3.26.45 \(\int \frac {e^{-2+3 e^x} (-2-6 e^x x)+e^{2 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} (-2+e^{4+x+x^2+2 x \log (x)+\log ^2(x)} (-12 x-8 x^2+(-8-8 x) \log (x)))}{e^{4 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} x^2+e^{-4+6 e^x} x^2+2 e^{-2+3 e^x+2 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} x^2} \, dx\)

Optimal. Leaf size=32 \[ \frac {2}{\left (e^{2 e^{4+x+(x+\log (x))^2}}+e^{-2+3 e^x}\right ) x} \]

________________________________________________________________________________________

Rubi [F]  time = 14.54, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {e^{-2+3 e^x} \left (-2-6 e^x x\right )+e^{2 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} \left (-2+e^{4+x+x^2+2 x \log (x)+\log ^2(x)} \left (-12 x-8 x^2+(-8-8 x) \log (x)\right )\right )}{e^{4 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} x^2+e^{-4+6 e^x} x^2+2 \exp \left (-2+3 e^x+2 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}\right ) x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(-2 + 3*E^x)*(-2 - 6*E^x*x) + E^(2*E^(4 + x + x^2 + 2*x*Log[x] + Log[x]^2))*(-2 + E^(4 + x + x^2 + 2*x*
Log[x] + Log[x]^2)*(-12*x - 8*x^2 + (-8 - 8*x)*Log[x])))/(E^(4*E^(4 + x + x^2 + 2*x*Log[x] + Log[x]^2))*x^2 +
E^(-4 + 6*E^x)*x^2 + 2*E^(-2 + 3*E^x + 2*E^(4 + x + x^2 + 2*x*Log[x] + Log[x]^2))*x^2),x]

[Out]

