\(\int \frac {-6 e^{2+2 x} x^3+e^{\frac {e^{-2-2 x} (-4+x-x^2+\log (x))}{x^2}} (27+21 x-6 x^2+3 e^{2+2 x} x^2+6 x^3+(-6-6 x) \log (x))}{e^{2+2 x+\frac {2 e^{-2-2 x} (-4+x-x^2+\log (x))}{x^2}} x^4-2 e^{2+2 x+\frac {e^{-2-2 x} (-4+x-x^2+\log (x))}{x^2}} x^5+e^{2+2 x} x^6} \, dx\) [3961]

Optimal result

Integrand size = 153, antiderivative size = 32 \[ \int \frac {-6 e^{2+2 x} x^3+e^{\frac {e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} \left (27+21 x-6 x^2+3 e^{2+2 x} x^2+6 x^3+(-6-6 x) \log (x)\right )}{e^{2+2 x+\frac {2 e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} x^4-2 e^{2+2 x+\frac {e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} x^5+e^{2+2 x} x^6} \, dx=\frac {3}{x \left (-e^{e^{-2-2 x} \left (-1+\frac {-4+x+\log (x)}{x^2}\right )}+x\right )} \]

[Out]

3/x/(x-exp(((x+ln(x)-4)/x^2-1)/exp(2+2*x)))

Rubi [F]

\[ \int \frac {-6 e^{2+2 x} x^3+e^{\frac {e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} \left (27+21 x-6 x^2+3 e^{2+2 x} x^2+6 x^3+(-6-6 x) \log (x)\right )}{e^{2+2 x+\frac {2 e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} x^4-2 e^{2+2 x+\frac {e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} x^5+e^{2+2 x} x^6} \, dx=\int \frac {-6 e^{2+2 x} x^3+e^{\frac {e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} \left (27+21 x-6 x^2+3 e^{2+2 x} x^2+6 x^3+(-6-6 x) \log (x)\right )}{\exp \left (2+2 x+\frac {2 e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}\right ) x^4-2 \exp \left (2+2 x+\frac {e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}\right ) x^5+e^{2+2 x} x^6} \, dx \]

[In]

Int[(-6*E^(2 + 2*x)*x^3 + E^((E^(-2 - 2*x)*(-4 + x - x^2 + Log[x]))/x^2)*(27 + 21*x - 6*x^2 + 3*E^(2 + 2*x)*x^
2 + 6*x^3 + (-6 - 6*x)*Log[x]))/(E^(2 + 2*x + (2*E^(-2 - 2*x)*(-4 + x - x^2 + Log[x]))/x^2)*x^4 - 2*E^(2 + 2*x
+ (E^(-2 - 2*x)*(-4 + x - x^2 + Log[x]))/x^2)*x^5 + E^(2 + 2*x)*x^6),x]

[Out]

