\(\int \frac {e^{2 x-\frac {4}{x^2 \log (5)}} (8-16 x+8 x^2+(-2 x^4+2 x^5) \log (5)+e^{\frac {4}{x^2 \log (5)}} (2 x^4+2 x^5) \log (5)+e^{\frac {2}{x^2 \log (5)}} (-8 x+8 x^2+(-2 x^3+4 x^5) \log (5)))}{x^3 \log (5)} \, dx\) [3049]

Optimal result

Integrand size = 107, antiderivative size = 29 \[ \int \frac {e^{2 x-\frac {4}{x^2 \log (5)}} \left (8-16 x+8 x^2+\left (-2 x^4+2 x^5\right ) \log (5)+e^{\frac {4}{x^2 \log (5)}} \left (2 x^4+2 x^5\right ) \log (5)+e^{\frac {2}{x^2 \log (5)}} \left (-8 x+8 x^2+\left (-2 x^3+4 x^5\right ) \log (5)\right )\right )}{x^3 \log (5)} \, dx=e^{2 x} \left (e^{-\frac {2}{x^2 \log (5)}} (1-x)-x\right )^2 \]

[Out]

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

Rubi [F]

\[ \int \frac {e^{2 x-\frac {4}{x^2 \log (5)}} \left (8-16 x+8 x^2+\left (-2 x^4+2 x^5\right ) \log (5)+e^{\frac {4}{x^2 \log (5)}} \left (2 x^4+2 x^5\right ) \log (5)+e^{\frac {2}{x^2 \log (5)}} \left (-8 x+8 x^2+\left (-2 x^3+4 x^5\right ) \log (5)\right )\right )}{x^3 \log (5)} \, dx=\int \frac {e^{2 x-\frac {4}{x^2 \log (5)}} \left (8-16 x+8 x^2+\left (-2 x^4+2 x^5\right ) \log (5)+e^{\frac {4}{x^2 \log (5)}} \left (2 x^4+2 x^5\right ) \log (5)+e^{\frac {2}{x^2 \log (5)}} \left (-8 x+8 x^2+\left (-2 x^3+4 x^5\right ) \log (5)\right )\right )}{x^3 \log (5)} \, dx \]

[In]

Int[(E^(2*x - 4/(x^2*Log[5]))*(8 - 16*x + 8*x^2 + (-2*x^4 + 2*x^5)*Log[5] + E^(4/(x^2*Log[5]))*(2*x^4 + 2*x^5)
*Log[5] + E^(2/(x^2*Log[5]))*(-8*x + 8*x^2 + (-2*x^3 + 4*x^5)*Log[5])))/(x^3*Log[5]),x]

[Out]

E^(2*x)*x^2 - 2*Defer[Int][E^(2*x - 2/(x^2*Log[5])), x] + (8*Defer[Int][E^(2*x - 4/(x^2*Log[5]))/x^3, x])/Log[
5] - (16*Defer[Int][E^(2*x - 4/(x^2*Log[5]))/x^2, x])/Log[5] - (8*Defer[Int][E^(2*x - 2/(x^2*Log[5]))/x^2, x])
/Log[5] + (8*Defer[Int][E^(2*x - 4/(x^2*Log[5]))/x, x])/Log[5] + (8*Defer[Int][E^(2*x - 2/(x^2*Log[5]))/x, x])
/Log[5] - 2*Defer[Int][E^(2*x - 4/(x^2*Log[5]))*x, x] + 2*Defer[Int][E^(2*x - 4/(x^2*Log[5]))*x^2, x] + (2*Log
[25]*Defer[Int][E^(2*x - 2/(x^2*Log[5]))*x^2, x])/Log[5]