-2*E^2*Defer[Int][1/((E^(3*E^x) + E^(2 + 2*E^(4 + x + x^2 + Log[x]^2)*x^(2*x)))*x^2), x] - 6*E^2*Defer[Int][E^
(3*E^x + x)/((E^(3*E^x) + E^(2 + 2*E^(4 + x + x^2 + Log[x]^2)*x^(2*x)))^2*x), x] - 8*E^4*Defer[Int][(E^(4 + x
+ x^2 + 2*E^(4 + x + x^2 + Log[x]^2)*x^(2*x) + Log[x]^2)*x^(2*x))/(E^(3*E^x) + E^(2 + 2*E^(4 + x + x^2 + Log[x
]^2)*x^(2*x)))^2, x] - 12*E^4*Defer[Int][(E^(4 + x + x^2 + 2*E^(4 + x + x^2 + Log[x]^2)*x^(2*x) + Log[x]^2)*x^
(-1 + 2*x))/(E^(3*E^x) + E^(2 + 2*E^(4 + x + x^2 + Log[x]^2)*x^(2*x)))^2, x] - 8*E^4*Defer[Int][(E^(4 + x + x^
2 + 2*E^(4 + x + x^2 + Log[x]^2)*x^(2*x) + Log[x]^2)*x^(-2 + 2*x)*Log[x])/(E^(3*E^x) + E^(2 + 2*E^(4 + x + x^2
+ Log[x]^2)*x^(2*x)))^2, x] - 8*E^4*Defer[Int][(E^(4 + x + x^2 + 2*E^(4 + x + x^2 + Log[x]^2)*x^(2*x) + Log[x
]^2)*x^(-1 + 2*x)*Log[x])/(E^(3*E^x) + E^(2 + 2*E^(4 + x + x^2 + Log[x]^2)*x^(2*x)))^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^4 \left (e^{-2+3 e^x} \left (-2-6 e^x x\right )+e^{2 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} \left (-2+e^{4+x+x^2+2 x \log (x)+\log ^2(x)} \left (-12 x-8 x^2+(-8-8 x) \log (x)\right )\right )\right )}{\left (e^{3 e^x}+e^{2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}}\right )^2 x^2} \, dx\\ &=e^4 \int \frac {e^{-2+3 e^x} \left (-2-6 e^x x\right )+e^{2 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} \left (-2+e^{4+x+x^2+2 x \log (x)+\log ^2(x)} \left (-12 x-8 x^2+(-8-8 x) \log (x)\right )\right )}{\left (e^{3 e^x}+e^{2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}}\right )^2 x^2} \, dx\\ &=e^4 \int \left (-\frac {2 \left (e^{3 e^x}+e^{2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}}+3 e^{3 e^x+x} x\right )}{e^2 \left (e^{3 e^x}+e^{2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}}\right )^2 x^2}-\frac {4 \exp \left (4+x+x^2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}+\log ^2(x)\right ) x^{-2+2 x} \left (3 x+2 x^2+2 \log (x)+2 x \log (x)\right )}{\left (e^{3 e^x}+e^{2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}}\right )^2}\right ) \, dx\\ &=-\left (\left (2 e^2\right ) \int \frac {e^{3 e^x}+e^{2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}}+3 e^{3 e^x+x} x}{\left (e^{3 e^x}+e^{2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}}\right )^2 x^2} \, dx\right )-\left (4 e^4\right ) \int \frac {\exp \left (4+x+x^2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}+\log ^2(x)\right ) x^{-2+2 x} \left (3 x+2 x^2+2 \log (x)+2 x \log (x)\right )}{\left (e^{3 e^x}+e^{2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}}\right )^2} \, dx\\ &=-\left (\left (2 e^2\right ) \int \left (\frac {1}{\left (e^{3 e^x}+e^{2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}}\right ) x^2}+\frac {3 e^{3 e^x+x}}{\left (e^{3 e^x}+e^{2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}}\right )^2 x}\right ) \, dx\right )-\left (4 e^4\right ) \int \left (\frac {2 \exp \left (4+x+x^2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}+\log ^2(x)\right ) x^{2 x}}{\left (e^{3 e^x}+e^{2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}}\right )^2}+\frac {3 \exp \left (4+x+x^2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}+\log ^2(x)\right ) x^{-1+2 x}}{\left (e^{3 e^x}+e^{2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}}\right )^2}+\frac {2 \exp \left (4+x+x^2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}+\log ^2(x)\right ) x^{-2+2 x} \log (x)}{\left (e^{3 e^x}+e^{2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}}\right )^2}+\frac {2 \exp \left (4+x+x^2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}+\log ^2(x)\right ) x^{-1+2 x} \log (x)}{\left (e^{3 e^x}+e^{2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}}\right )^2}\right ) \, dx\\ &=-\left (\left (2 e^2\right ) \int \frac {1}{\left (e^{3 e^x}+e^{2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}}\right ) x^2} \, dx\right )-\left (6 e^2\right ) \int \frac {e^{3 e^x+x}}{\left (e^{3 e^x}+e^{2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}}\right )^2 x} \, dx-\left (8 e^4\right ) \int \frac {\exp \left (4+x+x^2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}+\log ^2(x)\right ) x^{2 x}}{\left (e^{3 e^x}+e^{2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}}\right )^2} \, dx-\left (8 e^4\right ) \int \frac {\exp \left (4+x+x^2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}+\log ^2(x)\right ) x^{-2+2 x} \log (x)}{\left (e^{3 e^x}+e^{2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}}\right )^2} \, dx-\left (8 e^4\right ) \int \frac {\exp \left (4+x+x^2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}+\log ^2(x)\right ) x^{-1+2 x} \log (x)}{\left (e^{3 e^x}+e^{2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}}\right )^2} \, dx-\left (12 e^4\right ) \int \frac {\exp \left (4+x+x^2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}+\log ^2(x)\right ) x^{-1+2 x}}{\left (e^{3 e^x}+e^{2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}}\right )^2} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.47, size = 41, normalized size = 1.28 \begin {gather*} \frac {2 e^2}{\left (e^{3 e^x}+e^{2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}}\right ) x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(-2 + 3*E^x)*(-2 - 6*E^x*x) + E^(2*E^(4 + x + x^2 + 2*x*Log[x] + Log[x]^2))*(-2 + E^(4 + x + x^2
+ 2*x*Log[x] + Log[x]^2)*(-12*x - 8*x^2 + (-8 - 8*x)*Log[x])))/(E^(4*E^(4 + x + x^2 + 2*x*Log[x] + Log[x]^2))*
x^2 + E^(-4 + 6*E^x)*x^2 + 2*E^(-2 + 3*E^x + 2*E^(4 + x + x^2 + 2*x*Log[x] + Log[x]^2))*x^2),x]

[Out]

(2*E^2)/((E^(3*E^x) + E^(2 + 2*E^(4 + x + x^2 + Log[x]^2)*x^(2*x)))*x)

