\(\int \frac {-x^3+e^{-2+x+\frac {e^{-2+x} (1+e^{5/x} x^2)}{x^2}} ((2-x) \log (2)+e^{5/x} (5 x-x^3) \log (2))}{25 x^3+10 x^4+x^5+e^{\frac {e^{-2+x} (1+e^{5/x} x^2)}{x^2}} (10 x^3+2 x^4) \log (2)+e^{\frac {2 e^{-2+x} (1+e^{5/x} x^2)}{x^2}} x^3 \log ^2(2)} \, dx\) [300]

Optimal result

Integrand size = 150, antiderivative size = 27 \[ \int \frac {-x^3+e^{-2+x+\frac {e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} \left ((2-x) \log (2)+e^{5/x} \left (5 x-x^3\right ) \log (2)\right )}{25 x^3+10 x^4+x^5+e^{\frac {e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} \left (10 x^3+2 x^4\right ) \log (2)+e^{\frac {2 e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} x^3 \log ^2(2)} \, dx=\frac {1}{5+x+e^{e^{-2+x} \left (e^{5/x}+\frac {1}{x^2}\right )} \log (2)} \]

[Out]

1/(5+ln(2)*exp((exp(5/x)+1/x^2)*exp(-2+x))+x)

Rubi [F]

\[ \int \frac {-x^3+e^{-2+x+\frac {e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} \left ((2-x) \log (2)+e^{5/x} \left (5 x-x^3\right ) \log (2)\right )}{25 x^3+10 x^4+x^5+e^{\frac {e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} \left (10 x^3+2 x^4\right ) \log (2)+e^{\frac {2 e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} x^3 \log ^2(2)} \, dx=\int \frac {-x^3+e^{-2+x+\frac {e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} \left ((2-x) \log (2)+e^{5/x} \left (5 x-x^3\right ) \log (2)\right )}{25 x^3+10 x^4+x^5+e^{\frac {e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} \left (10 x^3+2 x^4\right ) \log (2)+e^{\frac {2 e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} x^3 \log ^2(2)} \, dx \]

[In]

Int[(-x^3 + E^(-2 + x + (E^(-2 + x)*(1 + E^(5/x)*x^2))/x^2)*((2 - x)*Log[2] + E^(5/x)*(5*x - x^3)*Log[2]))/(25
*x^3 + 10*x^4 + x^5 + E^((E^(-2 + x)*(1 + E^(5/x)*x^2))/x^2)*(10*x^3 + 2*x^4)*Log[2] + E^((2*E^(-2 + x)*(1 + E
^(5/x)*x^2))/x^2)*x^3*Log[2]^2),x]

[Out]

-Defer[Int][(5 + x + E^(E^(-2 + x)*(E^(5/x) + x^(-2)))*Log[2])^(-2), x] - Log[2]*Defer[Int][E^(-2 + E^(-2 + x)
*(E^(5/x) + x^(-2)) + 5/x + x)/(5 + x + E^(E^(-2 + x)*(E^(5/x) + x^(-2)))*Log[2])^2, x] + 2*Log[2]*Defer[Int][
E^(-2 + E^(-2 + x)*(E^(5/x) + x^(-2)) + x)/(x^3*(5 + x + E^(E^(-2 + x)*(E^(5/x) + x^(-2)))*Log[2])^2), x] - Lo
g[2]*Defer[Int][E^(-2 + E^(-2 + x)*(E^(5/x) + x^(-2)) + x)/(x^2*(5 + x + E^(E^(-2 + x)*(E^(5/x) + x^(-2)))*Log
[2])^2), x] + 5*Log[2]*Defer[Int][E^(-2 + E^(-2 + x)*(E^(5/x) + x^(-2)) + 5/x + x)/(x^2*(5 + x + E^(E^(-2 + x)
*(E^(5/x) + x^(-2)))*Log[2])^2), x]

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

Mathematica [F(-1)]