27*Defer[Int][E^(-2 + 2*E^(-2 - 2*x) + (8*E^(-2 - 2*x))/x^2 - 2*x)/(x^3*(E^(E^(-2 - 2*x) + (4*E^(-2 - 2*x))/x^
2)*x - E^(E^(-2 - 2*x)/x)*x^(E^(-2 - 2*x)/x^2))^2), x] - 6*Log[x]*Defer[Int][E^(-2 + 2*E^(-2 - 2*x) + (8*E^(-2
- 2*x))/x^2 - 2*x)/(x^3*(E^(E^(-2 - 2*x) + (4*E^(-2 - 2*x))/x^2)*x - E^(E^(-2 - 2*x)/x)*x^(E^(-2 - 2*x)/x^2))
^2), x] + 21*Defer[Int][E^(-2 + 2*E^(-2 - 2*x) + (8*E^(-2 - 2*x))/x^2 - 2*x)/(x^2*(E^(E^(-2 - 2*x) + (4*E^(-2
- 2*x))/x^2)*x - E^(E^(-2 - 2*x)/x)*x^(E^(-2 - 2*x)/x^2))^2), x] - 6*Log[x]*Defer[Int][E^(-2 + 2*E^(-2 - 2*x)
+ (8*E^(-2 - 2*x))/x^2 - 2*x)/(x^2*(E^(E^(-2 - 2*x) + (4*E^(-2 - 2*x))/x^2)*x - E^(E^(-2 - 2*x)/x)*x^(E^(-2 -
2*x)/x^2))^2), x] - 6*Defer[Int][E^(-2 + 2*E^(-2 - 2*x) + (8*E^(-2 - 2*x))/x^2 - 2*x)/(x*(E^(E^(-2 - 2*x) + (4
*E^(-2 - 2*x))/x^2)*x - E^(E^(-2 - 2*x)/x)*x^(E^(-2 - 2*x)/x^2))^2), x] - 3*Defer[Int][E^((2*E^(-2 - 2*x)*(4 +
x^2))/x^2)/(x*(E^(E^(-2 - 2*x) + (4*E^(-2 - 2*x))/x^2)*x - E^(E^(-2 - 2*x)/x)*x^(E^(-2 - 2*x)/x^2))^2), x] -
3*Defer[Int][E^((E^(-2 - 2*x)*(4 + x^2))/x^2)/(x^2*(E^(E^(-2 - 2*x) + (4*E^(-2 - 2*x))/x^2)*x - E^(E^(-2 - 2*x
)/x)*x^(E^(-2 - 2*x)/x^2))), x] + 6*Defer[Int][E^(-2 + 2*E^(-2 - 2*x) + (8*E^(-2 - 2*x))/x^2 - 2*x)/(-(E^(E^(-
2 - 2*x) + (4*E^(-2 - 2*x))/x^2)*x) + E^(E^(-2 - 2*x)/x)*x^(E^(-2 - 2*x)/x^2))^2, x] - 27*Defer[Int][E^(-2 - 2
*x)/(x^4*(x - x^(1/(E^(2*(1 + x))*x^2))/E^((4 - x + x^2)/(E^(2*(1 + x))*x^2)))), x] - 21*Defer[Int][E^(-2 - 2*
x)/(x^3*(x - x^(1/(E^(2*(1 + x))*x^2))/E^((4 - x + x^2)/(E^(2*(1 + x))*x^2)))), x] - 6*Defer[Int][E^(-2 - 2*x)
/(x*(x - x^(1/(E^(2*(1 + x))*x^2))/E^((4 - x + x^2)/(E^(2*(1 + x))*x^2)))), x] - 6*Log[x]*Defer[Int][E^(-2 - 2
*x)/(x^4*(-x + x^(1/(E^(2*(1 + x))*x^2))/E^((4 - x + x^2)/(E^(2*(1 + x))*x^2)))), x] - 6*Log[x]*Defer[Int][E^(
-2 - 2*x)/(x^3*(-x + x^(1/(E^(2*(1 + x))*x^2))/E^((4 - x + x^2)/(E^(2*(1 + x))*x^2)))), x] - 6*Defer[Int][E^(-
2 - 2*x)/(x^2*(-x + x^(1/(E^(2*(1 + x))*x^2))/E^((4 - x + x^2)/(E^(2*(1 + x))*x^2)))), x] + 6*Defer[Int][Defer
[Int][E^((2 + 8/x^2)/E^(2*(1 + x)) - 2*(1 + x))/(x^3*(E^((4 + x^2)/(E^(2*(1 + x))*x^2))*x - E^(1/(E^(2*(1 + x)
)*x))*x^(1/(E^(2*(1 + x))*x^2)))^2), x]/x, x] + 6*Defer[Int][Defer[Int][E^((2 + 8/x^2)/E^(2*(1 + x)) - 2*(1 +
x))/(x^2*(E^((4 + x^2)/(E^(2*(1 + x))*x^2))*x - E^(1/(E^(2*(1 + x))*x))*x^(1/(E^(2*(1 + x))*x^2)))^2), x]/x, x
] + 6*Defer[Int][Defer[Int][E^(-2 - 2*x)/(x^4*(-x + E^((-4 + x - x^2)/(E^(2*(1 + x))*x^2))*x^(1/(E^(2*(1 + x))
*x^2)))), x]/x, x] + 6*Defer[Int][Defer[Int][E^(-2 - 2*x)/(x^3*(-x + E^((-4 + x - x^2)/(E^(2*(1 + x))*x^2))*x^
(1/(E^(2*(1 + x))*x^2)))), x]/x, x]

Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {3 e^{-2+e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}-2 x} \left (9+7 x-2 x^2+e^{2+2 x} x^2+2 x^3-2 \log (x)-2 x \log (x)\right )}{x^4 \left (e^{e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}} x-e^{\frac {e^{-2-2 x}}{x}} x^{\frac {e^{-2-2 x}}{x^2}}\right )}-\frac {3 \exp \left (-2+2 e^{-2-2 x}+\frac {8 e^{-2-2 x}}{x^2}-2 x\right ) \left (-9-7 x+2 x^2+e^{2+2 x} x^2-2 x^3+2 \log (x)+2 x \log (x)\right )}{x^3 \left (e^{e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}} x-e^{\frac {e^{-2-2 x}}{x}} x^{\frac {e^{-2-2 x}}{x^2}}\right )^2}\right ) \, dx \\ & = -\left (3 \int \frac {e^{-2+e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}-2 x} \left (9+7 x-2 x^2+e^{2+2 x} x^2+2 x^3-2 \log (x)-2 x \log (x)\right )}{x^4 \left (e^{e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}} x-e^{\frac {e^{-2-2 x}}{x}} x^{\frac {e^{-2-2 x}}{x^2}}\right )} \, dx\right )-3 \int \frac {\exp \left (-2+2 e^{-2-2 x}+\frac {8 e^{-2-2 x}}{x^2}-2 x\right ) \left (-9-7 x+2 x^2+e^{2+2 x} x^2-2 x^3+2 \log (x)+2 x \log (x)\right )}{x^3 \left (e^{e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}} x-e^{\frac {e^{-2-2 x}}{x}} x^{\frac {e^{-2-2 x}}{x^2}}\right )^2} \, dx \\ & = -\left (3 \int \frac {e^{-2-2 x} \left (9+7 x+\left (-2+e^{2+2 x}\right ) x^2+2 x^3-2 (1+x) \log (x)\right )}{x^4 \left (x-e^{-\frac {e^{-2 (1+x)} \left (4-x+x^2\right )}{x^2}} x^{\frac {e^{-2 (1+x)}}{x^2}}\right )} \, dx\right )-3 \int \left (-\frac {9 \exp \left (-2+2 e^{-2-2 x}+\frac {8 e^{-2-2 x}}{x^2}-2 x\right )}{x^3 \left (e^{e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}} x-e^{\frac {e^{-2-2 x}}{x}} x^{\frac {e^{-2-2 x}}{x^2}}\right )^2}-\frac {7 \exp \left (-2+2 e^{-2-2 x}+\frac {8 e^{-2-2 x}}{x^2}-2 x\right )}{x^2 \left (e^{e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}} x-e^{\frac {e^{-2-2 x}}{x}} x^{\frac {e^{-2-2 x}}{x^2}}\right )^2}+\frac {e^{2 e^{-2-2 x}+\frac {8 e^{-2-2 x}}{x^2}}}{x \left (e^{e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}} x-e^{\frac {e^{-2-2 x}}{x}} x^{\frac {e^{-2-2 x}}{x^2}}\right )^2}+\frac {2 \exp \left (-2+2 e^{-2-2 x}+\frac {8 e^{-2-2 x}}{x^2}-2 x\right )}{x \left (e^{e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}} x-e^{\frac {e^{-2-2 x}}{x}} x^{\frac {e^{-2-2 x}}{x^2}}\right )^2}-\frac {2 \exp \left (-2+2 e^{-2-2 x}+\frac {8 e^{-2-2 x}}{x^2}-2 x\right )}{\left (-e^{e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}} x+e^{\frac {e^{-2-2 x}}{x}} x^{\frac {e^{-2-2 x}}{x^2}}\right )^2}+\frac {2 \exp \left (-2+2 e^{-2-2 x}+\frac {8 e^{-2-2 x}}{x^2}-2 x\right ) \log (x)}{x^3 \left (e^{e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}} x-e^{\frac {e^{-2-2 x}}{x}} x^{\frac {e^{-2-2 x}}{x^2}}\right )^2}+\frac {2 \exp \left (-2+2 e^{-2-2 x}+\frac {8 e^{-2-2 x}}{x^2}-2 x\right ) \log (x)}{x^2 \left (e^{e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}} x-e^{\frac {e^{-2-2 x}}{x}} x^{\frac {e^{-2-2 x}}{x^2}}\right )^2}\right ) \, dx \\ & = -\left (3 \int \frac {e^{2 e^{-2-2 x}+\frac {8 e^{-2-2 x}}{x^2}}}{x \left (e^{e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}} x-e^{\frac {e^{-2-2 x}}{x}} x^{\frac {e^{-2-2 x}}{x^2}}\right )^2} \, dx\right )-3 \int \left (\frac {9 e^{-2-2 x+\frac {e^{-2-2 x} \left (4+x^2\right )}{x^2}}}{x^4 \left (e^{e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}} x-e^{\frac {e^{-2-2 x}}{x}} x^{\frac {e^{-2-2 x}}{x^2}}\right )}+\frac {7 e^{-2-2 x+\frac {e^{-2-2 x} \left (4+x^2\right )}{x^2}}}{x^3 \left (e^{e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}} x-e^{\frac {e^{-2-2 x}}{x}} x^{\frac {e^{-2-2 x}}{x^2}}\right )}+\frac {e^{e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}}}{x^2 \left (e^{e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}} x-e^{\frac {e^{-2-2 x}}{x}} x^{\frac {e^{-2-2 x}}{x^2}}\right )}+\frac {2 e^{-2-2 x+\frac {e^{-2-2 x} \left (4+x^2\right )}{x^2}}}{x \left (e^{e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}} x-e^{\frac {e^{-2-2 x}}{x}} x^{\frac {e^{-2-2 x}}{x^2}}\right )}+\frac {2 e^{-2-2 x+\frac {e^{-2-2 x} \left (4+x^2\right )}{x^2}}}{x^2 \left (-e^{e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}} x+e^{\frac {e^{-2-2 x}}{x}} x^{\frac {e^{-2-2 x}}{x^2}}\right )}+\frac {2 e^{-2-2 x+\frac {e^{-2-2 x} \left (4+x^2\right )}{x^2}} \log (x)}{x^4 \left (-e^{e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}} x+e^{\frac {e^{-2-2 x}}{x}} x^{\frac {e^{-2-2 x}}{x^2}}\right )}+\frac {2 e^{-2-2 x+\frac {e^{-2-2 x} \left (4+x^2\right )}{x^2}} \log (x)}{x^3 \left (-e^{e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}} x+e^{\frac {e^{-2-2 x}}{x}} x^{\frac {e^{-2-2 x}}{x^2}}\right )}\right ) \, dx-6 \int \frac {e^{-2+2 e^{-2-2 x}+\frac {8 e^{-2-2 x}}{x^2}-2 x}}{x \left (e^{e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}} x-e^{\frac {e^{-2-2 x}}{x}} x^{\frac {e^{-2-2 x}}{x^2}}\right )^2} \, dx+6 \int \frac {e^{-2+2 e^{-2-2 x}+\frac {8 e^{-2-2 x}}{x^2}-2 x}}{\left (-e^{e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}} x+e^{\frac {e^{-2-2 x}}{x}} x^{\frac {e^{-2-2 x}}{x^2}}\right )^2} \, dx-6 \int \frac {e^{-2+2 e^{-2-2 x}+\frac {8 e^{-2-2 x}}{x^2}-2 x} \log (x)}{x^3 \left (e^{e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}} x-e^{\frac {e^{-2-2 x}}{x}} x^{\frac {e^{-2-2 x}}{x^2}}\right )^2} \, dx-6 \int \frac {e^{-2+2 e^{-2-2 x}+\frac {8 e^{-2-2 x}}{x^2}-2 x} \log (x)}{x^2 \left (e^{e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}} x-e^{\frac {e^{-2-2 x}}{x}} x^{\frac {e^{-2-2 x}}{x^2}}\right )^2} \, dx+21 \int \frac {e^{-2+2 e^{-2-2 x}+\frac {8 e^{-2-2 x}}{x^2}-2 x}}{x^2 \left (e^{e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}} x-e^{\frac {e^{-2-2 x}}{x}} x^{\frac {e^{-2-2 x}}{x^2}}\right )^2} \, dx+27 \int \frac {e^{-2+2 e^{-2-2 x}+\frac {8 e^{-2-2 x}}{x^2}-2 x}}{x^3 \left (e^{e^{-2-2 x}+\frac {4 e^{-2-2 x}}{x^2}} x-e^{\frac {e^{-2-2 x}}{x}} x^{\frac {e^{-2-2 x}}{x^2}}\right )^2} \, dx \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [F]

