3.69.76 \(\int \frac {e^{\frac {-x^3+\log (\frac {x^4}{\log ^2(x)})+x \log (\frac {\log (3 x)}{\log (x)})}{-x^2+\log (\frac {\log (3 x)}{\log (x)})}} ((2 x^2+(-4 x^2+x^5) \log (x)) \log (3 x)+(-\log (x)+(1+2 x^2 \log (x)) \log (3 x)) \log (\frac {x^4}{\log ^2(x)})+(-2+(4-2 x^3) \log (x)) \log (3 x) \log (\frac {\log (3 x)}{\log (x)})+x \log (x) \log (3 x) \log ^2(\frac {\log (3 x)}{\log (x)}))}{x^5 \log (x) \log (3 x)-2 x^3 \log (x) \log (3 x) \log (\frac {\log (3 x)}{\log (x)})+x \log (x) \log (3 x) \log ^2(\frac {\log (3 x)}{\log (x)})} \, dx\)

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

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Rubi [F]  time = 19.78, 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 {\exp \left (\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}\right ) \left (\left (2 x^2+\left (-4 x^2+x^5\right ) \log (x)\right ) \log (3 x)+\left (-\log (x)+\left (1+2 x^2 \log (x)\right ) \log (3 x)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )+\left (-2+\left (4-2 x^3\right ) \log (x)\right ) \log (3 x) \log \left (\frac {\log (3 x)}{\log (x)}\right )+x \log (x) \log (3 x) \log ^2\left (\frac {\log (3 x)}{\log (x)}\right )\right )}{x^5 \log (x) \log (3 x)-2 x^3 \log (x) \log (3 x) \log \left (\frac {\log (3 x)}{\log (x)}\right )+x \log (x) \log (3 x) \log ^2\left (\frac {\log (3 x)}{\log (x)}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