Timed out. \[ \int \frac {-x^3+e^{-2+x+\frac {e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} \left ((2-x) \log (2)+e^{5/x} \left (5 x-x^3\right ) \log (2)\right )}{25 x^3+10 x^4+x^5+e^{\frac {e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} \left (10 x^3+2 x^4\right ) \log (2)+e^{\frac {2 e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} x^3 \log ^2(2)} \, dx=\text {\$Aborted} \]

[In]

Integrate[(-x^3 + E^(-2 + x + (E^(-2 + x)*(1 + E^(5/x)*x^2))/x^2)*((2 - x)*Log[2] + E^(5/x)*(5*x - x^3)*Log[2]
))/(25*x^3 + 10*x^4 + x^5 + E^((E^(-2 + x)*(1 + E^(5/x)*x^2))/x^2)*(10*x^3 + 2*x^4)*Log[2] + E^((2*E^(-2 + x)*
(1 + E^(5/x)*x^2))/x^2)*x^3*Log[2]^2),x]

[Out]

$Aborted

Maple [A] (verified)

Time = 28.83 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.11

method	result	size
risch	\(\frac {1}{\ln \left (2\right ) {\mathrm e}^{\frac {\left (x^{2} {\mathrm e}^{\frac {5}{x}}+1\right ) {\mathrm e}^{-2+x}}{x^{2}}}+x +5}\)	\(30\)
parallelrisch	\(\frac {1}{\ln \left (2\right ) {\mathrm e}^{\frac {\left (x^{2} {\mathrm e}^{\frac {5}{x}}+1\right ) {\mathrm e}^{-2+x}}{x^{2}}}+x +5}\)	\(30\)

[In]

int((((-x^3+5*x)*ln(2)*exp(5/x)+(2-x)*ln(2))*exp(-2+x)*exp((x^2*exp(5/x)+1)*exp(-2+x)/x^2)-x^3)/(x^3*ln(2)^2*e
xp((x^2*exp(5/x)+1)*exp(-2+x)/x^2)^2+(2*x^4+10*x^3)*ln(2)*exp((x^2*exp(5/x)+1)*exp(-2+x)/x^2)+x^5+10*x^4+25*x^
3),x,method=_RETURNVERBOSE)

[Out]

1/(ln(2)*exp((x^2*exp(5/x)+1)*exp(-2+x)/x^2)+x+5)

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 50 vs. \(2 (24) = 48\).

Time = 0.25 (sec) , antiderivative size = 50, normalized size of antiderivative = 1.85 \[ \int \frac {-x^3+e^{-2+x+\frac {e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} \left ((2-x) \log (2)+e^{5/x} \left (5 x-x^3\right ) \log (2)\right )}{25 x^3+10 x^4+x^5+e^{\frac {e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} \left (10 x^3+2 x^4\right ) \log (2)+e^{\frac {2 e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} x^3 \log ^2(2)} \, dx=\frac {e^{\left (x - 2\right )}}{{\left (x + 5\right )} e^{\left (x - 2\right )} + e^{\left (\frac {x^{3} - 2 \, x^{2} + {\left (x^{2} e^{\frac {5}{x}} + 1\right )} e^{\left (x - 2\right )}}{x^{2}}\right )} \log \left (2\right )} \]

[In]

integrate((((-x^3+5*x)*log(2)*exp(5/x)+(2-x)*log(2))*exp(-2+x)*exp((x^2*exp(5/x)+1)*exp(-2+x)/x^2)-x^3)/(x^3*l
og(2)^2*exp((x^2*exp(5/x)+1)*exp(-2+x)/x^2)^2+(2*x^4+10*x^3)*log(2)*exp((x^2*exp(5/x)+1)*exp(-2+x)/x^2)+x^5+10
*x^4+25*x^3),x, algorithm="fricas")

[Out]

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

Sympy [A] (verification not implemented)

