\(\int \frac {e^{-2+\frac {e^{-2-2 x} (7744 e^2+e^x (-704 e-704 e^{2+\frac {2}{x}})+e^{2 x} (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}))}{x^2}-2 x} (e^{2 x} (e^{1+\frac {2}{x}} (-64-64 x)+e^{2+\frac {4}{x}} (-64-32 x)-32 x)+e^2 (-15488 x-15488 x^2)+e^x (e (1408 x+704 x^2)+e^{2+\frac {2}{x}} (1408+1408 x+704 x^2)))}{x^4} \, dx\) [3841]

Optimal result

Integrand size = 167, antiderivative size = 31 \[ \int \frac {e^{-2+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x} \left (e^{2 x} \left (e^{1+\frac {2}{x}} (-64-64 x)+e^{2+\frac {4}{x}} (-64-32 x)-32 x\right )+e^2 \left (-15488 x-15488 x^2\right )+e^x \left (e \left (1408 x+704 x^2\right )+e^{2+\frac {2}{x}} \left (1408+1408 x+704 x^2\right )\right )\right )}{x^4} \, dx=e^{\frac {16 \left (-\frac {1}{e}-e^{2/x}+22 e^{-x}\right )^2}{x^2}} \]

[Out]

exp(16*(22/exp(x)-1/exp(1)-exp(2/x))^2/x^2)

Rubi [F]

\[ \int \frac {e^{-2+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x} \left (e^{2 x} \left (e^{1+\frac {2}{x}} (-64-64 x)+e^{2+\frac {4}{x}} (-64-32 x)-32 x\right )+e^2 \left (-15488 x-15488 x^2\right )+e^x \left (e \left (1408 x+704 x^2\right )+e^{2+\frac {2}{x}} \left (1408+1408 x+704 x^2\right )\right )\right )}{x^4} \, dx=\int \frac {\exp \left (-2+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x\right ) \left (e^{2 x} \left (e^{1+\frac {2}{x}} (-64-64 x)+e^{2+\frac {4}{x}} (-64-32 x)-32 x\right )+e^2 \left (-15488 x-15488 x^2\right )+e^x \left (e \left (1408 x+704 x^2\right )+e^{2+\frac {2}{x}} \left (1408+1408 x+704 x^2\right )\right )\right )}{x^4} \, dx \]

[In]

Int[(E^(-2 + (E^(-2 - 2*x)*(7744*E^2 + E^x*(-704*E - 704*E^(2 + 2/x)) + E^(2*x)*(16 + 32*E^(1 + 2/x) + 16*E^(2
+ 4/x))))/x^2 - 2*x)*(E^(2*x)*(E^(1 + 2/x)*(-64 - 64*x) + E^(2 + 4/x)*(-64 - 32*x) - 32*x) + E^2*(-15488*x -
15488*x^2) + E^x*(E*(1408*x + 704*x^2) + E^(2 + 2/x)*(1408 + 1408*x + 704*x^2))))/x^4,x]

[Out]