Rubi steps \begin{align*} \text {integral}& = \frac {\int \frac {e^{2 x-\frac {4}{x^2 \log (5)}} \left (8-16 x+8 x^2+\left (-2 x^4+2 x^5\right ) \log (5)+e^{\frac {4}{x^2 \log (5)}} \left (2 x^4+2 x^5\right ) \log (5)+e^{\frac {2}{x^2 \log (5)}} \left (-8 x+8 x^2+\left (-2 x^3+4 x^5\right ) \log (5)\right )\right )}{x^3} \, dx}{\log (5)} \\ & = \frac {\int \frac {2 e^{2 x-\frac {4}{x^2 \log (5)}} \left (1-x-e^{\frac {2}{x^2 \log (5)}} x\right ) \left (4-4 x-e^{\frac {2}{x^2 \log (5)}} x^3 \log (5)-x^4 \log (5)-e^{\frac {2}{x^2 \log (5)}} x^4 \log (5)\right )}{x^3} \, dx}{\log (5)} \\ & = \frac {2 \int \frac {e^{2 x-\frac {4}{x^2 \log (5)}} \left (1-x-e^{\frac {2}{x^2 \log (5)}} x\right ) \left (4-4 x-e^{\frac {2}{x^2 \log (5)}} x^3 \log (5)-x^4 \log (5)-e^{\frac {2}{x^2 \log (5)}} x^4 \log (5)\right )}{x^3} \, dx}{\log (5)} \\ & = \frac {2 \int \left (e^{2 x} x (1+x) \log (5)+\frac {e^{2 x-\frac {4}{x^2 \log (5)}} (-1+x) \left (-4+4 x+x^4 \log (5)\right )}{x^3}+\frac {e^{2 x-\frac {2}{x^2 \log (5)}} \left (-4+4 x-x^2 \log (5)+x^4 \log (25)\right )}{x^2}\right ) \, dx}{\log (5)} \\ & = 2 \int e^{2 x} x (1+x) \, dx+\frac {2 \int \frac {e^{2 x-\frac {4}{x^2 \log (5)}} (-1+x) \left (-4+4 x+x^4 \log (5)\right )}{x^3} \, dx}{\log (5)}+\frac {2 \int \frac {e^{2 x-\frac {2}{x^2 \log (5)}} \left (-4+4 x-x^2 \log (5)+x^4 \log (25)\right )}{x^2} \, dx}{\log (5)} \\ & = 2 \int \left (e^{2 x} x+e^{2 x} x^2\right ) \, dx+\frac {2 \int \left (\frac {4 e^{2 x-\frac {4}{x^2 \log (5)}}}{x^3}-\frac {8 e^{2 x-\frac {4}{x^2 \log (5)}}}{x^2}+\frac {4 e^{2 x-\frac {4}{x^2 \log (5)}}}{x}-e^{2 x-\frac {4}{x^2 \log (5)}} x \log (5)+e^{2 x-\frac {4}{x^2 \log (5)}} x^2 \log (5)\right ) \, dx}{\log (5)}+\frac {2 \int \left (-\frac {4 e^{2 x-\frac {2}{x^2 \log (5)}}}{x^2}+\frac {4 e^{2 x-\frac {2}{x^2 \log (5)}}}{x}-e^{2 x-\frac {2}{x^2 \log (5)}} \log (5)+e^{2 x-\frac {2}{x^2 \log (5)}} x^2 \log (25)\right ) \, dx}{\log (5)} \\ & = -\left (2 \int e^{2 x-\frac {2}{x^2 \log (5)}} \, dx\right )+2 \int e^{2 x} x \, dx-2 \int e^{2 x-\frac {4}{x^2 \log (5)}} x \, dx+2 \int e^{2 x} x^2 \, dx+2 \int e^{2 x-\frac {4}{x^2 \log (5)}} x^2 \, dx+\frac {8 \int \frac {e^{2 x-\frac {4}{x^2 \log (5)}}}{x^3} \, dx}{\log (5)}-\frac {8 \int \frac {e^{2 x-\frac {2}{x^2 \log (5)}}}{x^2} \, dx}{\log (5)}+\frac {8 \int \frac {e^{2 x-\frac {4}{x^2 \log (5)}}}{x} \, dx}{\log (5)}+\frac {8 \int \frac {e^{2 x-\frac {2}{x^2 \log (5)}}}{x} \, dx}{\log (5)}-\frac {16 \int \frac {e^{2 x-\frac {4}{x^2 \log (5)}}}{x^2} \, dx}{\log (5)}+\frac {(2 \log (25)) \int e^{2 x-\frac {2}{x^2 \log (5)}} x^2 \, dx}{\log (5)} \\ & = e^{2 x} x+e^{2 x} x^2-2 \int e^{2 x-\frac {2}{x^2 \log (5)}} \, dx-2 \int e^{2 x} x \, dx-2 \int e^{2 x-\frac {4}{x^2 \log (5)}} x \, dx+2 \int e^{2 x-\frac {4}{x^2 \log (5)}} x^2 \, dx+\frac {8 \int \frac {e^{2 x-\frac {4}{x^2 \log (5)}}}{x^3} \, dx}{\log (5)}-\frac {8 \int \frac {e^{2 x-\frac {2}{x^2 \log (5)}}}{x^2} \, dx}{\log (5)}+\frac {8 \int \frac {e^{2 x-\frac {4}{x^2 \log (5)}}}{x} \, dx}{\log (5)}+\frac {8 \int \frac {e^{2 x-\frac {2}{x^2 \log (5)}}}{x} \, dx}{\log (5)}-\frac {16 \int \frac {e^{2 x-\frac {4}{x^2 \log (5)}}}{x^2} \, dx}{\log (5)}+\frac {(2 \log (25)) \int e^{2 x-\frac {2}{x^2 \log (5)}} x^2 \, dx}{\log (5)}-\int e^{2 x} \, dx \\ & = -\frac {e^{2 x}}{2}+e^{2 x} x^2-2 \int e^{2 x-\frac {2}{x^2 \log (5)}} \, dx-2 \int e^{2 x-\frac {4}{x^2 \log (5)}} x \, dx+2 \int e^{2 x-\frac {4}{x^2 \log (5)}} x^2 \, dx+\frac {8 \int \frac {e^{2 x-\frac {4}{x^2 \log (5)}}}{x^3} \, dx}{\log (5)}-\frac {8 \int \frac {e^{2 x-\frac {2}{x^2 \log (5)}}}{x^2} \, dx}{\log (5)}+\frac {8 \int \frac {e^{2 x-\frac {4}{x^2 \log (5)}}}{x} \, dx}{\log (5)}+\frac {8 \int \frac {e^{2 x-\frac {2}{x^2 \log (5)}}}{x} \, dx}{\log (5)}-\frac {16 \int \frac {e^{2 x-\frac {4}{x^2 \log (5)}}}{x^2} \, dx}{\log (5)}+\frac {(2 \log (25)) \int e^{2 x-\frac {2}{x^2 \log (5)}} x^2 \, dx}{\log (5)}+\int e^{2 x} \, dx \\ & = e^{2 x} x^2-2 \int e^{2 x-\frac {2}{x^2 \log (5)}} \, dx-2 \int e^{2 x-\frac {4}{x^2 \log (5)}} x \, dx+2 \int e^{2 x-\frac {4}{x^2 \log (5)}} x^2 \, dx+\frac {8 \int \frac {e^{2 x-\frac {4}{x^2 \log (5)}}}{x^3} \, dx}{\log (5)}-\frac {8 \int \frac {e^{2 x-\frac {2}{x^2 \log (5)}}}{x^2} \, dx}{\log (5)}+\frac {8 \int \frac {e^{2 x-\frac {4}{x^2 \log (5)}}}{x} \, dx}{\log (5)}+\frac {8 \int \frac {e^{2 x-\frac {2}{x^2 \log (5)}}}{x} \, dx}{\log (5)}-\frac {16 \int \frac {e^{2 x-\frac {4}{x^2 \log (5)}}}{x^2} \, dx}{\log (5)}+\frac {(2 \log (25)) \int e^{2 x-\frac {2}{x^2 \log (5)}} x^2 \, dx}{\log (5)} \\ \end{align*}

