right )} - 2 e^{2 e^{6}} \log {\left (x \right )} + 25 + 10 e^{2 e^{6}} + e^{4 e^{6}}} \]
integrate((x*ln(x)**3+(-3*x*exp(exp(3)**2)**2-75*x**3-15*x)*ln(x)**2+(3*x* exp(exp(3)**2)**4+(150*x**3+30*x)*exp(exp(3)**2)**2-exp(x)*x+1875*x**5+750 *x**3+76*x)*ln(x)-x*exp(exp(3)**2)**6+(-75*x**3-15*x)*exp(exp(3)**2)**4+(e xp(x)*x-1875*x**5-750*x**3-76*x)*exp(exp(3)**2)**2+(25*x**3-100*x**2+5*x+2 )*exp(x)-15625*x**7-9375*x**5-1800*x**3-132*x)/(x*ln(x)**3+(-3*x*exp(exp(3 )**2)**2-75*x**3-15*x)*ln(x)**2+(3*x*exp(exp(3)**2)**4+(150*x**3+30*x)*exp (exp(3)**2)**2+1875*x**5+750*x**3+75*x)*ln(x)-x*exp(exp(3)**2)**6+(-75*x** 3-15*x)*exp(exp(3)**2)**4+(-1875*x**5-750*x**3-75*x)*exp(exp(3)**2)**2-156 25*x**7-9375*x**5-1875*x**3-125*x),x)
x + x/(625*x**4 + 250*x**2 + 50*x**2*exp(2*exp(6)) + (-50*x**2 - 10 - 2*ex p(2*exp(6)))*log(x) + log(x)**2 + 25 + 10*exp(2*exp(6)) + exp(4*exp(6))) - exp(x)/(625*x**4 - 50*x**2*log(x) + 250*x**2 + 50*x**2*exp(2*exp(6)) + lo g(x)**2 - 10*log(x) - 2*exp(2*exp(6))*log(x) + 25 + 10*exp(2*exp(6)) + exp (4*exp(6)))
Leaf count of result is larger than twice the leaf count of optimal. 117 vs. \(2 (27) = 54\).
Time = 0.24 (sec) , antiderivative size = 117, normalized size of antiderivative = 3.90 \[ \int \frac {-132 x-e^{6 e^6} x-1800 x^3-9375 x^5-15625 x^7+e^{4 e^6} \left (-15 x-75 x^3\right )+e^x \left (2+5 x-100 x^2+25 x^3\right )+e^{2 e^6} \left (-76 x+e^x x-750 x^3-1875 x^5\right )+\left (76 x+3 e^{4 e^6} x-e^x x+750 x^3+1875 x^5+e^{2 e^6} \left (30 x+150 x^3\right )\right ) \log (x)+\left (-15 x-3 e^{2 e^6} x-75 x^3\right ) \log ^2(x)+x \log ^3(x)}{-125 x-e^{6 e^6} x-1875 x^3-9375 x^5-15625 x^7+e^{4 e^6} \left (-15 x-75 x^3\right )+e^{2 e^6} \left (-75 x-750 x^3-1875 x^5\right )+\left (75 x+3 e^{4 e^6} x+750 x^3+1875 x^5+e^{2 e^6} \left (30 x+150 x^3\right )\right ) \log (x)+\left (-15 x-3 e^{2 e^6} x-75 x^3\right ) \log ^2(x)+x \log ^3(x)} \, dx=\frac {625 \, x^{5} + 50 \, x^{3} {\left (e^{\left (2 \, e^{6}\right )} + 5\right )} + x \log \left (x\right )^{2} + x {\left (e^{\left (4 \, e^{6}\right )} + 10 \, e^{\left (2 \, e^{6}\right )} + 26\right )} - 2 \, {\left (25 \, x^{3} + x {\left (e^{\left (2 \, e^{6}\right )} + 5\right )}\right )} \log \left (x\right ) - e^{x}}{625 \, x^{4} + 50 \, x^{2} {\left (e^{\left (2 \, e^{6}\right )} + 5\right )} - 2 \, {\left (25 \, x^{2} + e^{\left (2 \, e^{6}\right )} + 5\right )} \log \left (x\right ) + \log \left (x\right )^{2} + e^{\left (4 \, e^{6}\right )} + 10 \, e^{\left (2 \, e^{6}\right )} + 25} \]
