\(\int \frac {e^{-6+\frac {-4+4 e^3+e^6 (-1+4 x^2)+(-4 e^3+2 e^6) \log (5)-e^6 \log ^2(5)}{e^6 x^2}} (32-8 x+e^3 (-32+8 x)+e^6 (8-2 x+4 x^2-2 x^3)+(e^3 (32-8 x)+e^6 (-16+4 x)) \log (5)+e^6 (8-2 x) \log ^2(5))}{x^2} \, dx\) [6608]

Optimal result

Integrand size = 124, antiderivative size = 27 \[ \int \frac {e^{-6+\frac {-4+4 e^3+e^6 \left (-1+4 x^2\right )+\left (-4 e^3+2 e^6\right ) \log (5)-e^6 \log ^2(5)}{e^6 x^2}} \left (32-8 x+e^3 (-32+8 x)+e^6 \left (8-2 x+4 x^2-2 x^3\right )+\left (e^3 (32-8 x)+e^6 (-16+4 x)\right ) \log (5)+e^6 (8-2 x) \log ^2(5)\right )}{x^2} \, dx=e^{4-\frac {\left (-1+\frac {2}{e^3}+\log (5)\right )^2}{x^2}} (4-x) x \]

[Out]

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

Rubi [A] (verified)

Time = 1.58 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.26, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.016, Rules used = {6873, 2326} \[ \int \frac {e^{-6+\frac {-4+4 e^3+e^6 \left (-1+4 x^2\right )+\left (-4 e^3+2 e^6\right ) \log (5)-e^6 \log ^2(5)}{e^6 x^2}} \left (32-8 x+e^3 (-32+8 x)+e^6 \left (8-2 x+4 x^2-2 x^3\right )+\left (e^3 (32-8 x)+e^6 (-16+4 x)\right ) \log (5)+e^6 (8-2 x) \log ^2(5)\right )}{x^2} \, dx=(4-x) x e^{4-\frac {\left (2-e^3 (1-\log (5))\right )^2}{e^6 x^2}} \]

[In]

Int[(E^(-6 + (-4 + 4*E^3 + E^6*(-1 + 4*x^2) + (-4*E^3 + 2*E^6)*Log[5] - E^6*Log[5]^2)/(E^6*x^2))*(32 - 8*x + E
^3*(-32 + 8*x) + E^6*(8 - 2*x + 4*x^2 - 2*x^3) + (E^3*(32 - 8*x) + E^6*(-16 + 4*x))*Log[5] + E^6*(8 - 2*x)*Log
[5]^2))/x^2,x]

[Out]

E^(4 - (2 - E^3*(1 - Log[5]))^2/(E^6*x^2))*(4 - x)*x

Rule 2326

Int[(y_.)*(F_)^(u_)*((v_) + (w_)), x_Symbol] :> With[{z = v*(y/(Log[F]*D[u, x]))}, Simp[F^u*z, x] /; EqQ[D[z,
x], w*y]] /; FreeQ[F, x]

Rule 6873

Int[u_, x_Symbol] :> With[{v = NormalizeIntegrand[u, x]}, Int[v, x] /; v =!= u]

Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (-2+\frac {-4+4 e^3-e^6-4 e^3 \log (5)+2 e^6 \log (5)-e^6 \log ^2(5)}{e^6 x^2}\right ) \left (4 e^6 x^2-2 e^6 x^3+8 \left (2-e^3 (1-\log (5))\right )^2-2 x \left (2-e^3 (1-\log (5))\right )^2\right )}{x^2} \, dx \\ & = e^{4-\frac {\left (2-e^3 (1-\log (5))\right )^2}{e^6 x^2}} (4-x) x \\ \end{align*}

Mathematica [A] (verified)