-64*Defer[Int][E^(-1 + (E^(-2 - 2*x)*(7744*E^2 + E^x*(-704*E - 704*E^(2 + 2/x)) + E^(2*x)*(16 + 32*E^(1 + 2/x)
+ 16*E^(2 + 4/x))))/x^2 + 2/x)/x^4, x] - 64*Defer[Int][E^((E^(-2 - 2*x)*(7744*E^2 + E^x*(-704*E - 704*E^(2 +
2/x)) + E^(2*x)*(16 + 32*E^(1 + 2/x) + 16*E^(2 + 4/x))))/x^2 + 4/x)/x^4, x] + 1408*Defer[Int][E^((E^(-2 - 2*x)
*(7744*E^2 + E^x*(-704*E - 704*E^(2 + 2/x)) + E^(2*x)*(16 + 32*E^(1 + 2/x) + 16*E^(2 + 4/x))))/x^2 + 2/x - x)/
x^4, x] - 32*Defer[Int][E^(-2 + (16*(-22*E + E^x + E^(1 + 2/x + x))^2)/(E^(2*(1 + x))*x^2))/x^3, x] - 64*Defer
[Int][E^(-1 + (E^(-2 - 2*x)*(7744*E^2 + E^x*(-704*E - 704*E^(2 + 2/x)) + E^(2*x)*(16 + 32*E^(1 + 2/x) + 16*E^(
2 + 4/x))))/x^2 + 2/x)/x^3, x] - 32*Defer[Int][E^((E^(-2 - 2*x)*(7744*E^2 + E^x*(-704*E - 704*E^(2 + 2/x)) + E
^(2*x)*(16 + 32*E^(1 + 2/x) + 16*E^(2 + 4/x))))/x^2 + 4/x)/x^3, x] - 15488*Defer[Int][E^((E^(-2 - 2*x)*(7744*E
^2 + E^x*(-704*E - 704*E^(2 + 2/x)) + E^(2*x)*(16 + 32*E^(1 + 2/x) + 16*E^(2 + 4/x))))/x^2 - 2*x)/x^3, x] + 14
08*Defer[Int][E^(-1 + (E^(-2 - 2*x)*(7744*E^2 + E^x*(-704*E - 704*E^(2 + 2/x)) + E^(2*x)*(16 + 32*E^(1 + 2/x)
+ 16*E^(2 + 4/x))))/x^2 - x)/x^3, x] + 1408*Defer[Int][E^((E^(-2 - 2*x)*(7744*E^2 + E^x*(-704*E - 704*E^(2 + 2
/x)) + E^(2*x)*(16 + 32*E^(1 + 2/x) + 16*E^(2 + 4/x))))/x^2 + 2/x - x)/x^3, x] - 15488*Defer[Int][E^((E^(-2 -
2*x)*(7744*E^2 + E^x*(-704*E - 704*E^(2 + 2/x)) + E^(2*x)*(16 + 32*E^(1 + 2/x) + 16*E^(2 + 4/x))))/x^2 - 2*x)/
x^2, x] + 704*Defer[Int][E^(-1 + (E^(-2 - 2*x)*(7744*E^2 + E^x*(-704*E - 704*E^(2 + 2/x)) + E^(2*x)*(16 + 32*E
^(1 + 2/x) + 16*E^(2 + 4/x))))/x^2 - x)/x^2, x] + 704*Defer[Int][E^((E^(-2 - 2*x)*(7744*E^2 + E^x*(-704*E - 70
4*E^(2 + 2/x)) + E^(2*x)*(16 + 32*E^(1 + 2/x) + 16*E^(2 + 4/x))))/x^2 + 2/x - x)/x^2, x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {32 \exp \left (-2+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x\right ) \left (22 e-e^x-e^{1+\frac {2}{x}+x}\right ) \left (2 e^{1+\frac {2}{x}+x}-22 e x+e^x x+e^{1+\frac {2}{x}+x} x-22 e x^2\right )}{x^4} \, dx \\ & = 32 \int \frac {\exp \left (-2+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x\right ) \left (22 e-e^x-e^{1+\frac {2}{x}+x}\right ) \left (2 e^{1+\frac {2}{x}+x}-22 e x+e^x x+e^{1+\frac {2}{x}+x} x-22 e x^2\right )}{x^4} \, dx \\ & = 32 \int \left (-\frac {484 \exp \left (\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x\right ) (1+x)}{x^3}-\frac {\exp \left (-2+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}\right ) \left (1+e^{1+\frac {2}{x}}\right ) \left (2 e^{1+\frac {2}{x}}+x+e^{1+\frac {2}{x}} x\right )}{x^4}+\frac {22 \exp \left (-1+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-x\right ) \left (2 e^{1+\frac {2}{x}}+2 x+2 e^{1+\frac {2}{x}} x+x^2+e^{1+\frac {2}{x}} x^2\right )}{x^4}\right ) \, dx \\ & = -\left (32 \int \frac {\exp \left (-2+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}\right ) \left (1+e^{1+\frac {2}{x}}\right ) \left (2 e^{1+\frac {2}{x}}+x+e^{1+\frac {2}{x}} x\right )}{x^4} \, dx\right )+704 \int \frac {\exp \left (-1+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-x\right ) \left (2 e^{1+\frac {2}{x}}+2 x+2 e^{1+\frac {2}{x}} x+x^2+e^{1+\frac {2}{x}} x^2\right )}{x^4} \, dx-15488 \int \frac {\exp \left (\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x\right ) (1+x)}{x^3} \, dx \\ & = -\left (32 \int \left (\frac {\exp \left (-2+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}\right )}{x^3}+\frac {2 \exp \left (-1+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}+\frac {2}{x}\right ) (1+x)}{x^4}+\frac {\exp \left (\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}+\frac {4}{x}\right ) (2+x)}{x^4}\right ) \, dx\right )+704 \int \left (\frac {\exp \left (-1+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-x\right ) (2+x)}{x^3}+\frac {\exp \left (\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}+\frac {2}{x}-x\right ) \left (2+2 x+x^2\right )}{x^4}\right ) \, dx-15488 \int \left (\frac {\exp \left (\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x\right )}{x^3}+\frac {\exp \left (\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x\right )}{x^2}\right ) \, dx \\ & = -\left (32 \int \frac {\exp \left (-2+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}\right )}{x^3} \, dx\right )-32 \int \frac {\exp \left (\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}+\frac {4}{x}\right ) (2+x)}{x^4} \, dx-64 \int \frac {\exp \left (-1+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}+\frac {2}{x}\right ) (1+x)}{x^4} \, dx+704 \int \frac {\exp \left (-1+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-x\right ) (2+x)}{x^3} \, dx+704 \int \frac {\exp \left (\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}+\frac {2}{x}-x\right ) \left (2+2 x+x^2\right )}{x^4} \, dx-15488 \int \frac {\exp \left (\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x\right )}{x^3} \, dx-15488 \int \frac {\exp \left (\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x\right )}{x^2} \, dx \\ & = -\left (32 \int \left (\frac {2 e^{\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}+\frac {4}{x}}}{x^4}+\frac {e^{\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}+\frac {4}{x}}}{x^3}\right ) \, dx\right )-32 \int \frac {e^{-2+\frac {16 e^{-2 (1+x)} \left (-22 e+e^x+e^{1+\frac {2}{x}+x}\right )^2}{x^2}}}{x^3} \, dx-64 \int \left (\frac {e^{-1+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}+\frac {2}{x}}}{x^4}+\frac {e^{-1+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}+\frac {2}{x}}}{x^3}\right ) \, dx+704 \int \left (\frac {2 e^{-1+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-x}}{x^3}+\frac {e^{-1+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-x}}{x^2}\right ) \, dx+704 \int \left (\frac {2 e^{\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}+\frac {2}{x}-x}}{x^4}+\frac {2 e^{\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}+\frac {2}{x}-x}}{x^3}+\frac {e^{\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}+\frac {2}{x}-x}}{x^2}\right ) \, dx-15488 \int \frac {e^{\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x}}{x^3} \, dx-15488 \int \frac {e^{\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x}}{x^2} \, dx \\ & = -\left (32 \int \frac {e^{-2+\frac {16 e^{-2 (1+x)} \left (-22 e+e^x+e^{1+\frac {2}{x}+x}\right )^2}{x^2}}}{x^3} \, dx\right )-32 \int \frac {e^{\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}+\frac {4}{x}}}{x^3} \, dx-64 \int \frac {e^{-1+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}+\frac {2}{x}}}{x^4} \, dx-64 \int \frac {e^{\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}+\frac {4}{x}}}{x^4} \, dx-64 \int \frac {e^{-1+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}+\frac {2}{x}}}{x^3} \, dx+704 \int \frac {e^{-1+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-x}}{x^2} \, dx+704 \int \frac {e^{\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}+\frac {2}{x}-x}}{x^2} \, dx+1408 \int \frac {e^{\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}+\frac {2}{x}-x}}{x^4} \, dx+1408 \int \frac {e^{-1+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-x}}{x^3} \, dx+1408 \int \frac {e^{\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}+\frac {2}{x}-x}}{x^3} \, dx-15488 \int \frac {e^{\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x}}{x^3} \, dx-15488 \int \frac {e^{\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x}}{x^2} \, dx \\ \end{align*}