Mathematica [A] (verified)

Time = 5.06 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.17 \[ \int \frac {e^{2 x-\frac {4}{x^2 \log (5)}} \left (8-16 x+8 x^2+\left (-2 x^4+2 x^5\right ) \log (5)+e^{\frac {4}{x^2 \log (5)}} \left (2 x^4+2 x^5\right ) \log (5)+e^{\frac {2}{x^2 \log (5)}} \left (-8 x+8 x^2+\left (-2 x^3+4 x^5\right ) \log (5)\right )\right )}{x^3 \log (5)} \, dx=e^{2 x-\frac {4}{x^2 \log (5)}} \left (-1+x+e^{\frac {2}{x^2 \log (5)}} x\right )^2 \]

[In]

Integrate[(E^(2*x - 4/(x^2*Log[5]))*(8 - 16*x + 8*x^2 + (-2*x^4 + 2*x^5)*Log[5] + E^(4/(x^2*Log[5]))*(2*x^4 +
2*x^5)*Log[5] + E^(2/(x^2*Log[5]))*(-8*x + 8*x^2 + (-2*x^3 + 4*x^5)*Log[5])))/(x^3*Log[5]),x]

[Out]

E^(2*x - 4/(x^2*Log[5]))*(-1 + x + E^(2/(x^2*Log[5]))*x)^2

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(60\) vs. \(2(29)=58\).

Time = 3.42 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.10

method	result	size
risch	\({\mathrm e}^{2 x} x^{2}+2 x \left (-1+x \right ) {\mathrm e}^{\frac {2 x^{3} \ln \left (5\right )-2}{x^{2} \ln \left (5\right )}}+\left (x^{2}-2 x +1\right ) {\mathrm e}^{\frac {2 x^{3} \ln \left (5\right )-4}{x^{2} \ln \left (5\right )}}\)	\(61\)
parallelrisch	\(-\frac {\left (-2 \ln \left (5\right ) x^{4} {\mathrm e}^{2 x} {\mathrm e}^{\frac {4}{x^{2} \ln \left (5\right )}}-4 \ln \left (5\right ) x^{4} {\mathrm e}^{2 x} {\mathrm e}^{\frac {2}{x^{2} \ln \left (5\right )}}-2 \ln \left (5\right ) x^{4} {\mathrm e}^{2 x}+4 \ln \left (5\right ) x^{3} {\mathrm e}^{2 x} {\mathrm e}^{\frac {2}{x^{2} \ln \left (5\right )}}+4 \ln \left (5\right ) x^{3} {\mathrm e}^{2 x}-2 x^{2} \ln \left (5\right ) {\mathrm e}^{2 x}\right ) {\mathrm e}^{-\frac {4}{x^{2} \ln \left (5\right )}}}{2 \ln \left (5\right ) x^{2}}\)	\(121\)

[In]

int(((2*x^5+2*x^4)*ln(5)*exp(2/x^2/ln(5))^2+((4*x^5-2*x^3)*ln(5)+8*x^2-8*x)*exp(2/x^2/ln(5))+(2*x^5-2*x^4)*ln(
5)+8*x^2-16*x+8)*exp(x)^2/x^3/ln(5)/exp(2/x^2/ln(5))^2,x,method=_RETURNVERBOSE)

[Out]

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

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 60 vs. \(2 (23) = 46\).