\[ \int \frac {-6 e^{2+2 x} x^3+e^{\frac {e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} \left (27+21 x-6 x^2+3 e^{2+2 x} x^2+6 x^3+(-6-6 x) \log (x)\right )}{e^{2+2 x+\frac {2 e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} x^4-2 e^{2+2 x+\frac {e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} x^5+e^{2+2 x} x^6} \, dx=\int \frac {-6 e^{2+2 x} x^3+e^{\frac {e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} \left (27+21 x-6 x^2+3 e^{2+2 x} x^2+6 x^3+(-6-6 x) \log (x)\right )}{e^{2+2 x+\frac {2 e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} x^4-2 e^{2+2 x+\frac {e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} x^5+e^{2+2 x} x^6} \, dx \]

[In]

Integrate[(-6*E^(2 + 2*x)*x^3 + E^((E^(-2 - 2*x)*(-4 + x - x^2 + Log[x]))/x^2)*(27 + 21*x - 6*x^2 + 3*E^(2 + 2
*x)*x^2 + 6*x^3 + (-6 - 6*x)*Log[x]))/(E^(2 + 2*x + (2*E^(-2 - 2*x)*(-4 + x - x^2 + Log[x]))/x^2)*x^4 - 2*E^(2
+ 2*x + (E^(-2 - 2*x)*(-4 + x - x^2 + Log[x]))/x^2)*x^5 + E^(2 + 2*x)*x^6),x]

[Out]

Integrate[(-6*E^(2 + 2*x)*x^3 + E^((E^(-2 - 2*x)*(-4 + x - x^2 + Log[x]))/x^2)*(27 + 21*x - 6*x^2 + 3*E^(2 + 2
*x)*x^2 + 6*x^3 + (-6 - 6*x)*Log[x]))/(E^(2 + 2*x + (2*E^(-2 - 2*x)*(-4 + x - x^2 + Log[x]))/x^2)*x^4 - 2*E^(2
+ 2*x + (E^(-2 - 2*x)*(-4 + x - x^2 + Log[x]))/x^2)*x^5 + E^(2 + 2*x)*x^6), x]

Maple [A] (verified)

Time = 17.29 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.03

method	result	size
risch	\(\frac {3}{x \left (x -{\mathrm e}^{\frac {\left (\ln \left (x \right )-x^{2}+x -4\right ) {\mathrm e}^{-2-2 x}}{x^{2}}}\right )}\)	\(33\)
parallelrisch	\(\frac {3}{x \left (x -{\mathrm e}^{\frac {\left (\ln \left (x \right )-x^{2}+x -4\right ) {\mathrm e}^{-2-2 x}}{x^{2}}}\right )}\)	\(35\)

[In]

int((((-6*x-6)*ln(x)+3*x^2*exp(2+2*x)+6*x^3-6*x^2+21*x+27)*exp((ln(x)-x^2+x-4)/x^2/exp(2+2*x))-6*x^3*exp(2+2*x
))/(x^4*exp(2+2*x)*exp((ln(x)-x^2+x-4)/x^2/exp(2+2*x))^2-2*x^5*exp(2+2*x)*exp((ln(x)-x^2+x-4)/x^2/exp(2+2*x))+
x^6*exp(2+2*x)),x,method=_RETURNVERBOSE)

[Out]

3/x/(x-exp((ln(x)-x^2+x-4)/x^2*exp(-2-2*x)))

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (30) = 60\).

Time = 0.27 (sec) , antiderivative size = 63, normalized size of antiderivative = 1.97 \[ \int \frac {-6 e^{2+2 x} x^3+e^{\frac {e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} \left (27+21 x-6 x^2+3 e^{2+2 x} x^2+6 x^3+(-6-6 x) \log (x)\right )}{e^{2+2 x+\frac {2 e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} x^4-2 e^{2+2 x+\frac {e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} x^5+e^{2+2 x} x^6} \, dx=\frac {3 \, e^{\left (2 \, x + 2\right )}}{x^{2} e^{\left (2 \, x + 2\right )} - x e^{\left (-\frac {{\left (x^{2} - 2 \, {\left (x^{3} + x^{2}\right )} e^{\left (2 \, x + 2\right )} - x - \log \left (x\right ) + 4\right )} e^{\left (-2 \, x - 2\right )}}{x^{2}}\right )}} \]

[In]

integrate((((-6*x-6)*log(x)+3*x^2*exp(2+2*x)+6*x^3-6*x^2+21*x+27)*exp((log(x)-x^2+x-4)/x^2/exp(2+2*x))-6*x^3*e
xp(2+2*x))/(x^4*exp(2+2*x)*exp((log(x)-x^2+x-4)/x^2/exp(2+2*x))^2-2*x^5*exp(2+2*x)*exp((log(x)-x^2+x-4)/x^2/ex
p(2+2*x))+x^6*exp(2+2*x)),x, algorithm="fricas")

[Out]

3*e^(2*x + 2)/(x^2*e^(2*x + 2) - x*e^(-(x^2 - 2*(x^3 + x^2)*e^(2*x + 2) - x - log(x) + 4)*e^(-2*x - 2)/x^2))

Sympy [A] (verification not implemented)