Mathematica [F]

\[ \int \frac {e^{-2+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x} \left (e^{2 x} \left (e^{1+\frac {2}{x}} (-64-64 x)+e^{2+\frac {4}{x}} (-64-32 x)-32 x\right )+e^2 \left (-15488 x-15488 x^2\right )+e^x \left (e \left (1408 x+704 x^2\right )+e^{2+\frac {2}{x}} \left (1408+1408 x+704 x^2\right )\right )\right )}{x^4} \, dx=\int \frac {e^{-2+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x} \left (e^{2 x} \left (e^{1+\frac {2}{x}} (-64-64 x)+e^{2+\frac {4}{x}} (-64-32 x)-32 x\right )+e^2 \left (-15488 x-15488 x^2\right )+e^x \left (e \left (1408 x+704 x^2\right )+e^{2+\frac {2}{x}} \left (1408+1408 x+704 x^2\right )\right )\right )}{x^4} \, dx \]

[In]

Integrate[(E^(-2 + (E^(-2 - 2*x)*(7744*E^2 + E^x*(-704*E - 704*E^(2 + 2/x)) + E^(2*x)*(16 + 32*E^(1 + 2/x) + 1
6*E^(2 + 4/x))))/x^2 - 2*x)*(E^(2*x)*(E^(1 + 2/x)*(-64 - 64*x) + E^(2 + 4/x)*(-64 - 32*x) - 32*x) + E^2*(-1548
8*x - 15488*x^2) + E^x*(E*(1408*x + 704*x^2) + E^(2 + 2/x)*(1408 + 1408*x + 704*x^2))))/x^4,x]

[Out]

Integrate[(E^(-2 + (E^(-2 - 2*x)*(7744*E^2 + E^x*(-704*E - 704*E^(2 + 2/x)) + E^(2*x)*(16 + 32*E^(1 + 2/x) + 1
6*E^(2 + 4/x))))/x^2 - 2*x)*(E^(2*x)*(E^(1 + 2/x)*(-64 - 64*x) + E^(2 + 4/x)*(-64 - 32*x) - 32*x) + E^2*(-1548
8*x - 15488*x^2) + E^x*(E*(1408*x + 704*x^2) + E^(2 + 2/x)*(1408 + 1408*x + 704*x^2))))/x^4, x]

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(69\) vs. \(2(29)=58\).

Time = 787.35 (sec) , antiderivative size = 70, normalized size of antiderivative = 2.26

method	result	size
risch	\({\mathrm e}^{\frac {16 \left (-44 \,{\mathrm e}^{1+x}-44 \,{\mathrm e}^{\frac {x^{2}+2 x +2}{x}}+{\mathrm e}^{\frac {2 x^{2}+2 x +4}{x}}+2 \,{\mathrm e}^{\frac {2 x^{2}+x +2}{x}}+484 \,{\mathrm e}^{2}+{\mathrm e}^{2 x}\right ) {\mathrm e}^{-2-2 x}}{x^{2}}}\)	\(70\)
parallelrisch	\({\mathrm e}^{\frac {\left (\left (16 \,{\mathrm e}^{2} {\mathrm e}^{\frac {4}{x}}+32 \,{\mathrm e} \,{\mathrm e}^{\frac {2}{x}}+16\right ) {\mathrm e}^{2 x}+\left (-704 \,{\mathrm e}^{2} {\mathrm e}^{\frac {2}{x}}-704 \,{\mathrm e}\right ) {\mathrm e}^{x}+7744 \,{\mathrm e}^{2}\right ) {\mathrm e}^{-2} {\mathrm e}^{-2 x}}{x^{2}}}\)	\(72\)