Time = 0.11 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.00 \[ \int \frac {e^{-6+\frac {-4+4 e^3+e^6 \left (-1+4 x^2\right )+\left (-4 e^3+2 e^6\right ) \log (5)-e^6 \log ^2(5)}{e^6 x^2}} \left (32-8 x+e^3 (-32+8 x)+e^6 \left (8-2 x+4 x^2-2 x^3\right )+\left (e^3 (32-8 x)+e^6 (-16+4 x)\right ) \log (5)+e^6 (8-2 x) \log ^2(5)\right )}{x^2} \, dx=-5^{\frac {2 \left (-2+e^3\right )}{e^3 x^2}} e^{\frac {-4+4 e^3+e^6 \left (-1+4 x^2-\log ^2(5)\right )}{e^6 x^2}} (-4+x) x \]

[In]

Integrate[(E^(-6 + (-4 + 4*E^3 + E^6*(-1 + 4*x^2) + (-4*E^3 + 2*E^6)*Log[5] - E^6*Log[5]^2)/(E^6*x^2))*(32 - 8
*x + E^3*(-32 + 8*x) + E^6*(8 - 2*x + 4*x^2 - 2*x^3) + (E^3*(32 - 8*x) + E^6*(-16 + 4*x))*Log[5] + E^6*(8 - 2*
x)*Log[5]^2))/x^2,x]

[Out]

-(5^((2*(-2 + E^3))/(E^3*x^2))*E^((-4 + 4*E^3 + E^6*(-1 + 4*x^2 - Log[5]^2))/(E^6*x^2))*(-4 + x)*x)

Maple [A] (verified)

Time = 0.79 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.00

method	result	size
risch	\(25^{\frac {1}{x^{2}}} \left (\frac {1}{625}\right )^{\frac {{\mathrm e}^{-3}}{x^{2}}} \left (-x^{2} {\mathrm e}^{6}+4 x \,{\mathrm e}^{6}\right ) {\mathrm e}^{\frac {-\ln \left (5\right )^{2}-2 x^{2}-4 \,{\mathrm e}^{-6}+4 \,{\mathrm e}^{-3}-1}{x^{2}}}\)	\(54\)
gosper	\(-{\mathrm e}^{-\frac {\left ({\mathrm e}^{6} \ln \left (5\right )^{2}-4 x^{2} {\mathrm e}^{6}-2 \ln \left (5\right ) {\mathrm e}^{6}+4 \,{\mathrm e}^{3} \ln \left (5\right )+{\mathrm e}^{6}-4 \,{\mathrm e}^{3}+4\right ) {\mathrm e}^{-6}}{x^{2}}} \left (x -4\right ) x\)	\(59\)
parallelrisch	\({\mathrm e}^{-6} \left (-{\mathrm e}^{6} x^{2} {\mathrm e}^{\frac {\left (-{\mathrm e}^{6} \ln \left (5\right )^{2}+\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \left (5\right )+\left (4 x^{2}-1\right ) {\mathrm e}^{6}+4 \,{\mathrm e}^{3}-4\right ) {\mathrm e}^{-6}}{x^{2}}}+4 \,{\mathrm e}^{6} x \,{\mathrm e}^{\frac {\left (-{\mathrm e}^{6} \ln \left (5\right )^{2}+\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \left (5\right )+\left (4 x^{2}-1\right ) {\mathrm e}^{6}+4 \,{\mathrm e}^{3}-4\right ) {\mathrm e}^{-6}}{x^{2}}}\right )\)	\(125\)
norman	\(\frac {\left (4 x^{2} {\mathrm e}^{3} {\mathrm e}^{\frac {\left (-{\mathrm e}^{6} \ln \left (5\right )^{2}+\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \left (5\right )+\left (4 x^{2}-1\right ) {\mathrm e}^{6}+4 \,{\mathrm e}^{3}-4\right ) {\mathrm e}^{-6}}{x^{2}}}-x^{3} {\mathrm e}^{3} {\mathrm e}^{\frac {\left (-{\mathrm e}^{6} \ln \left (5\right )^{2}+\left (2 \,{\mathrm e}^{6}-4 \,{\mathrm e}^{3}\right ) \ln \left (5\right )+\left (4 x^{2}-1\right ) {\mathrm e}^{6}+4 \,{\mathrm e}^{3}-4\right ) {\mathrm e}^{-6}}{x^{2}}}\right ) {\mathrm e}^{-3}}{x}\)	\(126\)
default	\(\text {Expression too large to display}\)	\(826\)
derivativedivides	\(\text {Expression too large to display}\)	\(827\)
meijerg	\(\text {Expression too large to display}\)	\(1041\)