Time = 0.30 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.97 \[ \int \frac {-6 e^{2+2 x} x^3+e^{\frac {e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} \left (27+21 x-6 x^2+3 e^{2+2 x} x^2+6 x^3+(-6-6 x) \log (x)\right )}{e^{2+2 x+\frac {2 e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} x^4-2 e^{2+2 x+\frac {e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} x^5+e^{2+2 x} x^6} \, dx=- \frac {3}{- x^{2} + x e^{\frac {\left (- x^{2} + x + \log {\left (x \right )} - 4\right ) e^{- 2 x - 2}}{x^{2}}}} \]

[In]

integrate((((-6*x-6)*ln(x)+3*x**2*exp(2+2*x)+6*x**3-6*x**2+21*x+27)*exp((ln(x)-x**2+x-4)/x**2/exp(2+2*x))-6*x*
*3*exp(2+2*x))/(x**4*exp(2+2*x)*exp((ln(x)-x**2+x-4)/x**2/exp(2+2*x))**2-2*x**5*exp(2+2*x)*exp((ln(x)-x**2+x-4
)/x**2/exp(2+2*x))+x**6*exp(2+2*x)),x)

[Out]

-3/(-x**2 + x*exp((-x**2 + x + log(x) - 4)*exp(-2*x - 2)/x**2))

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 74 vs. \(2 (30) = 60\).

Time = 0.38 (sec) , antiderivative size = 74, normalized size of antiderivative = 2.31 \[ \int \frac {-6 e^{2+2 x} x^3+e^{\frac {e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} \left (27+21 x-6 x^2+3 e^{2+2 x} x^2+6 x^3+(-6-6 x) \log (x)\right )}{e^{2+2 x+\frac {2 e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} x^4-2 e^{2+2 x+\frac {e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} x^5+e^{2+2 x} x^6} \, dx=\frac {3 \, e^{\left (\frac {4 \, e^{\left (-2 \, x - 2\right )}}{x^{2}} + e^{\left (-2 \, x - 2\right )}\right )}}{x^{2} e^{\left (\frac {4 \, e^{\left (-2 \, x - 2\right )}}{x^{2}} + e^{\left (-2 \, x - 2\right )}\right )} - x e^{\left (\frac {e^{\left (-2 \, x - 2\right )}}{x} + \frac {e^{\left (-2 \, x - 2\right )} \log \left (x\right )}{x^{2}}\right )}} \]

[In]

integrate((((-6*x-6)*log(x)+3*x^2*exp(2+2*x)+6*x^3-6*x^2+21*x+27)*exp((log(x)-x^2+x-4)/x^2/exp(2+2*x))-6*x^3*e
xp(2+2*x))/(x^4*exp(2+2*x)*exp((log(x)-x^2+x-4)/x^2/exp(2+2*x))^2-2*x^5*exp(2+2*x)*exp((log(x)-x^2+x-4)/x^2/ex
p(2+2*x))+x^6*exp(2+2*x)),x, algorithm="maxima")

[Out]

3*e^(4*e^(-2*x - 2)/x^2 + e^(-2*x - 2))/(x^2*e^(4*e^(-2*x - 2)/x^2 + e^(-2*x - 2)) - x*e^(e^(-2*x - 2)/x + e^(
-2*x - 2)*log(x)/x^2))

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 513 vs. \(2 (30) = 60\).