[In]

int((((-32*x-64)*exp(1)^2*exp(2/x)^2+(-64*x-64)*exp(1)*exp(2/x)-32*x)*exp(x)^2+((704*x^2+1408*x+1408)*exp(1)^2
*exp(2/x)+(704*x^2+1408*x)*exp(1))*exp(x)+(-15488*x^2-15488*x)*exp(1)^2)*exp(((16*exp(1)^2*exp(2/x)^2+32*exp(1
)*exp(2/x)+16)*exp(x)^2+(-704*exp(1)^2*exp(2/x)-704*exp(1))*exp(x)+7744*exp(1)^2)/x^2/exp(1)^2/exp(x)^2)/x^4/e
xp(1)^2/exp(x)^2,x,method=_RETURNVERBOSE)

[Out]

exp(16*(-44*exp(1+x)-44*exp((x^2+2*x+2)/x)+exp(2*(x^2+x+2)/x)+2*exp((2*x^2+x+2)/x)+484*exp(2)+exp(2*x))*exp(-2
-2*x)/x^2)

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 84 vs. \(2 (23) = 46\).

Time = 0.30 (sec) , antiderivative size = 84, normalized size of antiderivative = 2.71 \[ \int \frac {e^{-2+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x} \left (e^{2 x} \left (e^{1+\frac {2}{x}} (-64-64 x)+e^{2+\frac {4}{x}} (-64-32 x)-32 x\right )+e^2 \left (-15488 x-15488 x^2\right )+e^x \left (e \left (1408 x+704 x^2\right )+e^{2+\frac {2}{x}} \left (1408+1408 x+704 x^2\right )\right )\right )}{x^4} \, dx=e^{\left (2 \, x - \frac {2 \, {\left ({\left ({\left (x^{3} + x^{2}\right )} e^{4} - 8 \, e^{2} - 8 \, e^{\left (\frac {4 \, {\left (x + 1\right )}}{x}\right )} - 16 \, e^{\left (\frac {2 \, {\left (x + 1\right )}}{x} + 1\right )}\right )} e^{\left (2 \, x\right )} + 352 \, {\left (e^{3} + e^{\left (\frac {2 \, {\left (x + 1\right )}}{x} + 2\right )}\right )} e^{x} - 3872 \, e^{4}\right )} e^{\left (-2 \, x - 4\right )}}{x^{2}} + 2\right )} \]

[In]

integrate((((-32*x-64)*exp(1)^2*exp(2/x)^2+(-64*x-64)*exp(1)*exp(2/x)-32*x)*exp(x)^2+((704*x^2+1408*x+1408)*ex
p(1)^2*exp(2/x)+(704*x^2+1408*x)*exp(1))*exp(x)+(-15488*x^2-15488*x)*exp(1)^2)*exp(((16*exp(1)^2*exp(2/x)^2+32
*exp(1)*exp(2/x)+16)*exp(x)^2+(-704*exp(1)^2*exp(2/x)-704*exp(1))*exp(x)+7744*exp(1)^2)/x^2/exp(1)^2/exp(x)^2)
/x^4/exp(1)^2/exp(x)^2,x, algorithm="fricas")

[Out]

e^(2*x - 2*(((x^3 + x^2)*e^4 - 8*e^2 - 8*e^(4*(x + 1)/x) - 16*e^(2*(x + 1)/x + 1))*e^(2*x) + 352*(e^3 + e^(2*(
x + 1)/x + 2))*e^x - 3872*e^4)*e^(-2*x - 4)/x^2 + 2)

Sympy [F(-1)]

Timed out. \[ \int \frac {e^{-2+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x} \left (e^{2 x} \left (e^{1+\frac {2}{x}} (-64-64 x)+e^{2+\frac {4}{x}} (-64-32 x)-32 x\right )+e^2 \left (-15488 x-15488 x^2\right )+e^x \left (e \left (1408 x+704 x^2\right )+e^{2+\frac {2}{x}} \left (1408+1408 x+704 x^2\right )\right )\right )}{x^4} \, dx=\text {Timed out} \]