[In]

int(((-2*x+8)*exp(3)^2*ln(5)^2+((4*x-16)*exp(3)^2+(-8*x+32)*exp(3))*ln(5)+(-2*x^3+4*x^2-2*x+8)*exp(3)^2+(8*x-3
2)*exp(3)-8*x+32)*exp((-exp(3)^2*ln(5)^2+(2*exp(3)^2-4*exp(3))*ln(5)+(4*x^2-1)*exp(3)^2+4*exp(3)-4)/x^2/exp(3)
^2)/x^2/exp(3)^2,x,method=_RETURNVERBOSE)

[Out]

25^(1/x^2)*(1/625)^(1/x^2*exp(-3))*(-x^2*exp(6)+4*x*exp(6))*exp((-ln(5)^2-2*x^2-4*exp(-6)+4*exp(-3)-1)/x^2)

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 53 vs. \(2 (24) = 48\).

Time = 0.37 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.96 \[ \int \frac {e^{-6+\frac {-4+4 e^3+e^6 \left (-1+4 x^2\right )+\left (-4 e^3+2 e^6\right ) \log (5)-e^6 \log ^2(5)}{e^6 x^2}} \left (32-8 x+e^3 (-32+8 x)+e^6 \left (8-2 x+4 x^2-2 x^3\right )+\left (e^3 (32-8 x)+e^6 (-16+4 x)\right ) \log (5)+e^6 (8-2 x) \log ^2(5)\right )}{x^2} \, dx=-{\left (x^{2} - 4 \, x\right )} e^{\left (-\frac {{\left (e^{6} \log \left (5\right )^{2} + {\left (2 \, x^{2} + 1\right )} e^{6} - 2 \, {\left (e^{6} - 2 \, e^{3}\right )} \log \left (5\right ) - 4 \, e^{3} + 4\right )} e^{\left (-6\right )}}{x^{2}} + 6\right )} \]

[In]

integrate(((-2*x+8)*exp(3)^2*log(5)^2+((4*x-16)*exp(3)^2+(-8*x+32)*exp(3))*log(5)+(-2*x^3+4*x^2-2*x+8)*exp(3)^
2+(8*x-32)*exp(3)-8*x+32)*exp((-exp(3)^2*log(5)^2+(2*exp(3)^2-4*exp(3))*log(5)+(4*x^2-1)*exp(3)^2+4*exp(3)-4)/
x^2/exp(3)^2)/x^2/exp(3)^2,x, algorithm="fricas")

[Out]

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

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 53 vs. \(2 (22) = 44\).

Time = 0.42 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.96 \[ \int \frac {e^{-6+\frac {-4+4 e^3+e^6 \left (-1+4 x^2\right )+\left (-4 e^3+2 e^6\right ) \log (5)-e^6 \log ^2(5)}{e^6 x^2}} \left (32-8 x+e^3 (-32+8 x)+e^6 \left (8-2 x+4 x^2-2 x^3\right )+\left (e^3 (32-8 x)+e^6 (-16+4 x)\right ) \log (5)+e^6 (8-2 x) \log ^2(5)\right )}{x^2} \, dx=\left (- x^{2} + 4 x\right ) e^{\frac {\left (4 x^{2} - 1\right ) e^{6} - e^{6} \log {\left (5 \right )}^{2} - 4 + 4 e^{3} + \left (- 4 e^{3} + 2 e^{6}\right ) \log {\left (5 \right )}}{x^{2} e^{6}}} \]