Time = 0.66 (sec) , antiderivative size = 513, normalized size of antiderivative = 16.03 \[ \int \frac {-6 e^{2+2 x} x^3+e^{\frac {e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} \left (27+21 x-6 x^2+3 e^{2+2 x} x^2+6 x^3+(-6-6 x) \log (x)\right )}{e^{2+2 x+\frac {2 e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} x^4-2 e^{2+2 x+\frac {e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} x^5+e^{2+2 x} x^6} \, dx=\frac {3 \, {\left (2 \, x^{3} - x^{2} e^{\left (2 \, x + 2\right )} - 2 \, x^{2} - 2 \, x \log \left (x\right ) + 7 \, x - 2 \, \log \left (x\right ) + 9\right )}}{2 \, x^{5} - x^{4} e^{\left (2 \, x + 2\right )} - 2 \, x^{4} e^{\left (-2 \, x + \frac {2 \, x^{3} - x^{2} e^{\left (-2 \, x - 2\right )} + 2 \, x^{2} + x e^{\left (-2 \, x - 2\right )} + e^{\left (-2 \, x - 2\right )} \log \left (x\right ) - 4 \, e^{\left (-2 \, x - 2\right )}}{x^{2}} - 2\right )} - 2 \, x^{4} + 2 \, x^{3} e^{\left (-2 \, x + \frac {2 \, x^{3} - x^{2} e^{\left (-2 \, x - 2\right )} + 2 \, x^{2} + x e^{\left (-2 \, x - 2\right )} + e^{\left (-2 \, x - 2\right )} \log \left (x\right ) - 4 \, e^{\left (-2 \, x - 2\right )}}{x^{2}} - 2\right )} + x^{3} e^{\left (\frac {2 \, x^{3} - x^{2} e^{\left (-2 \, x - 2\right )} + 2 \, x^{2} + x e^{\left (-2 \, x - 2\right )} + e^{\left (-2 \, x - 2\right )} \log \left (x\right ) - 4 \, e^{\left (-2 \, x - 2\right )}}{x^{2}}\right )} - 2 \, x^{3} \log \left (x\right ) + 2 \, x^{2} e^{\left (-2 \, x + \frac {2 \, x^{3} - x^{2} e^{\left (-2 \, x - 2\right )} + 2 \, x^{2} + x e^{\left (-2 \, x - 2\right )} + e^{\left (-2 \, x - 2\right )} \log \left (x\right ) - 4 \, e^{\left (-2 \, x - 2\right )}}{x^{2}} - 2\right )} \log \left (x\right ) + 7 \, x^{3} - 7 \, x^{2} e^{\left (-2 \, x + \frac {2 \, x^{3} - x^{2} e^{\left (-2 \, x - 2\right )} + 2 \, x^{2} + x e^{\left (-2 \, x - 2\right )} + e^{\left (-2 \, x - 2\right )} \log \left (x\right ) - 4 \, e^{\left (-2 \, x - 2\right )}}{x^{2}} - 2\right )} - 2 \, x^{2} \log \left (x\right ) + 2 \, x e^{\left (-2 \, x + \frac {2 \, x^{3} - x^{2} e^{\left (-2 \, x - 2\right )} + 2 \, x^{2} + x e^{\left (-2 \, x - 2\right )} + e^{\left (-2 \, x - 2\right )} \log \left (x\right ) - 4 \, e^{\left (-2 \, x - 2\right )}}{x^{2}} - 2\right )} \log \left (x\right ) + 9 \, x^{2} - 9 \, x e^{\left (-2 \, x + \frac {2 \, x^{3} - x^{2} e^{\left (-2 \, x - 2\right )} + 2 \, x^{2} + x e^{\left (-2 \, x - 2\right )} + e^{\left (-2 \, x - 2\right )} \log \left (x\right ) - 4 \, e^{\left (-2 \, x - 2\right )}}{x^{2}} - 2\right )}} \]

[In]

integrate((((-6*x-6)*log(x)+3*x^2*exp(2+2*x)+6*x^3-6*x^2+21*x+27)*exp((log(x)-x^2+x-4)/x^2/exp(2+2*x))-6*x^3*e
xp(2+2*x))/(x^4*exp(2+2*x)*exp((log(x)-x^2+x-4)/x^2/exp(2+2*x))^2-2*x^5*exp(2+2*x)*exp((log(x)-x^2+x-4)/x^2/ex
p(2+2*x))+x^6*exp(2+2*x)),x, algorithm="giac")

[Out]

3*(2*x^3 - x^2*e^(2*x + 2) - 2*x^2 - 2*x*log(x) + 7*x - 2*log(x) + 9)/(2*x^5 - x^4*e^(2*x + 2) - 2*x^4*e^(-2*x
+ (2*x^3 - x^2*e^(-2*x - 2) + 2*x^2 + x*e^(-2*x - 2) + e^(-2*x - 2)*log(x) - 4*e^(-2*x - 2))/x^2 - 2) - 2*x^4
+ 2*x^3*e^(-2*x + (2*x^3 - x^2*e^(-2*x - 2) + 2*x^2 + x*e^(-2*x - 2) + e^(-2*x - 2)*log(x) - 4*e^(-2*x - 2))/
x^2 - 2) + x^3*e^((2*x^3 - x^2*e^(-2*x - 2) + 2*x^2 + x*e^(-2*x - 2) + e^(-2*x - 2)*log(x) - 4*e^(-2*x - 2))/x
^2) - 2*x^3*log(x) + 2*x^2*e^(-2*x + (2*x^3 - x^2*e^(-2*x - 2) + 2*x^2 + x*e^(-2*x - 2) + e^(-2*x - 2)*log(x)
- 4*e^(-2*x - 2))/x^2 - 2)*log(x) + 7*x^3 - 7*x^2*e^(-2*x + (2*x^3 - x^2*e^(-2*x - 2) + 2*x^2 + x*e^(-2*x - 2)
+ e^(-2*x - 2)*log(x) - 4*e^(-2*x - 2))/x^2 - 2) - 2*x^2*log(x) + 2*x*e^(-2*x + (2*x^3 - x^2*e^(-2*x - 2) + 2
*x^2 + x*e^(-2*x - 2) + e^(-2*x - 2)*log(x) - 4*e^(-2*x - 2))/x^2 - 2)*log(x) + 9*x^2 - 9*x*e^(-2*x + (2*x^3 -
x^2*e^(-2*x - 2) + 2*x^2 + x*e^(-2*x - 2) + e^(-2*x - 2)*log(x) - 4*e^(-2*x - 2))/x^2 - 2))

