\(\int \frac {-x^5+e^{2 (2 x-e^{25} x+x^2-x \log (x))} (-4+2 x-2 e^{25} x+4 x^2-2 x \log (x))+e^{\frac {3}{2} (2 x-e^{25} x+x^2-x \log (x))} (-12 x+6 x^2-6 e^{25} x^2+12 x^3-6 x^2 \log (x))+e^{2 x-e^{25} x+x^2-x \log (x)} (-12 x^2+6 x^3-6 e^{25} x^3+12 x^4-6 x^3 \log (x))+e^{\frac {1}{2} (2 x-e^{25} x+x^2-x \log (x))} (-4 x^3+2 x^4-2 e^{25} x^4+4 x^5-2 x^4 \log (x))}{x^5} \, dx\) [4015]

Optimal result

Integrand size = 216, antiderivative size = 31 \[ \int \frac {-x^5+e^{2 \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4+2 x-2 e^{25} x+4 x^2-2 x \log (x)\right )+e^{\frac {3}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-12 x+6 x^2-6 e^{25} x^2+12 x^3-6 x^2 \log (x)\right )+e^{2 x-e^{25} x+x^2-x \log (x)} \left (-12 x^2+6 x^3-6 e^{25} x^3+12 x^4-6 x^3 \log (x)\right )+e^{\frac {1}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4 x^3+2 x^4-2 e^{25} x^4+4 x^5-2 x^4 \log (x)\right )}{x^5} \, dx=-x+\frac {\left (e^{\frac {1}{2} x \left (2-e^{25}+x-\log (x)\right )}+x\right )^4}{x^4} \]

[Out]

(exp(1/2*x*(2-exp(25)+x-ln(x)))+x)^4/x^4-x

Rubi [F]

\[ \int \frac {-x^5+e^{2 \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4+2 x-2 e^{25} x+4 x^2-2 x \log (x)\right )+e^{\frac {3}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-12 x+6 x^2-6 e^{25} x^2+12 x^3-6 x^2 \log (x)\right )+e^{2 x-e^{25} x+x^2-x \log (x)} \left (-12 x^2+6 x^3-6 e^{25} x^3+12 x^4-6 x^3 \log (x)\right )+e^{\frac {1}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4 x^3+2 x^4-2 e^{25} x^4+4 x^5-2 x^4 \log (x)\right )}{x^5} \, dx=\int \frac {-x^5+e^{2 \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4+2 x-2 e^{25} x+4 x^2-2 x \log (x)\right )+e^{\frac {3}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-12 x+6 x^2-6 e^{25} x^2+12 x^3-6 x^2 \log (x)\right )+e^{2 x-e^{25} x+x^2-x \log (x)} \left (-12 x^2+6 x^3-6 e^{25} x^3+12 x^4-6 x^3 \log (x)\right )+e^{\frac {1}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4 x^3+2 x^4-2 e^{25} x^4+4 x^5-2 x^4 \log (x)\right )}{x^5} \, dx \]

[In]

Int[(-x^5 + E^(2*(2*x - E^25*x + x^2 - x*Log[x]))*(-4 + 2*x - 2*E^25*x + 4*x^2 - 2*x*Log[x]) + E^((3*(2*x - E^
25*x + x^2 - x*Log[x]))/2)*(-12*x + 6*x^2 - 6*E^25*x^2 + 12*x^3 - 6*x^2*Log[x]) + E^(2*x - E^25*x + x^2 - x*Lo
g[x])*(-12*x^2 + 6*x^3 - 6*E^25*x^3 + 12*x^4 - 6*x^3*Log[x]) + E^((2*x - E^25*x + x^2 - x*Log[x])/2)*(-4*x^3 +
2*x^4 - 2*E^25*x^4 + 4*x^5 - 2*x^4*Log[x]))/x^5,x]

[Out]