[In]

integrate(((-2*x+8)*exp(3)**2*ln(5)**2+((4*x-16)*exp(3)**2+(-8*x+32)*exp(3))*ln(5)+(-2*x**3+4*x**2-2*x+8)*exp(
3)**2+(8*x-32)*exp(3)-8*x+32)*exp((-exp(3)**2*ln(5)**2+(2*exp(3)**2-4*exp(3))*ln(5)+(4*x**2-1)*exp(3)**2+4*exp
(3)-4)/x**2/exp(3)**2)/x**2/exp(3)**2,x)

[Out]

(-x**2 + 4*x)*exp(((4*x**2 - 1)*exp(6) - exp(6)*log(5)**2 - 4 + 4*exp(3) + (-4*exp(3) + 2*exp(6))*log(5))*exp(
-6)/x**2)

Maxima [C] (verification not implemented)

Result contains higher order function than in optimal. Order 4 vs. order 3.

Time = 0.60 (sec) , antiderivative size = 450, normalized size of antiderivative = 16.67 \[ \int \frac {e^{-6+\frac {-4+4 e^3+e^6 \left (-1+4 x^2\right )+\left (-4 e^3+2 e^6\right ) \log (5)-e^6 \log ^2(5)}{e^6 x^2}} \left (32-8 x+e^3 (-32+8 x)+e^6 \left (8-2 x+4 x^2-2 x^3\right )+\left (e^3 (32-8 x)+e^6 (-16+4 x)\right ) \log (5)+e^6 (8-2 x) \log ^2(5)\right )}{x^2} \, dx=2 \, x \sqrt {\frac {1}{x^{2}}} {\left | e^{3} \log \left (5\right ) - e^{3} + 2 \right |} e \Gamma \left (-\frac {1}{2}, \frac {{\left (e^{3} \log \left (5\right ) - e^{3} + 2\right )}^{2} e^{\left (-6\right )}}{x^{2}}\right ) - {\left (e^{3} \log \left (5\right ) - e^{3} + 2\right )}^{2} e^{\left (-2\right )} \Gamma \left (-1, \frac {{\left (e^{3} \log \left (5\right ) - e^{3} + 2\right )}^{2} e^{\left (-6\right )}}{x^{2}}\right ) + {\rm Ei}\left (-\frac {{\left (e^{3} \log \left (5\right ) - e^{3} + 2\right )}^{2} e^{\left (-6\right )}}{x^{2}}\right ) e^{4} \log \left (5\right )^{2} - \frac {4 \, \sqrt {\pi } \operatorname {erf}\left (\frac {{\left ({\left (\log \left (5\right ) - 1\right )} e^{3} + 2\right )} e^{\left (-3\right )}}{x}\right ) e^{7} \log \left (5\right )^{2}}{{\left (\log \left (5\right ) - 1\right )} e^{3} + 2} - 2 \, {\rm Ei}\left (-\frac {{\left (e^{3} \log \left (5\right ) - e^{3} + 2\right )}^{2} e^{\left (-6\right )}}{x^{2}}\right ) e^{4} \log \left (5\right ) + 4 \, {\rm Ei}\left (-\frac {{\left (e^{3} \log \left (5\right ) - e^{3} + 2\right )}^{2} e^{\left (-6\right )}}{x^{2}}\right ) e \log \left (5\right ) + \frac {8 \, \sqrt {\pi } \operatorname {erf}\left (\frac {{\left ({\left (\log \left (5\right ) - 1\right )} e^{3} + 2\right )} e^{\left (-3\right )}}{x}\right ) e^{7} \log \left (5\right )}{{\left (\log \left (5\right ) - 1\right )} e^{3} + 2} - \frac {16 \, \sqrt {\pi } \operatorname {erf}\left (\frac {{\left ({\left (\log \left (5\right ) - 1\right )} e^{3} + 2\right )} e^{\left (-3\right )}}{x}\right ) e^{4} \log \left (5\right )}{{\left (\log \left (5\right ) - 1\right )} e^{3} + 2} + {\rm Ei}\left (-\frac {{\left (e^{3} \log \left (5\right ) - e^{3} + 2\right )}^{2} e^{\left (-6\right )}}{x^{2}}\right ) e^{4} - 4 \, {\rm Ei}\left (-\frac {{\left (e^{3} \log \left (5\right ) - e^{3} + 2\right )}^{2} e^{\left (-6\right )}}{x^{2}}\right ) e + 4 \, {\rm Ei}\left (-\frac {{\left (e^{3} \log \left (5\right ) - e^{3} + 2\right )}^{2} e^{\left (-6\right )}}{x^{2}}\right ) e^{\left (-2\right )} - \frac {4 \, \sqrt {\pi } \operatorname {erf}\left (\frac {{\left ({\left (\log \left (5\right ) - 1\right )} e^{3} + 2\right )} e^{\left (-3\right )}}{x}\right ) e^{7}}{{\left (\log \left (5\right ) - 1\right )} e^{3} + 2} + \frac {16 \, \sqrt {\pi } \operatorname {erf}\left (\frac {{\left ({\left (\log \left (5\right ) - 1\right )} e^{3} + 2\right )} e^{\left (-3\right )}}{x}\right ) e^{4}}{{\left (\log \left (5\right ) - 1\right )} e^{3} + 2} - \frac {16 \, \sqrt {\pi } \operatorname {erf}\left (\frac {{\left ({\left (\log \left (5\right ) - 1\right )} e^{3} + 2\right )} e^{\left (-3\right )}}{x}\right ) e}{{\left (\log \left (5\right ) - 1\right )} e^{3} + 2} \]