Mupad [B] (verification not implemented)

Time = 9.47 (sec) , antiderivative size = 214, normalized size of antiderivative = 6.69 \[ \int \frac {-6 e^{2+2 x} x^3+e^{\frac {e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} \left (27+21 x-6 x^2+3 e^{2+2 x} x^2+6 x^3+(-6-6 x) \log (x)\right )}{e^{2+2 x+\frac {2 e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} x^4-2 e^{2+2 x+\frac {e^{-2-2 x} \left (-4+x-x^2+\log (x)\right )}{x^2}} x^5+e^{2+2 x} x^6} \, dx=-\frac {x^4\,\left (21\,{\mathrm {e}}^{2\,x+2}-6\,{\mathrm {e}}^{2\,x+2}\,\ln \left (x\right )\right )+x^3\,\left (27\,{\mathrm {e}}^{2\,x+2}-6\,{\mathrm {e}}^{2\,x+2}\,\ln \left (x\right )\right )-x^5\,\left (6\,{\mathrm {e}}^{2\,x+2}+3\,{\mathrm {e}}^{4\,x+4}\right )+6\,x^6\,{\mathrm {e}}^{2\,x+2}}{\left (x-x^{\frac {{\mathrm {e}}^{-2\,x-2}}{x^2}}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{-2}}{x}-{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{-2}-\frac {4\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{-2}}{x^2}}\right )\,\left (2\,x^6\,{\mathrm {e}}^{2\,x+2}-7\,x^5\,{\mathrm {e}}^{2\,x+2}-9\,x^4\,{\mathrm {e}}^{2\,x+2}-2\,x^7\,{\mathrm {e}}^{2\,x+2}+x^6\,{\mathrm {e}}^{4\,x+4}+2\,x^4\,{\mathrm {e}}^{2\,x+2}\,\ln \left (x\right )+2\,x^5\,{\mathrm {e}}^{2\,x+2}\,\ln \left (x\right )\right )} \]

[In]

int((exp((exp(- 2*x - 2)*(x + log(x) - x^2 - 4))/x^2)*(21*x - log(x)*(6*x + 6) + 3*x^2*exp(2*x + 2) - 6*x^2 +
6*x^3 + 27) - 6*x^3*exp(2*x + 2))/(x^6*exp(2*x + 2) - 2*x^5*exp((exp(- 2*x - 2)*(x + log(x) - x^2 - 4))/x^2)*e
xp(2*x + 2) + x^4*exp((2*exp(- 2*x - 2)*(x + log(x) - x^2 - 4))/x^2)*exp(2*x + 2)),x)

[Out]

-(x^4*(21*exp(2*x + 2) - 6*exp(2*x + 2)*log(x)) + x^3*(27*exp(2*x + 2) - 6*exp(2*x + 2)*log(x)) - x^5*(6*exp(2
*x + 2) + 3*exp(4*x + 4)) + 6*x^6*exp(2*x + 2))/((x - x^(exp(- 2*x - 2)/x^2)*exp((exp(-2*x)*exp(-2))/x - exp(-
2*x)*exp(-2) - (4*exp(-2*x)*exp(-2))/x^2))*(2*x^6*exp(2*x + 2) - 7*x^5*exp(2*x + 2) - 9*x^4*exp(2*x + 2) - 2*x
^7*exp(2*x + 2) + x^6*exp(4*x + 4) + 2*x^4*exp(2*x + 2)*log(x) + 2*x^5*exp(2*x + 2)*log(x)))