________________________________________________________________________________________

fricas [A]  time = 1.10, size = 48, normalized size = 1.50 \begin {gather*} \frac {2 \, e^{\left (3 \, e^{x} - 2\right )}}{x e^{\left (2 \, e^{\left (x^{2} + 2 \, x \log \relax (x) + \log \relax (x)^{2} + x + 4\right )} + 3 \, e^{x} - 2\right )} + x e^{\left (6 \, e^{x} - 4\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-8*x-8)*log(x)-8*x^2-12*x)*exp(log(x)^2+2*x*log(x)+x^2+x+4)-2)*exp(exp(log(x)^2+2*x*log(x)+x^2+x
+4))^2+(-6*exp(x)*x-2)*exp(3*exp(x)-2))/(x^2*exp(exp(log(x)^2+2*x*log(x)+x^2+x+4))^4+2*x^2*exp(3*exp(x)-2)*exp
(exp(log(x)^2+2*x*log(x)+x^2+x+4))^2+x^2*exp(3*exp(x)-2)^2),x, algorithm="fricas")

[Out]

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

________________________________________________________________________________________

giac [B]  time = 2.50, size = 394, normalized size = 12.31 \begin {gather*} \frac {2 \, {\left (4 \, x^{2} e^{\left (x^{2} + 2 \, x \log \relax (x) + \log \relax (x)^{2} + x + 10\right )} + 4 \, x e^{\left (x^{2} + 2 \, x \log \relax (x) + \log \relax (x)^{2} + x + 10\right )} \log \relax (x) + 6 \, x e^{\left (x^{2} + 2 \, x \log \relax (x) + \log \relax (x)^{2} + x + 10\right )} - 3 \, x e^{\left (x + 6\right )} + 4 \, e^{\left (x^{2} + 2 \, x \log \relax (x) + \log \relax (x)^{2} + x + 10\right )} \log \relax (x)\right )}}{4 \, x^{3} e^{\left (x^{2} + 2 \, x \log \relax (x) + \log \relax (x)^{2} + x + 2 \, e^{\left (x^{2} + 2 \, x \log \relax (x) + \log \relax (x)^{2} + x + 4\right )} + 10\right )} + 4 \, x^{3} e^{\left (x^{2} + 2 \, x \log \relax (x) + \log \relax (x)^{2} + x + 3 \, e^{x} + 8\right )} + 4 \, x^{2} e^{\left (x^{2} + 2 \, x \log \relax (x) + \log \relax (x)^{2} + x + 2 \, e^{\left (x^{2} + 2 \, x \log \relax (x) + \log \relax (x)^{2} + x + 4\right )} + 10\right )} \log \relax (x) + 4 \, x^{2} e^{\left (x^{2} + 2 \, x \log \relax (x) + \log \relax (x)^{2} + x + 3 \, e^{x} + 8\right )} \log \relax (x) + 6 \, x^{2} e^{\left (x^{2} + 2 \, x \log \relax (x) + \log \relax (x)^{2} + x + 2 \, e^{\left (x^{2} + 2 \, x \log \relax (x) + \log \relax (x)^{2} + x + 4\right )} + 10\right )} + 6 \, x^{2} e^{\left (x^{2} + 2 \, x \log \relax (x) + \log \relax (x)^{2} + x + 3 \, e^{x} + 8\right )} - 3 \, x^{2} e^{\left (x + 2 \, e^{\left (x^{2} + 2 \, x \log \relax (x) + \log \relax (x)^{2} + x + 4\right )} + 6\right )} - 3 \, x^{2} e^{\left (x + 3 \, e^{x} + 4\right )} + 4 \, x e^{\left (x^{2} + 2 \, x \log \relax (x) + \log \relax (x)^{2} + x + 2 \, e^{\left (x^{2} + 2 \, x \log \relax (x) + \log \relax (x)^{2} + x + 4\right )} + 10\right )} \log \relax (x) + 4 \, x e^{\left (x^{2} + 2 \, x \log \relax (x) + \log \relax (x)^{2} + x + 3 \, e^{x} + 8\right )} \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-8*x-8)*log(x)-8*x^2-12*x)*exp(log(x)^2+2*x*log(x)+x^2+x+4)-2)*exp(exp(log(x)^2+2*x*log(x)+x^2+x
+4))^2+(-6*exp(x)*x-2)*exp(3*exp(x)-2))/(x^2*exp(exp(log(x)^2+2*x*log(x)+x^2+x+4))^4+2*x^2*exp(3*exp(x)-2)*exp
(exp(log(x)^2+2*x*log(x)+x^2+x+4))^2+x^2*exp(3*exp(x)-2)^2),x, algorithm="giac")