[In]

integrate(((-2*x+8)*exp(3)^2*log(5)^2+((4*x-16)*exp(3)^2+(-8*x+32)*exp(3))*log(5)+(-2*x^3+4*x^2-2*x+8)*exp(3)^
2+(8*x-32)*exp(3)-8*x+32)*exp((-exp(3)^2*log(5)^2+(2*exp(3)^2-4*exp(3))*log(5)+(4*x^2-1)*exp(3)^2+4*exp(3)-4)/
x^2/exp(3)^2)/x^2/exp(3)^2,x, algorithm="maxima")

[Out]

2*x*sqrt(x^(-2))*abs(e^3*log(5) - e^3 + 2)*e*gamma(-1/2, (e^3*log(5) - e^3 + 2)^2*e^(-6)/x^2) - (e^3*log(5) -
e^3 + 2)^2*e^(-2)*gamma(-1, (e^3*log(5) - e^3 + 2)^2*e^(-6)/x^2) + Ei(-(e^3*log(5) - e^3 + 2)^2*e^(-6)/x^2)*e^
4*log(5)^2 - 4*sqrt(pi)*erf(((log(5) - 1)*e^3 + 2)*e^(-3)/x)*e^7*log(5)^2/((log(5) - 1)*e^3 + 2) - 2*Ei(-(e^3*
log(5) - e^3 + 2)^2*e^(-6)/x^2)*e^4*log(5) + 4*Ei(-(e^3*log(5) - e^3 + 2)^2*e^(-6)/x^2)*e*log(5) + 8*sqrt(pi)*
erf(((log(5) - 1)*e^3 + 2)*e^(-3)/x)*e^7*log(5)/((log(5) - 1)*e^3 + 2) - 16*sqrt(pi)*erf(((log(5) - 1)*e^3 + 2
)*e^(-3)/x)*e^4*log(5)/((log(5) - 1)*e^3 + 2) + Ei(-(e^3*log(5) - e^3 + 2)^2*e^(-6)/x^2)*e^4 - 4*Ei(-(e^3*log(
5) - e^3 + 2)^2*e^(-6)/x^2)*e + 4*Ei(-(e^3*log(5) - e^3 + 2)^2*e^(-6)/x^2)*e^(-2) - 4*sqrt(pi)*erf(((log(5) -
1)*e^3 + 2)*e^(-3)/x)*e^7/((log(5) - 1)*e^3 + 2) + 16*sqrt(pi)*erf(((log(5) - 1)*e^3 + 2)*e^(-3)/x)*e^4/((log(
5) - 1)*e^3 + 2) - 16*sqrt(pi)*erf(((log(5) - 1)*e^3 + 2)*e^(-3)/x)*e/((log(5) - 1)*e^3 + 2)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 99 vs. \(2 (24) = 48\).