Time = 0.26 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.07 \[ \int \frac {e^{2 x-\frac {4}{x^2 \log (5)}} \left (8-16 x+8 x^2+\left (-2 x^4+2 x^5\right ) \log (5)+e^{\frac {4}{x^2 \log (5)}} \left (2 x^4+2 x^5\right ) \log (5)+e^{\frac {2}{x^2 \log (5)}} \left (-8 x+8 x^2+\left (-2 x^3+4 x^5\right ) \log (5)\right )\right )}{x^3 \log (5)} \, dx={\left (x^{2} e^{\left (\frac {4}{x^{2} \log \left (5\right )}\right )} + x^{2} + 2 \, {\left (x^{2} - x\right )} e^{\left (\frac {2}{x^{2} \log \left (5\right )}\right )} - 2 \, x + 1\right )} e^{\left (\frac {2 \, {\left (x^{3} \log \left (5\right ) - 2\right )}}{x^{2} \log \left (5\right )}\right )} \]

[In]

integrate(((2*x^5+2*x^4)*log(5)*exp(2/x^2/log(5))^2+((4*x^5-2*x^3)*log(5)+8*x^2-8*x)*exp(2/x^2/log(5))+(2*x^5-
2*x^4)*log(5)+8*x^2-16*x+8)*exp(x)^2/x^3/log(5)/exp(2/x^2/log(5))^2,x, algorithm="fricas")

[Out]

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

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 68 vs. \(2 (20) = 40\).

Time = 1.15 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.34 \[ \int \frac {e^{2 x-\frac {4}{x^2 \log (5)}} \left (8-16 x+8 x^2+\left (-2 x^4+2 x^5\right ) \log (5)+e^{\frac {4}{x^2 \log (5)}} \left (2 x^4+2 x^5\right ) \log (5)+e^{\frac {2}{x^2 \log (5)}} \left (-8 x+8 x^2+\left (-2 x^3+4 x^5\right ) \log (5)\right )\right )}{x^3 \log (5)} \, dx=x^{2} e^{2 x} + \left (2 x^{2} e^{2 x} - 2 x e^{2 x}\right ) e^{- \frac {2}{x^{2} \log {\left (5 \right )}}} + \left (x^{2} e^{2 x} - 2 x e^{2 x} + e^{2 x}\right ) e^{- \frac {4}{x^{2} \log {\left (5 \right )}}} \]

[In]

integrate(((2*x**5+2*x**4)*ln(5)*exp(2/x**2/ln(5))**2+((4*x**5-2*x**3)*ln(5)+8*x**2-8*x)*exp(2/x**2/ln(5))+(2*
x**5-2*x**4)*ln(5)+8*x**2-16*x+8)*exp(x)**2/x**3/ln(5)/exp(2/x**2/ln(5))**2,x)

[Out]

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

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 94 vs. \(2 (23) = 46\).

Time = 0.36 (sec) , antiderivative size = 94, normalized size of antiderivative = 3.24 \[ \int \frac {e^{2 x-\frac {4}{x^2 \log (5)}} \left (8-16 x+8 x^2+\left (-2 x^4+2 x^5\right ) \log (5)+e^{\frac {4}{x^2 \log (5)}} \left (2 x^4+2 x^5\right ) \log (5)+e^{\frac {2}{x^2 \log (5)}} \left (-8 x+8 x^2+\left (-2 x^3+4 x^5\right ) \log (5)\right )\right )}{x^3 \log (5)} \, dx=\frac {{\left (2 \, x^{2} - 2 \, x + 1\right )} e^{\left (2 \, x\right )} \log \left (5\right ) + {\left (2 \, x - 1\right )} e^{\left (2 \, x\right )} \log \left (5\right ) + 4 \, {\left (x^{2} \log \left (5\right ) - x \log \left (5\right )\right )} e^{\left (2 \, x - \frac {2}{x^{2} \log \left (5\right )}\right )} + 2 \, {\left (x^{2} \log \left (5\right ) - 2 \, x \log \left (5\right ) + \log \left (5\right )\right )} e^{\left (2 \, x - \frac {4}{x^{2} \log \left (5\right )}\right )}}{2 \, \log \left (5\right )} \]

[In]

integrate(((2*x^5+2*x^4)*log(5)*exp(2/x^2/log(5))^2+((4*x^5-2*x^3)*log(5)+8*x^2-8*x)*exp(2/x^2/log(5))+(2*x^5-
2*x^4)*log(5)+8*x^2-16*x+8)*exp(x)^2/x^3/log(5)/exp(2/x^2/log(5))^2,x, algorithm="maxima")

[Out]

1/2*((2*x^2 - 2*x + 1)*e^(2*x)*log(5) + (2*x - 1)*e^(2*x)*log(5) + 4*(x^2*log(5) - x*log(5))*e^(2*x - 2/(x^2*l
og(5))) + 2*(x^2*log(5) - 2*x*log(5) + log(5))*e^(2*x - 4/(x^2*log(5))))/log(5)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 132 vs. \(2 (23) = 46\).