[In]

integrate((((-32*x-64)*exp(1)**2*exp(2/x)**2+(-64*x-64)*exp(1)*exp(2/x)-32*x)*exp(x)**2+((704*x**2+1408*x+1408
)*exp(1)**2*exp(2/x)+(704*x**2+1408*x)*exp(1))*exp(x)+(-15488*x**2-15488*x)*exp(1)**2)*exp(((16*exp(1)**2*exp(
2/x)**2+32*exp(1)*exp(2/x)+16)*exp(x)**2+(-704*exp(1)**2*exp(2/x)-704*exp(1))*exp(x)+7744*exp(1)**2)/x**2/exp(
1)**2/exp(x)**2)/x**4/exp(1)**2/exp(x)**2,x)

[Out]

Timed out

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 68 vs. \(2 (23) = 46\).

Time = 1.41 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.19 \[ \int \frac {e^{-2+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x} \left (e^{2 x} \left (e^{1+\frac {2}{x}} (-64-64 x)+e^{2+\frac {4}{x}} (-64-32 x)-32 x\right )+e^2 \left (-15488 x-15488 x^2\right )+e^x \left (e \left (1408 x+704 x^2\right )+e^{2+\frac {2}{x}} \left (1408+1408 x+704 x^2\right )\right )\right )}{x^4} \, dx=e^{\left (\frac {16 \, e^{\left (-2\right )}}{x^{2}} + \frac {7744 \, e^{\left (-2 \, x\right )}}{x^{2}} - \frac {704 \, e^{\left (-x + \frac {2}{x}\right )}}{x^{2}} - \frac {704 \, e^{\left (-x - 1\right )}}{x^{2}} + \frac {16 \, e^{\frac {4}{x}}}{x^{2}} + \frac {32 \, e^{\left (\frac {2}{x} - 1\right )}}{x^{2}}\right )} \]

[In]

integrate((((-32*x-64)*exp(1)^2*exp(2/x)^2+(-64*x-64)*exp(1)*exp(2/x)-32*x)*exp(x)^2+((704*x^2+1408*x+1408)*ex
p(1)^2*exp(2/x)+(704*x^2+1408*x)*exp(1))*exp(x)+(-15488*x^2-15488*x)*exp(1)^2)*exp(((16*exp(1)^2*exp(2/x)^2+32
*exp(1)*exp(2/x)+16)*exp(x)^2+(-704*exp(1)^2*exp(2/x)-704*exp(1))*exp(x)+7744*exp(1)^2)/x^2/exp(1)^2/exp(x)^2)
/x^4/exp(1)^2/exp(x)^2,x, algorithm="maxima")

[Out]

e^(16*e^(-2)/x^2 + 7744*e^(-2*x)/x^2 - 704*e^(-x + 2/x)/x^2 - 704*e^(-x - 1)/x^2 + 16*e^(4/x)/x^2 + 32*e^(2/x
- 1)/x^2)

Giac [F]

\[ \int \frac {e^{-2+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x} \left (e^{2 x} \left (e^{1+\frac {2}{x}} (-64-64 x)+e^{2+\frac {4}{x}} (-64-32 x)-32 x\right )+e^2 \left (-15488 x-15488 x^2\right )+e^x \left (e \left (1408 x+704 x^2\right )+e^{2+\frac {2}{x}} \left (1408+1408 x+704 x^2\right )\right )\right )}{x^4} \, dx=\int { -\frac {32 \, {\left (484 \, {\left (x^{2} + x\right )} e^{2} + {\left ({\left (x + 2\right )} e^{\left (\frac {4}{x} + 2\right )} + 2 \, {\left (x + 1\right )} e^{\left (\frac {2}{x} + 1\right )} + x\right )} e^{\left (2 \, x\right )} - 22 \, {\left ({\left (x^{2} + 2 \, x\right )} e + {\left (x^{2} + 2 \, x + 2\right )} e^{\left (\frac {2}{x} + 2\right )}\right )} e^{x}\right )} e^{\left (-2 \, x + \frac {16 \, {\left ({\left (e^{\left (\frac {4}{x} + 2\right )} + 2 \, e^{\left (\frac {2}{x} + 1\right )} + 1\right )} e^{\left (2 \, x\right )} - 44 \, {\left (e + e^{\left (\frac {2}{x} + 2\right )}\right )} e^{x} + 484 \, e^{2}\right )} e^{\left (-2 \, x - 2\right )}}{x^{2}} - 2\right )}}{x^{4}} \,d x } \]