-x - 4*Defer[Int][E^(2*x*(2 - E^25 + x))*x^(-5 - 2*x), x] + 2*(1 - E^25)*Defer[Int][E^(2*x*(2 - E^25 + x))*x^(
-4 - 2*x), x] - 2*Log[x]*Defer[Int][E^(2*x*(2 - E^25 + x))*x^(-4 - 2*x), x] + 4*Defer[Int][E^(2*x*(2 - E^25 +
x))*x^(-3 - 2*x), x] - 12*Defer[Int][E^((3*x*(2 - E^25 + x))/2)*x^(-4 - (3*x)/2), x] + 6*(1 - E^25)*Defer[Int]
[E^((3*x*(2 - E^25 + x))/2)*x^(-3 - (3*x)/2), x] - 6*Log[x]*Defer[Int][E^((3*x*(2 - E^25 + x))/2)*x^(-3 - (3*x
)/2), x] + 12*Defer[Int][E^((3*x*(2 - E^25 + x))/2)*x^(-2 - (3*x)/2), x] - 12*Defer[Int][E^((2 - E^25)*x + x^2
)*x^(-3 - x), x] + 6*(1 - E^25)*Defer[Int][E^((2 - E^25)*x + x^2)*x^(-2 - x), x] - 6*Log[x]*Defer[Int][E^((2 -
E^25)*x + x^2)*x^(-2 - x), x] + 12*Defer[Int][E^((2 - E^25)*x + x^2)*x^(-1 - x), x] - 4*Defer[Int][E^((x*(2 -
E^25 + x))/2)*x^(-2 - x/2), x] + 2*(1 - E^25)*Defer[Int][E^((x*(2 - E^25 + x))/2)*x^(-1 - x/2), x] - 2*Log[x]
*Defer[Int][E^((x*(2 - E^25 + x))/2)*x^(-1 - x/2), x] + 4*Defer[Int][E^((x*(2 - E^25 + x))/2)/x^(x/2), x] + 2*
Defer[Int][Defer[Int][E^(2*x*(2 - E^25 + x))*x^(-4 - 2*x), x]/x, x] + 6*Defer[Int][Defer[Int][E^((3*x*(2 - E^2
5 + x))/2)*x^(-3 - (3*x)/2), x]/x, x] + 6*Defer[Int][Defer[Int][E^((2 - E^25)*x + x^2)*x^(-2 - x), x]/x, x] +
2*Defer[Int][Defer[Int][E^((x*(2 - E^25 + x))/2)*x^(-1 - x/2), x]/x, x]

