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

Optimal. Leaf size=30 \[ \frac {2 x \log (x)}{e^{e^{\log ^2(2)}-e^{x^2} (-3+x)}-x} \]

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Rubi [F]  time = 12.75, 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 {-2 e^{2 e^{x^2} (-3+x)} x+e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} \left (2+\left (2+e^{x^2} \left (2 x-12 x^2+4 x^3\right )\right ) \log (x)\right )}{e^{2 e^{\log ^2(2)}}-2 e^{e^{\log ^2(2)}+e^{x^2} (-3+x)} x+e^{2 e^{x^2} (-3+x)} x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 0.29, size = 45, normalized size = 1.50 \begin {gather*} 2 \left (-\log (x)-\frac {e^{e^{\log ^2(2)}} \log (x)}{-e^{e^{\log ^2(2)}}+e^{e^{x^2} (-3+x)} x}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

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

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fricas [A]  time = 0.64, size = 50, normalized size = 1.67 \begin {gather*} -\frac {2 \, x e^{\left ({\left (x - 3\right )} e^{\left (x^{2}\right )} + e^{\left (\log \relax (2)^{2}\right )}\right )} \log \relax (x)}{x e^{\left ({\left (x - 3\right )} e^{\left (x^{2}\right )} + e^{\left (\log \relax (2)^{2}\right )}\right )} - e^{\left (2 \, e^{\left (\log \relax (2)^{2}\right )}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((4*x^3-12*x^2+2*x)*exp(x^2)+2)*log(x)+2)*exp((x-3)*exp(x^2))*exp(exp(log(2)^2))-2*x*exp((x-3)*exp
(x^2))^2)/(exp(exp(log(2)^2))^2-2*x*exp((x-3)*exp(x^2))*exp(exp(log(2)^2))+x^2*exp((x-3)*exp(x^2))^2),x, algor
ithm="fricas")

[Out]

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

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giac [A]  time = 0.59, size = 46, normalized size = 1.53 \begin {gather*} -\frac {2 \, x e^{\left (x e^{\left (x^{2}\right )} - 3 \, e^{\left (x^{2}\right )}\right )} \log \relax (x)}{x e^{\left (x e^{\left (x^{2}\right )} - 3 \, e^{\left (x^{2}\right )}\right )} - e^{\left (e^{\left (\log \relax (2)^{2}\right )}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((4*x^3-12*x^2+2*x)*exp(x^2)+2)*log(x)+2)*exp((x-3)*exp(x^2))*exp(exp(log(2)^2))-2*x*exp((x-3)*exp
(x^2))^2)/(exp(exp(log(2)^2))^2-2*x*exp((x-3)*exp(x^2))*exp(exp(log(2)^2))+x^2*exp((x-3)*exp(x^2))^2),x, algor
ithm="giac")

[Out]

-2*x*e^(x*e^(x^2) - 3*e^(x^2))*log(x)/(x*e^(x*e^(x^2) - 3*e^(x^2)) - e^(e^(log(2)^2)))

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maple [A]  time = 0.40, size = 37, normalized size = 1.23

method	result	size
risch	\(-2 \ln \relax (x )+\frac {2 \,{\mathrm e}^{{\mathrm e}^{\ln \relax (2)^{2}}} \ln \relax (x )}{-x \,{\mathrm e}^{\left (x -3\right ) {\mathrm e}^{x^{2}}}+{\mathrm e}^{{\mathrm e}^{\ln \relax (2)^{2}}}}\)	\(37\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((((4*x^3-12*x^2+2*x)*exp(x^2)+2)*ln(x)+2)*exp((x-3)*exp(x^2))*exp(exp(ln(2)^2))-2*x*exp((x-3)*exp(x^2))^2
)/(exp(exp(ln(2)^2))^2-2*x*exp((x-3)*exp(x^2))*exp(exp(ln(2)^2))+x^2*exp((x-3)*exp(x^2))^2),x,method=_RETURNVE
RBOSE)

[Out]

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

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maxima [A]  time = 0.74, size = 49, normalized size = 1.63 \begin {gather*} -\frac {2 \, e^{\left (3 \, e^{\left (x^{2}\right )} + e^{\left (\log \relax (2)^{2}\right )}\right )} \log \relax (x)}{x e^{\left (x e^{\left (x^{2}\right )}\right )} - e^{\left (3 \, e^{\left (x^{2}\right )} + e^{\left (\log \relax (2)^{2}\right )}\right )}} - 2 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((4*x^3-12*x^2+2*x)*exp(x^2)+2)*log(x)+2)*exp((x-3)*exp(x^2))*exp(exp(log(2)^2))-2*x*exp((x-3)*exp
(x^2))^2)/(exp(exp(log(2)^2))^2-2*x*exp((x-3)*exp(x^2))*exp(exp(log(2)^2))+x^2*exp((x-3)*exp(x^2))^2),x, algor
ithm="maxima")

[Out]

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

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mupad [B]  time = 2.25, size = 161, normalized size = 5.37 \begin {gather*} -2\,\ln \relax (x)-\frac {2\,\left (x^2\,{\mathrm {e}}^{x^2+2\,{\mathrm {e}}^{{\ln \relax (2)}^2}}\,\ln \relax (x)-6\,x^3\,{\mathrm {e}}^{x^2+2\,{\mathrm {e}}^{{\ln \relax (2)}^2}}\,\ln \relax (x)+2\,x^4\,{\mathrm {e}}^{x^2+2\,{\mathrm {e}}^{{\ln \relax (2)}^2}}\,\ln \relax (x)+x\,{\mathrm {e}}^{2\,{\mathrm {e}}^{{\ln \relax (2)}^2}}\,\ln \relax (x)\right )}{\left ({\mathrm {e}}^{x\,{\mathrm {e}}^{x^2}-3\,{\mathrm {e}}^{x^2}}-\frac {{\mathrm {e}}^{{\mathrm {e}}^{{\ln \relax (2)}^2}}}{x}\right )\,\left (x^3\,{\mathrm {e}}^{x^2+{\mathrm {e}}^{{\ln \relax (2)}^2}}-6\,x^4\,{\mathrm {e}}^{x^2+{\mathrm {e}}^{{\ln \relax (2)}^2}}+2\,x^5\,{\mathrm {e}}^{x^2+{\mathrm {e}}^{{\ln \relax (2)}^2}}+x^2\,{\mathrm {e}}^{{\mathrm {e}}^{{\ln \relax (2)}^2}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [A]  time = 0.45, size = 39, normalized size = 1.30 \begin {gather*} - 2 \log {\relax (x )} - \frac {2 e^{e^{\log {\relax (2 )}^{2}}} \log {\relax (x )}}{x e^{\left (x - 3\right ) e^{x^{2}}} - e^{e^{\log {\relax (2 )}^{2}}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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