[Out]

2*(4*x^2*e^(x^2 + 2*x*log(x) + log(x)^2 + x + 10) + 4*x*e^(x^2 + 2*x*log(x) + log(x)^2 + x + 10)*log(x) + 6*x*
e^(x^2 + 2*x*log(x) + log(x)^2 + x + 10) - 3*x*e^(x + 6) + 4*e^(x^2 + 2*x*log(x) + log(x)^2 + x + 10)*log(x))/
(4*x^3*e^(x^2 + 2*x*log(x) + log(x)^2 + x + 2*e^(x^2 + 2*x*log(x) + log(x)^2 + x + 4) + 10) + 4*x^3*e^(x^2 + 2
*x*log(x) + log(x)^2 + x + 3*e^x + 8) + 4*x^2*e^(x^2 + 2*x*log(x) + log(x)^2 + x + 2*e^(x^2 + 2*x*log(x) + log
(x)^2 + x + 4) + 10)*log(x) + 4*x^2*e^(x^2 + 2*x*log(x) + log(x)^2 + x + 3*e^x + 8)*log(x) + 6*x^2*e^(x^2 + 2*
x*log(x) + log(x)^2 + x + 2*e^(x^2 + 2*x*log(x) + log(x)^2 + x + 4) + 10) + 6*x^2*e^(x^2 + 2*x*log(x) + log(x)
^2 + x + 3*e^x + 8) - 3*x^2*e^(x + 2*e^(x^2 + 2*x*log(x) + log(x)^2 + x + 4) + 6) - 3*x^2*e^(x + 3*e^x + 4) +
4*x*e^(x^2 + 2*x*log(x) + log(x)^2 + x + 2*e^(x^2 + 2*x*log(x) + log(x)^2 + x + 4) + 10)*log(x) + 4*x*e^(x^2 +
2*x*log(x) + log(x)^2 + x + 3*e^x + 8)*log(x))

________________________________________________________________________________________

maple [A]  time = 0.20, size = 35, normalized size = 1.09

method	result	size
risch	\(\frac {2}{x \left ({\mathrm e}^{2 x^{2 x} {\mathrm e}^{\ln \relax (x )^{2}+4+x^{2}+x}}+{\mathrm e}^{3 \,{\mathrm e}^{x}-2}\right )}\)	\(35\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((((-8*x-8)*ln(x)-8*x^2-12*x)*exp(ln(x)^2+2*x*ln(x)+x^2+x+4)-2)*exp(exp(ln(x)^2+2*x*ln(x)+x^2+x+4))^2+(-6*
exp(x)*x-2)*exp(3*exp(x)-2))/(x^2*exp(exp(ln(x)^2+2*x*ln(x)+x^2+x+4))^4+2*x^2*exp(3*exp(x)-2)*exp(exp(ln(x)^2+
2*x*ln(x)+x^2+x+4))^2+x^2*exp(3*exp(x)-2)^2),x,method=_RETURNVERBOSE)

[Out]

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

________________________________________________________________________________________

maxima [A]  time = 0.70, size = 37, normalized size = 1.16 \begin {gather*} \frac {2 \, e^{2}}{x e^{\left (3 \, e^{x}\right )} + x e^{\left (2 \, e^{\left (x^{2} + 2 \, x \log \relax (x) + \log \relax (x)^{2} + x + 4\right )} + 2\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-8*x-8)*log(x)-8*x^2-12*x)*exp(log(x)^2+2*x*log(x)+x^2+x+4)-2)*exp(exp(log(x)^2+2*x*log(x)+x^2+x
+4))^2+(-6*exp(x)*x-2)*exp(3*exp(x)-2))/(x^2*exp(exp(log(x)^2+2*x*log(x)+x^2+x+4))^4+2*x^2*exp(3*exp(x)-2)*exp
(exp(log(x)^2+2*x*log(x)+x^2+x+4))^2+x^2*exp(3*exp(x)-2)^2),x, algorithm="maxima")

[Out]