Time = 0.25 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.00 \[ \int \frac {-x^3+e^{-2+x+\frac {e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} \left ((2-x) \log (2)+e^{5/x} \left (5 x-x^3\right ) \log (2)\right )}{25 x^3+10 x^4+x^5+e^{\frac {e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} \left (10 x^3+2 x^4\right ) \log (2)+e^{\frac {2 e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} x^3 \log ^2(2)} \, dx=\frac {1}{x + e^{\frac {\left (x^{2} e^{\frac {5}{x}} + 1\right ) e^{x - 2}}{x^{2}}} \log {\left (2 \right )} + 5} \]

[In]

integrate((((-x**3+5*x)*ln(2)*exp(5/x)+(2-x)*ln(2))*exp(-2+x)*exp((x**2*exp(5/x)+1)*exp(-2+x)/x**2)-x**3)/(x**
3*ln(2)**2*exp((x**2*exp(5/x)+1)*exp(-2+x)/x**2)**2+(2*x**4+10*x**3)*ln(2)*exp((x**2*exp(5/x)+1)*exp(-2+x)/x**
2)+x**5+10*x**4+25*x**3),x)

[Out]

1/(x + exp((x**2*exp(5/x) + 1)*exp(x - 2)/x**2)*log(2) + 5)

Maxima [A] (verification not implemented)

none

Time = 0.35 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.00 \[ \int \frac {-x^3+e^{-2+x+\frac {e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} \left ((2-x) \log (2)+e^{5/x} \left (5 x-x^3\right ) \log (2)\right )}{25 x^3+10 x^4+x^5+e^{\frac {e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} \left (10 x^3+2 x^4\right ) \log (2)+e^{\frac {2 e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} x^3 \log ^2(2)} \, dx=\frac {1}{e^{\left (\frac {e^{\left (x - 2\right )}}{x^{2}} + e^{\left (x + \frac {5}{x} - 2\right )}\right )} \log \left (2\right ) + x + 5} \]

[In]

integrate((((-x^3+5*x)*log(2)*exp(5/x)+(2-x)*log(2))*exp(-2+x)*exp((x^2*exp(5/x)+1)*exp(-2+x)/x^2)-x^3)/(x^3*l
og(2)^2*exp((x^2*exp(5/x)+1)*exp(-2+x)/x^2)^2+(2*x^4+10*x^3)*log(2)*exp((x^2*exp(5/x)+1)*exp(-2+x)/x^2)+x^5+10
*x^4+25*x^3),x, algorithm="maxima")

[Out]

1/(e^(e^(x - 2)/x^2 + e^(x + 5/x - 2))*log(2) + x + 5)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 564 vs. \(2 (24) = 48\).