Defer[Int][E^((-x^3 + Log[x^4/Log[x]^2] + x*Log[Log[3*x]/Log[x]])/(-x^2 + Log[Log[3*x]/Log[x]])), x] + Log[9]*
Defer[Int][(E^((-x^3 + Log[x^4/Log[x]^2] + x*Log[Log[3*x]/Log[x]])/(-x^2 + Log[Log[3*x]/Log[x]]))*x*Log[x^4/Lo
g[x]^2])/(Log[3*x]*(x^2 - Log[Log[3*x]/Log[x]])^2), x] + Log[3]*Defer[Int][(E^((-x^3 + Log[x^4/Log[x]^2] + x*L
og[Log[3*x]/Log[x]])/(-x^2 + Log[Log[3*x]/Log[x]]))*Log[x^4/Log[x]^2])/(x*Log[x]*Log[3*x]*(x^2 - Log[Log[3*x]/
Log[x]])^2), x] + 2*Defer[Int][(E^((-x^3 + Log[x^4/Log[x]^2] + x*Log[Log[3*x]/Log[x]])/(-x^2 + Log[Log[3*x]/Lo
g[x]]))*x*Log[x]*Log[x^4/Log[x]^2])/(Log[3*x]*(x^2 - Log[Log[3*x]/Log[x]])^2), x] - 4*Defer[Int][E^((-x^3 + Lo
g[x^4/Log[x]^2] + x*Log[Log[3*x]/Log[x]])/(-x^2 + Log[Log[3*x]/Log[x]]))/(x*(x^2 - Log[Log[3*x]/Log[x]])), x]
+ 2*Defer[Int][E^((-x^3 + Log[x^4/Log[x]^2] + x*Log[Log[3*x]/Log[x]])/(-x^2 + Log[Log[3*x]/Log[x]]))/(x*Log[x]
*(x^2 - Log[Log[3*x]/Log[x]])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}\right ) \left (\left (2 x^2+\left (-4 x^2+x^5\right ) \log (x)\right ) \log (3 x)+\left (-\log (x)+\left (1+2 x^2 \log (x)\right ) \log (3 x)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )+\left (-2+\left (4-2 x^3\right ) \log (x)\right ) \log (3 x) \log \left (\frac {\log (3 x)}{\log (x)}\right )+x \log (x) \log (3 x) \log ^2\left (\frac {\log (3 x)}{\log (x)}\right )\right )}{x \log (x) \log (3 x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2} \, dx\\ &=\int \left (\exp \left (\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}\right )+\frac {\exp \left (\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}\right ) \left (\log (3)+x^2 \log (9) \log (x)+2 x^2 \log ^2(x)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )}{x \log (x) \log (3 x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}-\frac {2 \exp \left (\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}\right ) (-1+2 \log (x))}{x \log (x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )}\right ) \, dx\\ &=-\left (2 \int \frac {\exp \left (\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}\right ) (-1+2 \log (x))}{x \log (x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )} \, dx\right )+\int \exp \left (\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}\right ) \, dx+\int \frac {\exp \left (\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}\right ) \left (\log (3)+x^2 \log (9) \log (x)+2 x^2 \log ^2(x)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )}{x \log (x) \log (3 x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2} \, dx\\ &=-\left (2 \int \left (\frac {2 \exp \left (\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}\right )}{x \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )}-\frac {\exp \left (\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}\right )}{x \log (x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )}\right ) \, dx\right )+\int \exp \left (\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}\right ) \, dx+\int \left (\frac {\exp \left (\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}\right ) x \log (9) \log \left (\frac {x^4}{\log ^2(x)}\right )}{\log (3 x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}+\frac {\exp \left (\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}\right ) \log (3) \log \left (\frac {x^4}{\log ^2(x)}\right )}{x \log (x) \log (3 x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}+\frac {2 \exp \left (\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}\right ) x \log (x) \log \left (\frac {x^4}{\log ^2(x)}\right )}{\log (3 x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}\right ) \, dx\\ &=2 \int \frac {\exp \left (\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}\right ) x \log (x) \log \left (\frac {x^4}{\log ^2(x)}\right )}{\log (3 x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2} \, dx+2 \int \frac {\exp \left (\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}\right )}{x \log (x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )} \, dx-4 \int \frac {\exp \left (\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}\right )}{x \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )} \, dx+\log (3) \int \frac {\exp \left (\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )}{x \log (x) \log (3 x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2} \, dx+\log (9) \int \frac {\exp \left (\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}\right ) x \log \left (\frac {x^4}{\log ^2(x)}\right )}{\log (3 x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2} \, dx+\int \exp \left (\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}\right ) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.52, size = 31, normalized size = 0.97 \begin {gather*} e^x \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((-x^3 + Log[x^4/Log[x]^2] + x*Log[Log[3*x]/Log[x]])/(-x^2 + Log[Log[3*x]/Log[x]]))*((2*x^2 + (-4
*x^2 + x^5)*Log[x])*Log[3*x] + (-Log[x] + (1 + 2*x^2*Log[x])*Log[3*x])*Log[x^4/Log[x]^2] + (-2 + (4 - 2*x^3)*L
og[x])*Log[3*x]*Log[Log[3*x]/Log[x]] + x*Log[x]*Log[3*x]*Log[Log[3*x]/Log[x]]^2))/(x^5*Log[x]*Log[3*x] - 2*x^3
*Log[x]*Log[3*x]*Log[Log[3*x]/Log[x]] + x*Log[x]*Log[3*x]*Log[Log[3*x]/Log[x]]^2),x]

[Out]

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

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fricas [A]  time = 0.56, size = 50, normalized size = 1.56 \begin {gather*} e^{\left (\frac {x^{3} - x \log \left (\frac {\log \relax (3) + \log \relax (x)}{\log \relax (x)}\right ) - \log \left (\frac {x^{4}}{\log \relax (x)^{2}}\right )}{x^{2} - \log \left (\frac {\log \relax (3) + \log \relax (x)}{\log \relax (x)}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

e^((x^3 - x*log((log(3) + log(x))/log(x)) - log(x^4/log(x)^2))/(x^2 - log((log(3) + log(x))/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((x*log(x)*log(3*x)*log(log(3*x)/log(x))^2+((-2*x^3+4)*log(x)-2)*log(3*x)*log(log(3*x)/log(x))+((2*x^
2*log(x)+1)*log(3*x)-log(x))*log(x^4/log(x)^2)+((x^5-4*x^2)*log(x)+2*x^2)*log(3*x))*exp((x*log(log(3*x)/log(x)
)+log(x^4/log(x)^2)-x^3)/(log(log(3*x)/log(x))-x^2))/(x*log(x)*log(3*x)*log(log(3*x)/log(x))^2-2*x^3*log(x)*lo
g(3*x)*log(log(3*x)/log(x))+x^5*log(x)*log(3*x)),x, algorithm="giac")