Rubi steps \begin{align*} \text {integral}& = \int \left (-1+2 e^{2 x \left (2-e^{25}+x\right )} x^{-5-2 x} \left (-2+\left (1-e^{25}\right ) x+2 x^2-x \log (x)\right )+6 e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-4-\frac {3 x}{2}} \left (-2+\left (1-e^{25}\right ) x+2 x^2-x \log (x)\right )+6 e^{\left (2-e^{25}\right ) x+x^2} x^{-3-x} \left (-2+\left (1-e^{25}\right ) x+2 x^2-x \log (x)\right )+2 e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-2-\frac {x}{2}} \left (-2+\left (1-e^{25}\right ) x+2 x^2-x \log (x)\right )\right ) \, dx \\ & = -x+2 \int e^{2 x \left (2-e^{25}+x\right )} x^{-5-2 x} \left (-2+\left (1-e^{25}\right ) x+2 x^2-x \log (x)\right ) \, dx+2 \int e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-2-\frac {x}{2}} \left (-2+\left (1-e^{25}\right ) x+2 x^2-x \log (x)\right ) \, dx+6 \int e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-4-\frac {3 x}{2}} \left (-2+\left (1-e^{25}\right ) x+2 x^2-x \log (x)\right ) \, dx+6 \int e^{\left (2-e^{25}\right ) x+x^2} x^{-3-x} \left (-2+\left (1-e^{25}\right ) x+2 x^2-x \log (x)\right ) \, dx \\ & = -x+2 \int \left (-2 e^{2 x \left (2-e^{25}+x\right )} x^{-5-2 x}+e^{2 x \left (2-e^{25}+x\right )} \left (1-e^{25}\right ) x^{-4-2 x}+2 e^{2 x \left (2-e^{25}+x\right )} x^{-3-2 x}-e^{2 x \left (2-e^{25}+x\right )} x^{-4-2 x} \log (x)\right ) \, dx+2 \int \left (-2 e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-2-\frac {x}{2}}+e^{\frac {1}{2} x \left (2-e^{25}+x\right )} \left (1-e^{25}\right ) x^{-1-\frac {x}{2}}+2 e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-x/2}-e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-1-\frac {x}{2}} \log (x)\right ) \, dx+6 \int \left (-2 e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-4-\frac {3 x}{2}}+e^{\frac {3}{2} x \left (2-e^{25}+x\right )} \left (1-e^{25}\right ) x^{-3-\frac {3 x}{2}}+2 e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-2-\frac {3 x}{2}}-e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-3-\frac {3 x}{2}} \log (x)\right ) \, dx+6 \int \left (-2 e^{\left (2-e^{25}\right ) x+x^2} x^{-3-x}+e^{\left (2-e^{25}\right ) x+x^2} \left (1-e^{25}\right ) x^{-2-x}+2 e^{\left (2-e^{25}\right ) x+x^2} x^{-1-x}-e^{\left (2-e^{25}\right ) x+x^2} x^{-2-x} \log (x)\right ) \, dx \\ & = -x-2 \int e^{2 x \left (2-e^{25}+x\right )} x^{-4-2 x} \log (x) \, dx-2 \int e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-1-\frac {x}{2}} \log (x) \, dx-4 \int e^{2 x \left (2-e^{25}+x\right )} x^{-5-2 x} \, dx+4 \int e^{2 x \left (2-e^{25}+x\right )} x^{-3-2 x} \, dx-4 \int e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-2-\frac {x}{2}} \, dx+4 \int e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-x/2} \, dx-6 \int e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-3-\frac {3 x}{2}} \log (x) \, dx-6 \int e^{\left (2-e^{25}\right ) x+x^2} x^{-2-x} \log (x) \, dx-12 \int e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-4-\frac {3 x}{2}} \, dx+12 \int e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-2-\frac {3 x}{2}} \, dx-12 \int e^{\left (2-e^{25}\right ) x+x^2} x^{-3-x} \, dx+12 \int e^{\left (2-e^{25}\right ) x+x^2} x^{-1-x} \, dx+\left (2 \left (1-e^{25}\right )\right ) \int e^{2 x \left (2-e^{25}+x\right )} x^{-4-2 x} \, dx+\left (2 \left (1-e^{25}\right )\right ) \int e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-1-\frac {x}{2}} \, dx+\left (6 \left (1-e^{25}\right )\right ) \int e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-3-\frac {3 x}{2}} \, dx+\left (6 \left (1-e^{25}\right )\right ) \int e^{\left (2-e^{25}\right ) x+x^2} x^{-2-x} \, dx \\ & = -x+2 \int \frac {\int e^{2 x \left (2-e^{25}+x\right )} x^{-4-2 x} \, dx}{x} \, dx+2 \int \frac {\int e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-1-\frac {x}{2}} \, dx}{x} \, dx-4 \int e^{2 x \left (2-e^{25}+x\right )} x^{-5-2 x} \, dx+4 \int e^{2 x \left (2-e^{25}+x\right )} x^{-3-2 x} \, dx-4 \int e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-2-\frac {x}{2}} \, dx+4 \int e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-x/2} \, dx+6 \int \frac {\int e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-3-\frac {3 x}{2}} \, dx}{x} \, dx+6 \int \frac {\int e^{\left (2-e^{25}\right ) x+x^2} x^{-2-x} \, dx}{x} \, dx-12 \int e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-4-\frac {3 x}{2}} \, dx+12 \int e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-2-\frac {3 x}{2}} \, dx-12 \int e^{\left (2-e^{25}\right ) x+x^2} x^{-3-x} \, dx+12 \int e^{\left (2-e^{25}\right ) x+x^2} x^{-1-x} \, dx+\left (2 \left (1-e^{25}\right )\right ) \int e^{2 x \left (2-e^{25}+x\right )} x^{-4-2 x} \, dx+\left (2 \left (1-e^{25}\right )\right ) \int e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-1-\frac {x}{2}} \, dx+\left (6 \left (1-e^{25}\right )\right ) \int e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-3-\frac {3 x}{2}} \, dx+\left (6 \left (1-e^{25}\right )\right ) \int e^{\left (2-e^{25}\right ) x+x^2} x^{-2-x} \, dx-(2 \log (x)) \int e^{2 x \left (2-e^{25}+x\right )} x^{-4-2 x} \, dx-(2 \log (x)) \int e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-1-\frac {x}{2}} \, dx-(6 \log (x)) \int e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-3-\frac {3 x}{2}} \, dx-(6 \log (x)) \int e^{\left (2-e^{25}\right ) x+x^2} x^{-2-x} \, dx \\ \end{align*}