integrate((x*log(x)^3+(-3*x*exp(exp(3)^2)^2-75*x^3-15*x)*log(x)^2+(3*x*exp (exp(3)^2)^4+(150*x^3+30*x)*exp(exp(3)^2)^2-exp(x)*x+1875*x^5+750*x^3+76*x )*log(x)-x*exp(exp(3)^2)^6+(-75*x^3-15*x)*exp(exp(3)^2)^4+(exp(x)*x-1875*x ^5-750*x^3-76*x)*exp(exp(3)^2)^2+(25*x^3-100*x^2+5*x+2)*exp(x)-15625*x^7-9 375*x^5-1800*x^3-132*x)/(x*log(x)^3+(-3*x*exp(exp(3)^2)^2-75*x^3-15*x)*log (x)^2+(3*x*exp(exp(3)^2)^4+(150*x^3+30*x)*exp(exp(3)^2)^2+1875*x^5+750*x^3 +75*x)*log(x)-x*exp(exp(3)^2)^6+(-75*x^3-15*x)*exp(exp(3)^2)^4+(-1875*x^5- 750*x^3-75*x)*exp(exp(3)^2)^2-15625*x^7-9375*x^5-1875*x^3-125*x),x, algori thm=\
(625*x^5 + 50*x^3*(e^(2*e^6) + 5) + x*log(x)^2 + x*(e^(4*e^6) + 10*e^(2*e^ 6) + 26) - 2*(25*x^3 + x*(e^(2*e^6) + 5))*log(x) - e^x)/(625*x^4 + 50*x^2* (e^(2*e^6) + 5) - 2*(25*x^2 + e^(2*e^6) + 5)*log(x) + log(x)^2 + e^(4*e^6) + 10*e^(2*e^6) + 25)
Leaf count of result is larger than twice the leaf count of optimal. 132 vs. \(2 (27) = 54\).
Time = 0.33 (sec) , antiderivative size = 132, normalized size of antiderivative = 4.40 \[ \int \frac {-132 x-e^{6 e^6} x-1800 x^3-9375 x^5-15625 x^7+e^{4 e^6} \left (-15 x-75 x^3\right )+e^x \left (2+5 x-100 x^2+25 x^3\right )+e^{2 e^6} \left (-76 x+e^x x-750 x^3-1875 x^5\right )+\left (76 x+3 e^{4 e^6} x-e^x x+750 x^3+1875 x^5+e^{2 e^6} \left (30 x+150 x^3\right )\right ) \log (x)+\left (-15 x-3 e^{2 e^6} x-75 x^3\right ) \log ^2(x)+x \log ^3(x)}{-125 x-e^{6 e^6} x-1875 x^3-9375 x^5-15625 x^7+e^{4 e^6} \left (-15 x-75 x^3\right )+e^{2 e^6} \left (-75 x-750 x^3-1875 x^5\right )+\left (75 x+3 e^{4 e^6} x+750 x^3+1875 x^5+e^{2 e^6} \left (30 x+150 x^3\right )\right ) \log (x)+\left (-15 x-3 e^{2 e^6} x-75 x^3\right ) \log ^2(x)+x \log ^3(x)} \, dx=\frac {625 \, x^{5} + 50 \, x^{3} e^{\left (2 \, e^{6}\right )} - 50 \, x^{3} \log \left (x\right ) + 250 \, x^{3} - 2 \, x e^{\left (2 \, e^{6}\right )} \log \left (x\right ) + x \log \left (x\right )^{2} + x