3.17.87 \(\int e^{e^{2 (-5-x) \log (x)+2 \log (x) \log (3 e^x \log ^2(x))} x^2+2 (-5-x) \log (x)+2 \log (x) \log (3 e^x \log ^2(x))} (-4 x-2 x^2+2 x \log (3 e^x \log ^2(x))) \, dx\)

Optimal. Leaf size=21 \[ e^{x^{-8-2 x+2 \log \left (3 e^x \log ^2(x)\right )}} \]

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Rubi [F]  time = 3.37, 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 \exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) \left (-4 x-2 x^2+2 x \log \left (3 e^x \log ^2(x)\right )\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int 2 \exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x \left (-2-x+\log \left (3 e^x \log ^2(x)\right )\right ) \, dx\\ &=2 \int \exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x \left (-2-x+\log \left (3 e^x \log ^2(x)\right )\right ) \, dx\\ &=2 \int \left (-\exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x (2+x)+\exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x \log \left (3 e^x \log ^2(x)\right )\right ) \, dx\\ &=-\left (2 \int \exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x (2+x) \, dx\right )+2 \int \exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x \log \left (3 e^x \log ^2(x)\right ) \, dx\\ &=-\left (2 \int \left (2 \exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x+\exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2\right ) \, dx\right )+2 \int \exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x \log \left (3 e^x \log ^2(x)\right ) \, dx\\ &=-\left (2 \int \exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2 \, dx\right )+2 \int \exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x \log \left (3 e^x \log ^2(x)\right ) \, dx-4 \int \exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x \, dx\\ &=-\left (2 \int \exp \left (x^{-8-2 x+2 \log \left (3 e^x \log ^2(x)\right )}+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^{-8-2 x} \, dx\right )+2 \int \exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x \log \left (3 e^x \log ^2(x)\right ) \, dx-4 \int \exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 1.01, size = 21, normalized size = 1.00 \begin {gather*} e^{x^{-8-2 x+2 \log \left (3 e^x \log ^2(x)\right )}} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

E^x^(-8 - 2*x + 2*Log[3*E^x*Log[x]^2])

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fricas [A]  time = 0.89, size = 27, normalized size = 1.29 \begin {gather*} e^{\left (x^{2} e^{\left (-2 \, {\left (x + 5\right )} \log \relax (x) + 2 \, \log \left (3 \, e^{x} \log \relax (x)^{2}\right ) \log \relax (x)\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x*log(3*exp(x)*log(x)^2)-2*x^2-4*x)*exp(log(x)*log(3*exp(x)*log(x)^2)+(-x-5)*log(x))^2*exp(x^2*ex
p(log(x)*log(3*exp(x)*log(x)^2)+(-x-5)*log(x))^2),x, algorithm="fricas")

[Out]

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

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \mathit {undef} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x*log(3*exp(x)*log(x)^2)-2*x^2-4*x)*exp(log(x)*log(3*exp(x)*log(x)^2)+(-x-5)*log(x))^2*exp(x^2*ex
p(log(x)*log(3*exp(x)*log(x)^2)+(-x-5)*log(x))^2),x, algorithm="giac")

[Out]

undef

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maple [C]  time = 0.36, size = 104, normalized size = 4.95

method	result	size
risch	\({\mathrm e}^{x^{2} x^{-i \mathrm {csgn}\left (i \ln \relax (x )^{2}\right ) \pi +2 i \pi \,\mathrm {csgn}\left (i \ln \relax (x )\right )-i \pi \,\mathrm {csgn}\left (i \ln \relax (x )^{2}\right ) \mathrm {csgn}\left (i {\mathrm e}^{x} \ln \relax (x )^{2}\right ) \mathrm {csgn}\left (i {\mathrm e}^{x}\right )-i \mathrm {csgn}\left (i {\mathrm e}^{x} \ln \relax (x )^{2}\right ) \pi +4 \ln \left (\ln \relax (x )\right )+2 \ln \left (3 \,{\mathrm e}^{x}\right )+i \pi \,\mathrm {csgn}\left (i {\mathrm e}^{x}\right )} x^{-2 x -10}}\)	\(104\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 1.13, size = 20, normalized size = 0.95 \begin {gather*} e^{\left (\frac {e^{\left (2 \, \log \relax (3) \log \relax (x) + 4 \, \log \relax (x) \log \left (\log \relax (x)\right )\right )}}{x^{8}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x*log(3*exp(x)*log(x)^2)-2*x^2-4*x)*exp(log(x)*log(3*exp(x)*log(x)^2)+(-x-5)*log(x))^2*exp(x^2*ex
p(log(x)*log(3*exp(x)*log(x)^2)+(-x-5)*log(x))^2),x, algorithm="maxima")

[Out]

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

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mupad [B]  time = 1.23, size = 20, normalized size = 0.95 \begin {gather*} {\mathrm {e}}^{\frac {x^{2\,\ln \relax (3)}\,x^{2\,\ln \left ({\ln \relax (x)}^2\right )}}{x^8}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(2*log(x)*log(3*exp(x)*log(x)^2) - 2*log(x)*(x + 5))*exp(x^2*exp(2*log(x)*log(3*exp(x)*log(x)^2) - 2*l
og(x)*(x + 5)))*(4*x - 2*x*log(3*exp(x)*log(x)^2) + 2*x^2),x)

[Out]

exp((x^(2*log(3))*x^(2*log(log(x)^2)))/x^8)

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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