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(113\) vs. \(2(31)=62\).

Time = 4.34 (sec) , antiderivative size = 113, normalized size of antiderivative = 3.65 \[ \int \frac {-x^5+e^{2 \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4+2 x-2 e^{25} x+4 x^2-2 x \log (x)\right )+e^{\frac {3}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-12 x+6 x^2-6 e^{25} x^2+12 x^3-6 x^2 \log (x)\right )+e^{2 x-e^{25} x+x^2-x \log (x)} \left (-12 x^2+6 x^3-6 e^{25} x^3+12 x^4-6 x^3 \log (x)\right )+e^{\frac {1}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4 x^3+2 x^4-2 e^{25} x^4+4 x^5-2 x^4 \log (x)\right )}{x^5} \, dx=-x+e^{-2 \left (-2+e^{25}\right ) x+2 x^2} x^{-4-2 x}+4 e^{-\frac {3}{2} \left (-2+e^{25}\right ) x+\frac {3 x^2}{2}} x^{-3-\frac {3 x}{2}}+6 e^{-\left (\left (-2+e^{25}\right ) x\right )+x^2} x^{-2-x}+4 e^{-\frac {1}{2} \left (-2+e^{25}\right ) x+\frac {x^2}{2}} x^{-1-\frac {x}{2}} \]

[In]

Integrate[(-x^5 + E^(2*(2*x - E^25*x + x^2 - x*Log[x]))*(-4 + 2*x - 2*E^25*x + 4*x^2 - 2*x*Log[x]) + E^((3*(2*
x - E^25*x + x^2 - x*Log[x]))/2)*(-12*x + 6*x^2 - 6*E^25*x^2 + 12*x^3 - 6*x^2*Log[x]) + E^(2*x - E^25*x + x^2
- x*Log[x])*(-12*x^2 + 6*x^3 - 6*E^25*x^3 + 12*x^4 - 6*x^3*Log[x]) + E^((2*x - E^25*x + x^2 - x*Log[x])/2)*(-4
*x^3 + 2*x^4 - 2*E^25*x^4 + 4*x^5 - 2*x^4*Log[x]))/x^5,x]

[Out]

-x + E^(-2*(-2 + E^25)*x + 2*x^2)*x^(-4 - 2*x) + 4*E^((-3*(-2 + E^25)*x)/2 + (3*x^2)/2)*x^(-3 - (3*x)/2) + 6*E
^(-((-2 + E^25)*x) + x^2)*x^(-2 - x) + 4*E^(-1/2*((-2 + E^25)*x) + x^2/2)*x^(-1 - x/2)

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(81\) vs. \(2(27)=54\).