Time = 1.06 (sec) , antiderivative size = 564, normalized size of antiderivative = 20.89 \[ \int \frac {-x^3+e^{-2+x+\frac {e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} \left ((2-x) \log (2)+e^{5/x} \left (5 x-x^3\right ) \log (2)\right )}{25 x^3+10 x^4+x^5+e^{\frac {e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} \left (10 x^3+2 x^4\right ) \log (2)+e^{\frac {2 e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} x^3 \log ^2(2)} \, dx=\frac {x^{4} e^{\left (\frac {x^{2} - 2 \, x + 5}{x} + 2\right )} - x^{3} e^{2} + 5 \, x^{3} e^{\left (\frac {x^{2} - 2 \, x + 5}{x} + 2\right )} + x^{2} e^{x} - 5 \, x^{2} e^{\left (\frac {x^{2} - 2 \, x + 5}{x} + 2\right )} + 3 \, x e^{x} - 25 \, x e^{\left (\frac {x^{2} - 2 \, x + 5}{x} + 2\right )} - 10 \, e^{x}}{x^{5} e^{\left (\frac {x^{2} - 2 \, x + 5}{x} + 2\right )} + x^{4} e^{\left (\frac {x^{2} - 2 \, x + 5}{x} + \frac {x^{2} e^{\left (\frac {x^{2} - 2 \, x + 5}{x}\right )} + e^{\left (x - 2\right )}}{x^{2}} + 2\right )} \log \left (2\right ) - x^{4} e^{2} + 10 \, x^{4} e^{\left (\frac {x^{2} - 2 \, x + 5}{x} + 2\right )} + 5 \, x^{3} e^{\left (\frac {x^{2} - 2 \, x + 5}{x} + \frac {x^{2} e^{\left (\frac {x^{2} - 2 \, x + 5}{x}\right )} + e^{\left (x - 2\right )}}{x^{2}} + 2\right )} \log \left (2\right ) - x^{3} e^{\left (\frac {x^{2} e^{\left (\frac {x^{2} - 2 \, x + 5}{x}\right )} + e^{\left (x - 2\right )}}{x^{2}} + 2\right )} \log \left (2\right ) - 5 \, x^{3} e^{2} + x^{3} e^{x} + 20 \, x^{3} e^{\left (\frac {x^{2} - 2 \, x + 5}{x} + 2\right )} + x^{2} e^{\left (x + \frac {x^{2} e^{\left (\frac {x^{2} - 2 \, x + 5}{x}\right )} + e^{\left (x - 2\right )}}{x^{2}}\right )} \log \left (2\right ) - 5 \, x^{2} e^{\left (\frac {x^{2} - 2 \, x + 5}{x} + \frac {x^{2} e^{\left (\frac {x^{2} - 2 \, x + 5}{x}\right )} + e^{\left (x - 2\right )}}{x^{2}} + 2\right )} \log \left (2\right ) + 8 \, x^{2} e^{x} - 50 \, x^{2} e^{\left (\frac {x^{2} - 2 \, x + 5}{x} + 2\right )} + 3 \, x e^{\left (x + \frac {x^{2} e^{\left (\frac {x^{2} - 2 \, x + 5}{x}\right )} + e^{\left (x - 2\right )}}{x^{2}}\right )} \log \left (2\right ) - 25 \, x e^{\left (\frac {x^{2} - 2 \, x + 5}{x} + \frac {x^{2} e^{\left (\frac {x^{2} - 2 \, x + 5}{x}\right )} + e^{\left (x - 2\right )}}{x^{2}} + 2\right )} \log \left (2\right ) + 5 \, x e^{x} - 125 \, x e^{\left (\frac {x^{2} - 2 \, x + 5}{x} + 2\right )} - 10 \, e^{\left (x + \frac {x^{2} e^{\left (\frac {x^{2} - 2 \, x + 5}{x}\right )} + e^{\left (x - 2\right )}}{x^{2}}\right )} \log \left (2\right ) - 50 \, e^{x}} \]

[In]

integrate((((-x^3+5*x)*log(2)*exp(5/x)+(2-x)*log(2))*exp(-2+x)*exp((x^2*exp(5/x)+1)*exp(-2+x)/x^2)-x^3)/(x^3*l
og(2)^2*exp((x^2*exp(5/x)+1)*exp(-2+x)/x^2)^2+(2*x^4+10*x^3)*log(2)*exp((x^2*exp(5/x)+1)*exp(-2+x)/x^2)+x^5+10
*x^4+25*x^3),x, algorithm="giac")

[Out]