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

________________________________________________________________________________________

mupad [B]  time = 1.78, size = 259, normalized size = 8.09 \begin {gather*} \frac {x\,\left (12\,x^{2\,x}\,{\mathrm {e}}^{x+3\,{\mathrm {e}}^x+{\ln \relax (x)}^2+x^2+2}-6\,{\mathrm {e}}^{x+3\,{\mathrm {e}}^x-2}+8\,x^{2\,x}\,{\mathrm {e}}^{x+3\,{\mathrm {e}}^x+{\ln \relax (x)}^2+x^2+2}\,\ln \relax (x)\right )+8\,x^{2\,x}\,x^2\,{\mathrm {e}}^{x+3\,{\mathrm {e}}^x+{\ln \relax (x)}^2+x^2+2}+8\,x^{2\,x}\,{\mathrm {e}}^{x+3\,{\mathrm {e}}^x+{\ln \relax (x)}^2+x^2+2}\,\ln \relax (x)}{\left ({\mathrm {e}}^{3\,{\mathrm {e}}^x-2}+{\mathrm {e}}^{2\,x^{2\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^4\,{\mathrm {e}}^{{\ln \relax (x)}^2}\,{\mathrm {e}}^x}\right )\,\left (6\,x^{2\,x}\,x^2\,{\mathrm {e}}^{x+3\,{\mathrm {e}}^x+{\ln \relax (x)}^2+x^2+2}-3\,x^2\,{\mathrm {e}}^{x+3\,{\mathrm {e}}^x-2}+4\,x^{2\,x}\,x^3\,{\mathrm {e}}^{x+3\,{\mathrm {e}}^x+{\ln \relax (x)}^2+x^2+2}+4\,x^{2\,x}\,x^2\,{\mathrm {e}}^{x+3\,{\mathrm {e}}^x+{\ln \relax (x)}^2+x^2+2}\,\ln \relax (x)+4\,x\,x^{2\,x}\,{\mathrm {e}}^{x+3\,{\mathrm {e}}^x+{\ln \relax (x)}^2+x^2+2}\,\ln \relax (x)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(3*exp(x) - 2)*(6*x*exp(x) + 2) + exp(2*exp(x + log(x)^2 + 2*x*log(x) + x^2 + 4))*(exp(x + log(x)^2 +
2*x*log(x) + x^2 + 4)*(12*x + log(x)*(8*x + 8) + 8*x^2) + 2))/(x^2*exp(4*exp(x + log(x)^2 + 2*x*log(x) + x^2
+ 4)) + x^2*exp(6*exp(x) - 4) + 2*x^2*exp(3*exp(x) - 2)*exp(2*exp(x + log(x)^2 + 2*x*log(x) + x^2 + 4))),x)

[Out]

(x*(12*x^(2*x)*exp(x + 3*exp(x) + log(x)^2 + x^2 + 2) - 6*exp(x + 3*exp(x) - 2) + 8*x^(2*x)*exp(x + 3*exp(x) +
log(x)^2 + x^2 + 2)*log(x)) + 8*x^(2*x)*x^2*exp(x + 3*exp(x) + log(x)^2 + x^2 + 2) + 8*x^(2*x)*exp(x + 3*exp(
x) + log(x)^2 + x^2 + 2)*log(x))/((exp(3*exp(x) - 2) + exp(2*x^(2*x)*exp(x^2)*exp(4)*exp(log(x)^2)*exp(x)))*(6
*x^(2*x)*x^2*exp(x + 3*exp(x) + log(x)^2 + x^2 + 2) - 3*x^2*exp(x + 3*exp(x) - 2) + 4*x^(2*x)*x^3*exp(x + 3*ex
p(x) + log(x)^2 + x^2 + 2) + 4*x^(2*x)*x^2*exp(x + 3*exp(x) + log(x)^2 + x^2 + 2)*log(x) + 4*x*x^(2*x)*exp(x +
3*exp(x) + log(x)^2 + x^2 + 2)*log(x)))

________________________________________________________________________________________

sympy [A]  time = 15.23, size = 36, normalized size = 1.12 \begin {gather*} \frac {2}{x e^{3 e^{x} - 2} + x e^{2 e^{x^{2} + 2 x \log {\relax (x )} + x + \log {\relax (x )}^{2} + 4}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-8*x-8)*ln(x)-8*x**2-12*x)*exp(ln(x)**2+2*x*ln(x)+x**2+x+4)-2)*exp(exp(ln(x)**2+2*x*ln(x)+x**2+x
+4))**2+(-6*exp(x)*x-2)*exp(3*exp(x)-2))/(x**2*exp(exp(ln(x)**2+2*x*ln(x)+x**2+x+4))**4+2*x**2*exp(3*exp(x)-2)
*exp(exp(ln(x)**2+2*x*ln(x)+x**2+x+4))**2+x**2*exp(3*exp(x)-2)**2),x)

[Out]

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

________________________________________________________________________________________