Time = 2.49 (sec) , antiderivative size = 82, normalized size of antiderivative = 2.65

method	result	size
parallelrisch	\(\frac {-x^{5}+4 \,{\mathrm e}^{-\frac {x \left (\ln \left (x \right )+{\mathrm e}^{25}-x -2\right )}{2}} x^{3}+6 \,{\mathrm e}^{-x \left (\ln \left (x \right )+{\mathrm e}^{25}-x -2\right )} x^{2}+4 \,{\mathrm e}^{-\frac {3 x \left (\ln \left (x \right )+{\mathrm e}^{25}-x -2\right )}{2}} x +{\mathrm e}^{-2 x \left (\ln \left (x \right )+{\mathrm e}^{25}-x -2\right )}}{x^{4}}\)	\(82\)
risch	\(-x +\frac {x^{-2 x} {\mathrm e}^{-2 x \left ({\mathrm e}^{25}-x -2\right )}}{x^{4}}+\frac {4 x^{-\frac {3 x}{2}} {\mathrm e}^{-\frac {3 x \left ({\mathrm e}^{25}-x -2\right )}{2}}}{x^{3}}+\frac {6 x^{-x} {\mathrm e}^{-x \left ({\mathrm e}^{25}-x -2\right )}}{x^{2}}+\frac {4 x^{-\frac {x}{2}} {\mathrm e}^{-\frac {x \left ({\mathrm e}^{25}-x -2\right )}{2}}}{x}\)	\(94\)

[In]

int(((-2*x*ln(x)-2*x*exp(25)+4*x^2+2*x-4)*exp(-1/2*x*ln(x)-1/2*x*exp(25)+1/2*x^2+x)^4+(-6*x^2*ln(x)-6*x^2*exp(
25)+12*x^3+6*x^2-12*x)*exp(-1/2*x*ln(x)-1/2*x*exp(25)+1/2*x^2+x)^3+(-6*x^3*ln(x)-6*x^3*exp(25)+12*x^4+6*x^3-12
*x^2)*exp(-1/2*x*ln(x)-1/2*x*exp(25)+1/2*x^2+x)^2+(-2*x^4*ln(x)-2*x^4*exp(25)+4*x^5+2*x^4-4*x^3)*exp(-1/2*x*ln
(x)-1/2*x*exp(25)+1/2*x^2+x)-x^5)/x^5,x,method=_RETURNVERBOSE)

[Out]

1/x^4*(-x^5+4*exp(-1/2*x*(ln(x)+exp(25)-x-2))*x^3+6*exp(-1/2*x*(ln(x)+exp(25)-x-2))^2*x^2+4*exp(-1/2*x*(ln(x)+
exp(25)-x-2))^3*x+exp(-1/2*x*(ln(x)+exp(25)-x-2))^4)

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 100 vs. \(2 (27) = 54\).

Time = 0.26 (sec) , antiderivative size = 100, normalized size of antiderivative = 3.23 \[ \int \frac {-x^5+e^{2 \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4+2 x-2 e^{25} x+4 x^2-2 x \log (x)\right )+e^{\frac {3}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-12 x+6 x^2-6 e^{25} x^2+12 x^3-6 x^2 \log (x)\right )+e^{2 x-e^{25} x+x^2-x \log (x)} \left (-12 x^2+6 x^3-6 e^{25} x^3+12 x^4-6 x^3 \log (x)\right )+e^{\frac {1}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4 x^3+2 x^4-2 e^{25} x^4+4 x^5-2 x^4 \log (x)\right )}{x^5} \, dx=-\frac {x^{5} - 4 \, x^{3} e^{\left (\frac {1}{2} \, x^{2} - \frac {1}{2} \, x e^{25} - \frac {1}{2} \, x \log \left (x\right ) + x\right )} - 6 \, x^{2} e^{\left (x^{2} - x e^{25} - x \log \left (x\right ) + 2 \, x\right )} - 4 \, x e^{\left (\frac {3}{2} \, x^{2} - \frac {3}{2} \, x e^{25} - \frac {3}{2} \, x \log \left (x\right ) + 3 \, x\right )} - e^{\left (2 \, x^{2} - 2 \, x e^{25} - 2 \, x \log \left (x\right ) + 4 \, x\right )}}{x^{4}} \]