(x^4*e^((x^2 - 2*x + 5)/x + 2) - x^3*e^2 + 5*x^3*e^((x^2 - 2*x + 5)/x + 2) + x^2*e^x - 5*x^2*e^((x^2 - 2*x + 5
)/x + 2) + 3*x*e^x - 25*x*e^((x^2 - 2*x + 5)/x + 2) - 10*e^x)/(x^5*e^((x^2 - 2*x + 5)/x + 2) + x^4*e^((x^2 - 2
*x + 5)/x + (x^2*e^((x^2 - 2*x + 5)/x) + e^(x - 2))/x^2 + 2)*log(2) - x^4*e^2 + 10*x^4*e^((x^2 - 2*x + 5)/x +
2) + 5*x^3*e^((x^2 - 2*x + 5)/x + (x^2*e^((x^2 - 2*x + 5)/x) + e^(x - 2))/x^2 + 2)*log(2) - x^3*e^((x^2*e^((x^
2 - 2*x + 5)/x) + e^(x - 2))/x^2 + 2)*log(2) - 5*x^3*e^2 + x^3*e^x + 20*x^3*e^((x^2 - 2*x + 5)/x + 2) + x^2*e^
(x + (x^2*e^((x^2 - 2*x + 5)/x) + e^(x - 2))/x^2)*log(2) - 5*x^2*e^((x^2 - 2*x + 5)/x + (x^2*e^((x^2 - 2*x + 5
)/x) + e^(x - 2))/x^2 + 2)*log(2) + 8*x^2*e^x - 50*x^2*e^((x^2 - 2*x + 5)/x + 2) + 3*x*e^(x + (x^2*e^((x^2 - 2
*x + 5)/x) + e^(x - 2))/x^2)*log(2) - 25*x*e^((x^2 - 2*x + 5)/x + (x^2*e^((x^2 - 2*x + 5)/x) + e^(x - 2))/x^2
+ 2)*log(2) + 5*x*e^x - 125*x*e^((x^2 - 2*x + 5)/x + 2) - 10*e^(x + (x^2*e^((x^2 - 2*x + 5)/x) + e^(x - 2))/x^
2)*log(2) - 50*e^x)

Mupad [B] (verification not implemented)

Time = 7.76 (sec) , antiderivative size = 93, normalized size of antiderivative = 3.44 \[ \int \frac {-x^3+e^{-2+x+\frac {e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} \left ((2-x) \log (2)+e^{5/x} \left (5 x-x^3\right ) \log (2)\right )}{25 x^3+10 x^4+x^5+e^{\frac {e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} \left (10 x^3+2 x^4\right ) \log (2)+e^{\frac {2 e^{-2+x} \left (1+e^{5/x} x^2\right )}{x^2}} x^3 \log ^2(2)} \, dx=\frac {x\,\left (\ln \left (2\right )-{\mathrm {e}}^{5/x}\,\ln \left (32\right )\right )-\ln \left (4\right )+x^3\,{\mathrm {e}}^{5/x}\,\ln \left (2\right )}{{\ln \left (2\right )}^2\,\left ({\mathrm {e}}^{{\mathrm {e}}^{-2}\,{\mathrm {e}}^{5/x}\,{\mathrm {e}}^x+\frac {{\mathrm {e}}^{-2}\,{\mathrm {e}}^x}{x^2}}+\frac {x+5}{\ln \left (2\right )}\right )\,\left (x-5\,x\,{\mathrm {e}}^{5/x}+x^3\,{\mathrm {e}}^{5/x}-2\right )} \]

[In]

int(-(x^3 + exp((exp(x - 2)*(x^2*exp(5/x) + 1))/x^2)*exp(x - 2)*(log(2)*(x - 2) - exp(5/x)*log(2)*(5*x - x^3))
)/(25*x^3 + 10*x^4 + x^5 + x^3*exp((2*exp(x - 2)*(x^2*exp(5/x) + 1))/x^2)*log(2)^2 + exp((exp(x - 2)*(x^2*exp(
5/x) + 1))/x^2)*log(2)*(10*x^3 + 2*x^4)),x)

[Out]

(x*(log(2) - exp(5/x)*log(32)) - log(4) + x^3*exp(5/x)*log(2))/(log(2)^2*(exp(exp(-2)*exp(5/x)*exp(x) + (exp(-
2)*exp(x))/x^2) + (x + 5)/log(2))*(x - 5*x*exp(5/x) + x^3*exp(5/x) - 2))