e^{\left (4 \, e^{6}\right )} + 10 \, x e^{\left (2 \, e^{6}\right )} - 10 \, x \log \left (x\right ) + 26 \, x - e^{x}}{625 \, x^{4} + 50 \, x^{2} e^{\left (2 \, e^{6}\right )} - 50 \, x^{2} \log \left (x\right ) + 250 \, x^{2} - 2 \, e^{\left (2 \, e^{6}\right )} \log \left (x\right ) + \log \left (x\right )^{2} + e^{\left (4 \, e^{6}\right )} + 10 \, e^{\left (2 \, e^{6}\right )} - 10 \, \log \left (x\right ) + 25} \]
integrate((x*log(x)^3+(-3*x*exp(exp(3)^2)^2-75*x^3-15*x)*log(x)^2+(3*x*exp (exp(3)^2)^4+(150*x^3+30*x)*exp(exp(3)^2)^2-exp(x)*x+1875*x^5+750*x^3+76*x )*log(x)-x*exp(exp(3)^2)^6+(-75*x^3-15*x)*exp(exp(3)^2)^4+(exp(x)*x-1875*x ^5-750*x^3-76*x)*exp(exp(3)^2)^2+(25*x^3-100*x^2+5*x+2)*exp(x)-15625*x^7-9 375*x^5-1800*x^3-132*x)/(x*log(x)^3+(-3*x*exp(exp(3)^2)^2-75*x^3-15*x)*log (x)^2+(3*x*exp(exp(3)^2)^4+(150*x^3+30*x)*exp(exp(3)^2)^2+1875*x^5+750*x^3 +75*x)*log(x)-x*exp(exp(3)^2)^6+(-75*x^3-15*x)*exp(exp(3)^2)^4+(-1875*x^5- 750*x^3-75*x)*exp(exp(3)^2)^2-15625*x^7-9375*x^5-1875*x^3-125*x),x, algori thm=\
(625*x^5 + 50*x^3*e^(2*e^6) - 50*x^3*log(x) + 250*x^3 - 2*x*e^(2*e^6)*log( x) + x*log(x)^2 + x*e^(4*e^6) + 10*x*e^(2*e^6) - 10*x*log(x) + 26*x - e^x) /(625*x^4 + 50*x^2*e^(2*e^6) - 50*x^2*log(x) + 250*x^2 - 2*e^(2*e^6)*log(x ) + log(x)^2 + e^(4*e^6) + 10*e^(2*e^6) - 10*log(x) + 25)
Timed out. \[ \int \frac {-132 x-e^{6 e^6} x-1800 x^3-9375 x^5-15625 x^7+e^{4 e^6} \left (-15 x-75 x^3\right )+e^x \left (2+5 x-100 x^2+25 x^3\right )+e^{2 e^6} \left (-76 x+e^x x-750 x^3-1875 x^5\right )+\left (76 x+3 e^{4 e^6} x-e^x x+750 x^3+1875 x^5+e^{2 e^6} \left (30 x+150 x^3\right )\right ) \log (x)+\left (-15 x-3 e^{2 e^6} x-75 x^3\right ) \log ^2(x)+x \log ^3(x)}{-125 x-e^{6 e^6} x-1875 x^3-9375 x^5-15625 x^7+e^{4 e^6} \left (-15 x-75 x^3\right )+e^{2 e^6} \left (-75 x-750 x^3-1875 x^5\right )+\left (75 x+3 e^{4 e^6} x+750 x^3+1875 x^5+e^{2 e^6} \left (30 x+150 x^3\right )\right ) \log (x)+\left (-15 x-3 e^{2 e^6} x-75 x^3\right ) \log ^2(x)+x \log ^3(x)} \, dx=\int \frac {132\,x+x\,{\mathrm {e}}^{6\,{\mathrm {e}}^6}+{\ln \left (x\right )}^2\,\left (15\,x+3\,x\,{\mathrm {e}}^{2\,{\mathrm {e}}^6}+75\,x^3\right )-x\,{\ln \left (x\right )}^3-\ln \left (x\right )\,\left (76\,x+3\,x\,{\mathrm {e}}^{4\,{\mathrm {e}}^6}-x\,{\mathrm {e}}^x+750\,x^3+1875\,x^5+{\mathrm {e}}^{2\,{\mathrm {e}}^6}\,\left (150\,x^3+30\,x\right )\right )+1800\,x^3+9375\,x^5+15625\,x^7-{\mathrm {e}}^x\,\left (25\,x^3-100\,x^2+5\,x+2\right )+{\mathrm {e}}^{2\,{\mathrm {e}}^6}\,\left (76\,x-x\,{\mathrm {e}}^x+750\,x^3+1875\,x^5\right )+{\mathrm {e}}^{4\,{\mathrm {e}}^6}\,\left (75\,x^3+15\,x\right )}{125\,x+x\,{\mathrm {e}}^{6\,{\mathrm {e}}^6}+{\ln \left (x\right )}^2\,\left (15\,x+3\,x\,{\mathrm {e}}^{2\,{\mathrm {e}}^6}+75\,x^3\right )-x\,{\ln \left (x\right )}^3+{\mathrm {e}}^{2\,{\mathrm {e}}^6}\,\left (1875\,x^5+750\,x^3+75\,x\right )+1875\,x^3+9375\,x^5+15625\,x^7-\ln \left (x\right )\,\left (75\,x+3\,x\,{\mathrm {e}}^{4\,{\mathrm {e}}^6}+750\,x^3+1875\,x^5+{\mathrm {e}}^{2\,{\mathrm {e}}^6}\,\left (150\,x^3+30\,x\right )\right )+{\mathrm {e}}^{4\,{\mathrm {e}}^6}\,\left (75\,x^3+15\,x\right )} \,d x \]
int((132*x + x*exp(6*exp(6)) + log(x)^2*(15*x + 3*x*exp(2*exp(6)) + 75*x^3 ) - x*log(x)^3 - log(x)*(76*x + 3*x*exp(4*exp(6)) - x*exp(x) + 750*x^3 + 1 875*x^5 + exp(2*exp(6))*(30*x + 150*x^3)) + 1800*x^3 + 9375*x^5 + 15625*x^ 7 - exp(x)*(5*x - 100*x^2 + 25*x^3 + 2) + exp(2*exp(6))*(76*x - x*exp(x) + 750*x^3 + 1875*x^5) + exp(4*exp(6))*(15*x + 75*x^3))/(125*x + x*exp(6*exp (6)) + log(x)^2*(15*x + 3*x*exp(2*exp(6)) + 75*x^3) - x*log(x)^3 + exp(2*e xp(6))*(75*x + 750*x^3 + 1875*x^5) + 1875*x^3 + 9375*x^5 + 15625*x^7 - log (x)*(75*x + 3*x*exp(4*exp(6)) + 750*x^3 + 1875*x^5 + exp(2*exp(6))*(30*x + 150*x^3)) + exp(4*exp(6))*(15*x + 75*x^3)),x)
int((132*x + x*exp(6*exp(6)) + log(x)^2*(15*x + 3*x*exp(2*exp(6)) + 75*x^3 ) - x*log(x)^3 - log(x)*(76*x + 3*x*exp(4*exp(6)) - x*exp(x) + 750*x^3 + 1 875*x^5 + exp(2*exp(6))*(30*x + 150*x^3)) + 1800*x^3 + 9375*x^5 + 15625*x^ 7 - exp(x)*(5*x - 100*x^2 + 25*x^3 + 2) + exp(2*exp(6))*(76*x - x*exp(x) + 750*x^3 + 1875*x^5) + exp(4*exp(6))*(15*x + 75*x^3))/(125*x + x*exp(6*exp (6)) + log(x)^2*(15*x + 3*x*exp(2*exp(6)) + 75*x^3) - x*log(x)^3 + exp(2*e xp(6))*(75*x + 750*x^3 + 1875*x^5) + 1875*x^3 + 9375*x^5 + 15625*x^7 - log (x)*(75*x + 3*x*exp(4*exp(6)) + 750*x^3 + 1875*x^5 + exp(2*exp(6))*(30*x + 150*x^3)) + exp(4*exp(6))*(15*x + 75*x^3)), x)