[In]

integrate(((-2*x*log(x)-2*x*exp(25)+4*x^2+2*x-4)*exp(-1/2*x*log(x)-1/2*x*exp(25)+1/2*x^2+x)^4+(-6*x^2*log(x)-6
*x^2*exp(25)+12*x^3+6*x^2-12*x)*exp(-1/2*x*log(x)-1/2*x*exp(25)+1/2*x^2+x)^3+(-6*x^3*log(x)-6*x^3*exp(25)+12*x
^4+6*x^3-12*x^2)*exp(-1/2*x*log(x)-1/2*x*exp(25)+1/2*x^2+x)^2+(-2*x^4*log(x)-2*x^4*exp(25)+4*x^5+2*x^4-4*x^3)*
exp(-1/2*x*log(x)-1/2*x*exp(25)+1/2*x^2+x)-x^5)/x^5,x, algorithm="fricas")

[Out]

-(x^5 - 4*x^3*e^(1/2*x^2 - 1/2*x*e^25 - 1/2*x*log(x) + x) - 6*x^2*e^(x^2 - x*e^25 - x*log(x) + 2*x) - 4*x*e^(3
/2*x^2 - 3/2*x*e^25 - 3/2*x*log(x) + 3*x) - e^(2*x^2 - 2*x*e^25 - 2*x*log(x) + 4*x))/x^4

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 116 vs. \(2 (22) = 44\).

Time = 0.23 (sec) , antiderivative size = 116, normalized size of antiderivative = 3.74 \[ \int \frac {-x^5+e^{2 \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4+2 x-2 e^{25} x+4 x^2-2 x \log (x)\right )+e^{\frac {3}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-12 x+6 x^2-6 e^{25} x^2+12 x^3-6 x^2 \log (x)\right )+e^{2 x-e^{25} x+x^2-x \log (x)} \left (-12 x^2+6 x^3-6 e^{25} x^3+12 x^4-6 x^3 \log (x)\right )+e^{\frac {1}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4 x^3+2 x^4-2 e^{25} x^4+4 x^5-2 x^4 \log (x)\right )}{x^5} \, dx=- x + \frac {4 x^{9} e^{\frac {x^{2}}{2} - \frac {x \log {\left (x \right )}}{2} - \frac {x e^{25}}{2} + x} + 6 x^{8} e^{x^{2} - x \log {\left (x \right )} - x e^{25} + 2 x} + 4 x^{7} e^{\frac {3 x^{2}}{2} - \frac {3 x \log {\left (x \right )}}{2} - \frac {3 x e^{25}}{2} + 3 x} + x^{6} e^{2 x^{2} - 2 x \log {\left (x \right )} - 2 x e^{25} + 4 x}}{x^{10}} \]

[In]

integrate(((-2*x*ln(x)-2*x*exp(25)+4*x**2+2*x-4)*exp(-1/2*x*ln(x)-1/2*x*exp(25)+1/2*x**2+x)**4+(-6*x**2*ln(x)-
6*x**2*exp(25)+12*x**3+6*x**2-12*x)*exp(-1/2*x*ln(x)-1/2*x*exp(25)+1/2*x**2+x)**3+(-6*x**3*ln(x)-6*x**3*exp(25
)+12*x**4+6*x**3-12*x**2)*exp(-1/2*x*ln(x)-1/2*x*exp(25)+1/2*x**2+x)**2+(-2*x**4*ln(x)-2*x**4*exp(25)+4*x**5+2
*x**4-4*x**3)*exp(-1/2*x*ln(x)-1/2*x*exp(25)+1/2*x**2+x)-x**5)/x**5,x)

[Out]

-x + (4*x**9*exp(x**2/2 - x*log(x)/2 - x*exp(25)/2 + x) + 6*x**8*exp(x**2 - x*log(x) - x*exp(25) + 2*x) + 4*x*
*7*exp(3*x**2/2 - 3*x*log(x)/2 - 3*x*exp(25)/2 + 3*x) + x**6*exp(2*x**2 - 2*x*log(x) - 2*x*exp(25) + 4*x))/x**
10

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 99 vs. \(2 (27) = 54\).