Time = 0.51 (sec) , antiderivative size = 99, normalized size of antiderivative = 3.67 \[ \int \frac {e^{-6+\frac {-4+4 e^3+e^6 \left (-1+4 x^2\right )+\left (-4 e^3+2 e^6\right ) \log (5)-e^6 \log ^2(5)}{e^6 x^2}} \left (32-8 x+e^3 (-32+8 x)+e^6 \left (8-2 x+4 x^2-2 x^3\right )+\left (e^3 (32-8 x)+e^6 (-16+4 x)\right ) \log (5)+e^6 (8-2 x) \log ^2(5)\right )}{x^2} \, dx=-x^{2} e^{\left (\frac {{\left (x^{2} e^{6} - e^{6} \log \left (5\right )^{2} + 2 \, e^{6} \log \left (5\right ) - 4 \, e^{3} \log \left (5\right ) - e^{6} + 4 \, e^{3} - 4\right )} e^{\left (-6\right )}}{x^{2}} + 3\right )} + 4 \, x e^{\left (\frac {{\left (x^{2} e^{6} - e^{6} \log \left (5\right )^{2} + 2 \, e^{6} \log \left (5\right ) - 4 \, e^{3} \log \left (5\right ) - e^{6} + 4 \, e^{3} - 4\right )} e^{\left (-6\right )}}{x^{2}} + 3\right )} \]

[In]

integrate(((-2*x+8)*exp(3)^2*log(5)^2+((4*x-16)*exp(3)^2+(-8*x+32)*exp(3))*log(5)+(-2*x^3+4*x^2-2*x+8)*exp(3)^
2+(8*x-32)*exp(3)-8*x+32)*exp((-exp(3)^2*log(5)^2+(2*exp(3)^2-4*exp(3))*log(5)+(4*x^2-1)*exp(3)^2+4*exp(3)-4)/
x^2/exp(3)^2)/x^2/exp(3)^2,x, algorithm="giac")

[Out]

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

Mupad [B] (verification not implemented)

Time = 11.66 (sec) , antiderivative size = 56, normalized size of antiderivative = 2.07 \[ \int \frac {e^{-6+\frac {-4+4 e^3+e^6 \left (-1+4 x^2\right )+\left (-4 e^3+2 e^6\right ) \log (5)-e^6 \log ^2(5)}{e^6 x^2}} \left (32-8 x+e^3 (-32+8 x)+e^6 \left (8-2 x+4 x^2-2 x^3\right )+\left (e^3 (32-8 x)+e^6 (-16+4 x)\right ) \log (5)+e^6 (8-2 x) \log ^2(5)\right )}{x^2} \, dx=-\frac {{25}^{\frac {1}{x^2}}\,x\,{\mathrm {e}}^{\frac {4\,{\mathrm {e}}^{-3}}{x^2}}\,{\mathrm {e}}^{-\frac {4\,{\mathrm {e}}^{-6}}{x^2}}\,{\mathrm {e}}^4\,{\mathrm {e}}^{-\frac {{\ln \left (5\right )}^2}{x^2}}\,{\mathrm {e}}^{-\frac {1}{x^2}}\,\left (x-4\right )}{{25}^{\frac {2\,{\mathrm {e}}^{-3}}{x^2}}} \]

[In]

int(-(exp(-6)*exp(-(exp(-6)*(exp(6)*log(5)^2 - exp(6)*(4*x^2 - 1) - 4*exp(3) + log(5)*(4*exp(3) - 2*exp(6)) +
4))/x^2)*(8*x - log(5)*(exp(6)*(4*x - 16) - exp(3)*(8*x - 32)) + exp(6)*(2*x - 4*x^2 + 2*x^3 - 8) - exp(3)*(8*
x - 32) + exp(6)*log(5)^2*(2*x - 8) - 32))/x^2,x)

[Out]

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