[In]

integrate((((-32*x-64)*exp(1)^2*exp(2/x)^2+(-64*x-64)*exp(1)*exp(2/x)-32*x)*exp(x)^2+((704*x^2+1408*x+1408)*ex
p(1)^2*exp(2/x)+(704*x^2+1408*x)*exp(1))*exp(x)+(-15488*x^2-15488*x)*exp(1)^2)*exp(((16*exp(1)^2*exp(2/x)^2+32
*exp(1)*exp(2/x)+16)*exp(x)^2+(-704*exp(1)^2*exp(2/x)-704*exp(1))*exp(x)+7744*exp(1)^2)/x^2/exp(1)^2/exp(x)^2)
/x^4/exp(1)^2/exp(x)^2,x, algorithm="giac")

[Out]

integrate(-32*(484*(x^2 + x)*e^2 + ((x + 2)*e^(4/x + 2) + 2*(x + 1)*e^(2/x + 1) + x)*e^(2*x) - 22*((x^2 + 2*x)
*e + (x^2 + 2*x + 2)*e^(2/x + 2))*e^x)*e^(-2*x + 16*((e^(4/x + 2) + 2*e^(2/x + 1) + 1)*e^(2*x) - 44*(e + e^(2/
x + 2))*e^x + 484*e^2)*e^(-2*x - 2)/x^2 - 2)/x^4, x)

Mupad [B] (verification not implemented)

Time = 9.81 (sec) , antiderivative size = 73, normalized size of antiderivative = 2.35 \[ \int \frac {e^{-2+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x} \left (e^{2 x} \left (e^{1+\frac {2}{x}} (-64-64 x)+e^{2+\frac {4}{x}} (-64-32 x)-32 x\right )+e^2 \left (-15488 x-15488 x^2\right )+e^x \left (e \left (1408 x+704 x^2\right )+e^{2+\frac {2}{x}} \left (1408+1408 x+704 x^2\right )\right )\right )}{x^4} \, dx={\mathrm {e}}^{\frac {16\,{\mathrm {e}}^{-2}}{x^2}}\,{\mathrm {e}}^{\frac {16\,{\mathrm {e}}^{4/x}}{x^2}}\,{\mathrm {e}}^{-\frac {704\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{-1}}{x^2}}\,{\mathrm {e}}^{-\frac {704\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{2/x}}{x^2}}\,{\mathrm {e}}^{\frac {32\,{\mathrm {e}}^{-1}\,{\mathrm {e}}^{2/x}}{x^2}}\,{\mathrm {e}}^{\frac {7744\,{\mathrm {e}}^{-2\,x}}{x^2}} \]

[In]

int(-(exp(-2*x)*exp(-2)*exp((exp(-2*x)*exp(-2)*(7744*exp(2) + exp(2*x)*(32*exp(1)*exp(2/x) + 16*exp(2)*exp(4/x
) + 16) - exp(x)*(704*exp(1) + 704*exp(2)*exp(2/x))))/x^2)*(exp(2*x)*(32*x + exp(2)*exp(4/x)*(32*x + 64) + exp
(1)*exp(2/x)*(64*x + 64)) + exp(2)*(15488*x + 15488*x^2) - exp(x)*(exp(1)*(1408*x + 704*x^2) + exp(2)*exp(2/x)
*(1408*x + 704*x^2 + 1408))))/x^4,x)

[Out]

exp((16*exp(-2))/x^2)*exp((16*exp(4/x))/x^2)*exp(-(704*exp(-x)*exp(-1))/x^2)*exp(-(704*exp(-x)*exp(2/x))/x^2)*
exp((32*exp(-1)*exp(2/x))/x^2)*exp((7744*exp(-2*x))/x^2)