Time = 0.29 (sec) , antiderivative size = 99, normalized size of antiderivative = 3.19 \[ \int \frac {-x^5+e^{2 \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4+2 x-2 e^{25} x+4 x^2-2 x \log (x)\right )+e^{\frac {3}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-12 x+6 x^2-6 e^{25} x^2+12 x^3-6 x^2 \log (x)\right )+e^{2 x-e^{25} x+x^2-x \log (x)} \left (-12 x^2+6 x^3-6 e^{25} x^3+12 x^4-6 x^3 \log (x)\right )+e^{\frac {1}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4 x^3+2 x^4-2 e^{25} x^4+4 x^5-2 x^4 \log (x)\right )}{x^5} \, dx=-x + \frac {4 \, x^{3} e^{\left (\frac {1}{2} \, x^{2} - \frac {1}{2} \, x e^{25} + \frac {3}{2} \, x \log \left (x\right ) + x\right )} + 6 \, x^{2} e^{\left (x^{2} - x e^{25} + x \log \left (x\right ) + 2 \, x\right )} + 4 \, x e^{\left (\frac {3}{2} \, x^{2} - \frac {3}{2} \, x e^{25} + \frac {1}{2} \, x \log \left (x\right ) + 3 \, x\right )} + e^{\left (2 \, x^{2} - 2 \, x e^{25} + 4 \, x\right )}}{x^{4} x^{2 \, x}} \]

[In]

integrate(((-2*x*log(x)-2*x*exp(25)+4*x^2+2*x-4)*exp(-1/2*x*log(x)-1/2*x*exp(25)+1/2*x^2+x)^4+(-6*x^2*log(x)-6
*x^2*exp(25)+12*x^3+6*x^2-12*x)*exp(-1/2*x*log(x)-1/2*x*exp(25)+1/2*x^2+x)^3+(-6*x^3*log(x)-6*x^3*exp(25)+12*x
^4+6*x^3-12*x^2)*exp(-1/2*x*log(x)-1/2*x*exp(25)+1/2*x^2+x)^2+(-2*x^4*log(x)-2*x^4*exp(25)+4*x^5+2*x^4-4*x^3)*
exp(-1/2*x*log(x)-1/2*x*exp(25)+1/2*x^2+x)-x^5)/x^5,x, algorithm="maxima")

[Out]

-x + (4*x^3*e^(1/2*x^2 - 1/2*x*e^25 + 3/2*x*log(x) + x) + 6*x^2*e^(x^2 - x*e^25 + x*log(x) + 2*x) + 4*x*e^(3/2
*x^2 - 3/2*x*e^25 + 1/2*x*log(x) + 3*x) + e^(2*x^2 - 2*x*e^25 + 4*x))/(x^4*x^(2*x))

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 100 vs. \(2 (27) = 54\).

Time = 0.37 (sec) , antiderivative size = 100, normalized size of antiderivative = 3.23 \[ \int \frac {-x^5+e^{2 \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4+2 x-2 e^{25} x+4 x^2-2 x \log (x)\right )+e^{\frac {3}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-12 x+6 x^2-6 e^{25} x^2+12 x^3-6 x^2 \log (x)\right )+e^{2 x-e^{25} x+x^2-x \log (x)} \left (-12 x^2+6 x^3-6 e^{25} x^3+12 x^4-6 x^3 \log (x)\right )+e^{\frac {1}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4 x^3+2 x^4-2 e^{25} x^4+4 x^5-2 x^4 \log (x)\right )}{x^5} \, dx=-\frac {x^{5} - 4 \, x^{3} e^{\left (\frac {1}{2} \, x^{2} - \frac {1}{2} \, x e^{25} - \frac {1}{2} \, x \log \left (x\right ) + x\right )} - 6 \, x^{2} e^{\left (x^{2} - x e^{25} - x \log \left (x\right ) + 2 \, x\right )} - 4 \, x e^{\left (\frac {3}{2} \, x^{2} - \frac {3}{2} \, x e^{25} - \frac {3}{2} \, x \log \left (x\right ) + 3 \, x\right )} - e^{\left (2 \, x^{2} - 2 \, x e^{25} - 2 \, x \log \left (x\right ) + 4 \, x\right )}}{x^{4}} \]