Time = 0.26 (sec) , antiderivative size = 132, normalized size of antiderivative = 4.55 \[ \int \frac {e^{2 x-\frac {4}{x^2 \log (5)}} \left (8-16 x+8 x^2+\left (-2 x^4+2 x^5\right ) \log (5)+e^{\frac {4}{x^2 \log (5)}} \left (2 x^4+2 x^5\right ) \log (5)+e^{\frac {2}{x^2 \log (5)}} \left (-8 x+8 x^2+\left (-2 x^3+4 x^5\right ) \log (5)\right )\right )}{x^3 \log (5)} \, dx=\frac {x^{2} e^{\left (2 \, x\right )} \log \left (5\right ) + 2 \, x^{2} e^{\left (\frac {2 \, {\left (x^{3} \log \left (5\right ) - 1\right )}}{x^{2} \log \left (5\right )}\right )} \log \left (5\right ) + x^{2} e^{\left (\frac {2 \, {\left (x^{3} \log \left (5\right ) - 2\right )}}{x^{2} \log \left (5\right )}\right )} \log \left (5\right ) - 2 \, x e^{\left (\frac {2 \, {\left (x^{3} \log \left (5\right ) - 1\right )}}{x^{2} \log \left (5\right )}\right )} \log \left (5\right ) - 2 \, x e^{\left (\frac {2 \, {\left (x^{3} \log \left (5\right ) - 2\right )}}{x^{2} \log \left (5\right )}\right )} \log \left (5\right ) + e^{\left (\frac {2 \, {\left (x^{3} \log \left (5\right ) - 2\right )}}{x^{2} \log \left (5\right )}\right )} \log \left (5\right )}{\log \left (5\right )} \]

[In]

integrate(((2*x^5+2*x^4)*log(5)*exp(2/x^2/log(5))^2+((4*x^5-2*x^3)*log(5)+8*x^2-8*x)*exp(2/x^2/log(5))+(2*x^5-
2*x^4)*log(5)+8*x^2-16*x+8)*exp(x)^2/x^3/log(5)/exp(2/x^2/log(5))^2,x, algorithm="giac")

[Out]

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

Mupad [B] (verification not implemented)

Time = 10.57 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.10 \[ \int \frac {e^{2 x-\frac {4}{x^2 \log (5)}} \left (8-16 x+8 x^2+\left (-2 x^4+2 x^5\right ) \log (5)+e^{\frac {4}{x^2 \log (5)}} \left (2 x^4+2 x^5\right ) \log (5)+e^{\frac {2}{x^2 \log (5)}} \left (-8 x+8 x^2+\left (-2 x^3+4 x^5\right ) \log (5)\right )\right )}{x^3 \log (5)} \, dx={\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{-\frac {4}{x^2\,\ln \left (5\right )}}\,{\left (x+x\,{\mathrm {e}}^{\frac {2}{x^2\,\ln \left (5\right )}}-1\right )}^2 \]

[In]

int(-(exp(2*x)*exp(-4/(x^2*log(5)))*(16*x + log(5)*(2*x^4 - 2*x^5) + exp(2/(x^2*log(5)))*(8*x + log(5)*(2*x^3
- 4*x^5) - 8*x^2) - 8*x^2 - exp(4/(x^2*log(5)))*log(5)*(2*x^4 + 2*x^5) - 8))/(x^3*log(5)),x)

[Out]

exp(2*x)*exp(-4/(x^2*log(5)))*(x + x*exp(2/(x^2*log(5))) - 1)^2