[Out]

undef

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maple [F]  time = 180.00, size = 0, normalized size = 0.00 \[\int \frac {\left (x \ln \relax (x ) \ln \left (3 x \right ) \ln \left (\frac {\ln \left (3 x \right )}{\ln \relax (x )}\right )^{2}+\left (\left (-2 x^{3}+4\right ) \ln \relax (x )-2\right ) \ln \left (3 x \right ) \ln \left (\frac {\ln \left (3 x \right )}{\ln \relax (x )}\right )+\left (\left (2 x^{2} \ln \relax (x )+1\right ) \ln \left (3 x \right )-\ln \relax (x )\right ) \ln \left (\frac {x^{4}}{\ln \relax (x )^{2}}\right )+\left (\left (x^{5}-4 x^{2}\right ) \ln \relax (x )+2 x^{2}\right ) \ln \left (3 x \right )\right ) {\mathrm e}^{\frac {x \ln \left (\frac {\ln \left (3 x \right )}{\ln \relax (x )}\right )+\ln \left (\frac {x^{4}}{\ln \relax (x )^{2}}\right )-x^{3}}{\ln \left (\frac {\ln \left (3 x \right )}{\ln \relax (x )}\right )-x^{2}}}}{x \ln \relax (x ) \ln \left (3 x \right ) \ln \left (\frac {\ln \left (3 x \right )}{\ln \relax (x )}\right )^{2}-2 x^{3} \ln \relax (x ) \ln \left (3 x \right ) \ln \left (\frac {\ln \left (3 x \right )}{\ln \relax (x )}\right )+x^{5} \ln \relax (x ) \ln \left (3 x \right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (x \log \left (3 \, x\right ) \log \relax (x) \log \left (\frac {\log \left (3 \, x\right )}{\log \relax (x)}\right )^{2} - 2 \, {\left ({\left (x^{3} - 2\right )} \log \relax (x) + 1\right )} \log \left (3 \, x\right ) \log \left (\frac {\log \left (3 \, x\right )}{\log \relax (x)}\right ) + {\left ({\left (2 \, x^{2} \log \relax (x) + 1\right )} \log \left (3 \, x\right ) - \log \relax (x)\right )} \log \left (\frac {x^{4}}{\log \relax (x)^{2}}\right ) + {\left (2 \, x^{2} + {\left (x^{5} - 4 \, x^{2}\right )} \log \relax (x)\right )} \log \left (3 \, x\right )\right )} e^{\left (\frac {x^{3} - x \log \left (\frac {\log \left (3 \, x\right )}{\log \relax (x)}\right ) - \log \left (\frac {x^{4}}{\log \relax (x)^{2}}\right )}{x^{2} - \log \left (\frac {\log \left (3 \, x\right )}{\log \relax (x)}\right )}\right )}}{x^{5} \log \left (3 \, x\right ) \log \relax (x) - 2 \, x^{3} \log \left (3 \, x\right ) \log \relax (x) \log \left (\frac {\log \left (3 \, x\right )}{\log \relax (x)}\right ) + x \log \left (3 \, x\right ) \log \relax (x) \log \left (\frac {\log \left (3 \, x\right )}{\log \relax (x)}\right )^{2}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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mupad [B]  time = 5.48, size = 100, normalized size = 3.12 \begin {gather*} {\mathrm {e}}^{-\frac {x^3}{\ln \left (\frac {\ln \left (3\,x\right )}{\ln \relax (x)}\right )-x^2}}\,{\left (\frac {1}{{\ln \relax (x)}^2}\right )}^{\frac {1}{\ln \left (\frac {\ln \left (3\,x\right )}{\ln \relax (x)}\right )-x^2}}\,{\left (x^4\right )}^{\frac {1}{\ln \left (\frac {\ln \left (3\,x\right )}{\ln \relax (x)}\right )-x^2}}\,{\left (\frac {\ln \left (3\,x\right )}{\ln \relax (x)}\right )}^{\frac {x}{\ln \left (\frac {\ln \left (3\,x\right )}{\ln \relax (x)}\right )-x^2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

exp(-x^3/(log(log(3*x)/log(x)) - x^2))*(1/log(x)^2)^(1/(log(log(3*x)/log(x)) - x^2))*(x^4)^(1/(log(log(3*x)/lo
g(x)) - x^2))*(log(3*x)/log(x))^(x/(log(log(3*x)/log(x)) - x^2))

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sympy [A]  time = 61.87, size = 42, normalized size = 1.31 \begin {gather*} e^{\frac {- x^{3} + x \log {\left (\frac {\log {\relax (x )} + \log {\relax (3 )}}{\log {\relax (x )}} \right )} + \log {\left (\frac {x^{4}}{\log {\relax (x )}^{2}} \right )}}{- x^{2} + \log {\left (\frac {\log {\relax (x )} + \log {\relax (3 )}}{\log {\relax (x )}} \right )}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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