[In]

integrate(((-2*x*log(x)-2*x*exp(25)+4*x^2+2*x-4)*exp(-1/2*x*log(x)-1/2*x*exp(25)+1/2*x^2+x)^4+(-6*x^2*log(x)-6
*x^2*exp(25)+12*x^3+6*x^2-12*x)*exp(-1/2*x*log(x)-1/2*x*exp(25)+1/2*x^2+x)^3+(-6*x^3*log(x)-6*x^3*exp(25)+12*x
^4+6*x^3-12*x^2)*exp(-1/2*x*log(x)-1/2*x*exp(25)+1/2*x^2+x)^2+(-2*x^4*log(x)-2*x^4*exp(25)+4*x^5+2*x^4-4*x^3)*
exp(-1/2*x*log(x)-1/2*x*exp(25)+1/2*x^2+x)-x^5)/x^5,x, algorithm="giac")

[Out]

-(x^5 - 4*x^3*e^(1/2*x^2 - 1/2*x*e^25 - 1/2*x*log(x) + x) - 6*x^2*e^(x^2 - x*e^25 - x*log(x) + 2*x) - 4*x*e^(3
/2*x^2 - 3/2*x*e^25 - 3/2*x*log(x) + 3*x) - e^(2*x^2 - 2*x*e^25 - 2*x*log(x) + 4*x))/x^4

Mupad [B] (verification not implemented)

Time = 10.25 (sec) , antiderivative size = 101, normalized size of antiderivative = 3.26 \[ \int \frac {-x^5+e^{2 \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4+2 x-2 e^{25} x+4 x^2-2 x \log (x)\right )+e^{\frac {3}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-12 x+6 x^2-6 e^{25} x^2+12 x^3-6 x^2 \log (x)\right )+e^{2 x-e^{25} x+x^2-x \log (x)} \left (-12 x^2+6 x^3-6 e^{25} x^3+12 x^4-6 x^3 \log (x)\right )+e^{\frac {1}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4 x^3+2 x^4-2 e^{25} x^4+4 x^5-2 x^4 \log (x)\right )}{x^5} \, dx=\frac {4\,{\mathrm {e}}^{3\,x-\frac {3\,x\,{\mathrm {e}}^{25}}{2}-\frac {3\,x\,\ln \left (x\right )}{2}+\frac {3\,x^2}{2}}}{x^3}-x+\frac {4\,{\mathrm {e}}^{x-\frac {x\,{\mathrm {e}}^{25}}{2}-\frac {x\,\ln \left (x\right )}{2}+\frac {x^2}{2}}}{x}+\frac {6\,{\mathrm {e}}^{2\,x-x\,{\mathrm {e}}^{25}+x^2}}{x^x\,x^2}+\frac {{\mathrm {e}}^{4\,x-2\,x\,{\mathrm {e}}^{25}+2\,x^2}}{x^{2\,x}\,x^4} \]

[In]

int(-(exp(3*x - (3*x*exp(25))/2 - (3*x*log(x))/2 + (3*x^2)/2)*(12*x + 6*x^2*log(x) + 6*x^2*exp(25) - 6*x^2 - 1
2*x^3) + exp(x - (x*exp(25))/2 - (x*log(x))/2 + x^2/2)*(2*x^4*log(x) + 2*x^4*exp(25) + 4*x^3 - 2*x^4 - 4*x^5)
+ exp(2*x - x*exp(25) - x*log(x) + x^2)*(6*x^3*log(x) + 6*x^3*exp(25) + 12*x^2 - 6*x^3 - 12*x^4) + exp(4*x - 2
*x*exp(25) - 2*x*log(x) + 2*x^2)*(2*x*exp(25) - 2*x + 2*x*log(x) - 4*x^2 + 4) + x^5)/x^5,x)

[Out]

(4*exp(3*x - (3*x*exp(25))/2 - (3*x*log(x))/2 + (3*x^2)/2))/x^3 - x + (4*exp(x - (x*exp(25))/2 - (x*log(x))/2
+ x^2/2))/x + (6*exp(2*x - x*exp(25) + x^2))/(x^x*x^2) + exp(4*x - 2*x*exp(25) + 2*x^2)/(x^(2*x)*x^4)