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

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

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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 = {} $$\begin{array}{c}\int \frac{\exp \left(\frac{-x^3+\log \left(\frac{x^4}{{\log }^2(x)}\right)+x\log \left(\frac{\log (3x)}{\log (x)}\right)}{-x^2+\log \left(\frac{\log (3x)}{\log (x)}\right)}\right)((2x^2+(-4x^2+x^5)\log (x))\log (3x)+(-\log (x)+(1+2x^2\log (x))\log (3x))\log \left(\frac{x^4}{{\log }^2(x)}\right)+(-2+(4-2x^3)\log (x))\log (3x)\log \left(\frac{\log (3x)}{\log (x)}\right)+x\log (x)\log (3x){\log }^2\left(\frac{\log (3x)}{\log (x)}\right))}{x^5\log (x)\log (3x)-2x^3\log (x)\log (3x)\log \left(\frac{\log (3x)}{\log (x)}\right)+x\log (x)\log (3x){\log }^2\left(\frac{\log (3x)}{\log (x)}\right)}dx\end{array}$$

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{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{\exp \left(\frac{-x^3+\log \left(\frac{x^4}{{\log }^2(x)}\right)+x\log \left(\frac{\log (3x)}{\log (x)}\right)}{-x^2+\log \left(\frac{\log (3x)}{\log (x)}\right)}\right)((2x^2+(-4x^2+x^5)\log (x))\log (3x)+(-\log (x)+(1+2x^2\log (x))\log (3x))\log \left(\frac{x^4}{{\log }^2(x)}\right)+(-2+(4-2x^3)\log (x))\log (3x)\log \left(\frac{\log (3x)}{\log (x)}\right)+x\log (x)\log (3x){\log }^2\left(\frac{\log (3x)}{\log (x)}\right))}{x\log (x)\log (3x){(x^2-\log \left(\frac{\log (3x)}{\log (x)}\right))}^2}dx\\ & =\int (\exp \left(\frac{-x^3+\log \left(\frac{x^4}{{\log }^2(x)}\right)+x\log \left(\frac{\log (3x)}{\log (x)}\right)}{-x^2+\log \left(\frac{\log (3x)}{\log (x)}\right)}\right)+\frac{\exp \left(\frac{-x^3+\log \left(\frac{x^4}{{\log }^2(x)}\right)+x\log \left(\frac{\log (3x)}{\log (x)}\right)}{-x^2+\log \left(\frac{\log (3x)}{\log (x)}\right)}\right)(\log (3)+x^2\log (9)\log (x)+2x^2{\log }^2(x))\log \left(\frac{x^4}{{\log }^2(x)}\right)}{x\log (x)\log (3x){(x^2-\log \left(\frac{\log (3x)}{\log (x)}\right))}^2}-\frac{2\exp \left(\frac{-x^3+\log \left(\frac{x^4}{{\log }^2(x)}\right)+x\log \left(\frac{\log (3x)}{\log (x)}\right)}{-x^2+\log \left(\frac{\log (3x)}{\log (x)}\right)}\right)(-1+2\log (x))}{x\log (x)(x^2-\log \left(\frac{\log (3x)}{\log (x)}\right))})dx\\ & =-(2\int \frac{\exp \left(\frac{-x^3+\log \left(\frac{x^4}{{\log }^2(x)}\right)+x\log \left(\frac{\log (3x)}{\log (x)}\right)}{-x^2+\log \left(\frac{\log (3x)}{\log (x)}\right)}\right)(-1+2\log (x))}{x\log (x)(x^2-\log \left(\frac{\log (3x)}{\log (x)}\right))}dx)+\int \exp \left(\frac{-x^3+\log \left(\frac{x^4}{{\log }^2(x)}\right)+x\log \left(\frac{\log (3x)}{\log (x)}\right)}{-x^2+\log \left(\frac{\log (3x)}{\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 (3x)}{\log (x)}\right)}{-x^2+\log \left(\frac{\log (3x)}{\log (x)}\right)}\right)(\log (3)+x^2\log (9)\log (x)+2x^2{\log }^2(x))\log \left(\frac{x^4}{{\log }^2(x)}\right)}{x\log (x)\log (3x){(x^2-\log \left(\frac{\log (3x)}{\log (x)}\right))}^2}dx\\ & =-(2\int (\frac{2\exp \left(\frac{-x^3+\log \left(\frac{x^4}{{\log }^2(x)}\right)+x\log \left(\frac{\log (3x)}{\log (x)}\right)}{-x^2+\log \left(\frac{\log (3x)}{\log (x)}\right)}\right)}{x(x^2-\log \left(\frac{\log (3x)}{\log (x)}\right))}-\frac{\exp \left(\frac{-x^3+\log \left(\frac{x^4}{{\log }^2(x)}\right)+x\log \left(\frac{\log (3x)}{\log (x)}\right)}{-x^2+\log \left(\frac{\log (3x)}{\log (x)}\right)}\right)}{x\log (x)(x^2-\log \left(\frac{\log (3x)}{\log (x)}\right))})dx)+\int \exp \left(\frac{-x^3+\log \left(\frac{x^4}{{\log }^2(x)}\right)+x\log \left(\frac{\log (3x)}{\log (x)}\right)}{-x^2+\log \left(\frac{\log (3x)}{\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 (3x)}{\log (x)}\right)}{-x^2+\log \left(\frac{\log (3x)}{\log (x)}\right)}\right)x\log (9)\log \left(\frac{x^4}{{\log }^2(x)}\right)}{\log (3x){(x^2-\log \left(\frac{\log (3x)}{\log (x)}\right))}^2}+\frac{\exp \left(\frac{-x^3+\log \left(\frac{x^4}{{\log }^2(x)}\right)+x\log \left(\frac{\log (3x)}{\log (x)}\right)}{-x^2+\log \left(\frac{\log (3x)}{\log (x)}\right)}\right)\log (3)\log \left(\frac{x^4}{{\log }^2(x)}\right)}{x\log (x)\log (3x){(x^2-\log \left(\frac{\log (3x)}{\log (x)}\right))}^2}+\frac{2\exp \left(\frac{-x^3+\log \left(\frac{x^4}{{\log }^2(x)}\right)+x\log \left(\frac{\log (3x)}{\log (x)}\right)}{-x^2+\log \left(\frac{\log (3x)}{\log (x)}\right)}\right)x\log (x)\log \left(\frac{x^4}{{\log }^2(x)}\right)}{\log (3x){(x^2-\log \left(\frac{\log (3x)}{\log (x)}\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 (3x)}{\log (x)}\right)}{-x^2+\log \left(\frac{\log (3x)}{\log (x)}\right)}\right)x\log (x)\log \left(\frac{x^4}{{\log }^2(x)}\right)}{\log (3x){(x^2-\log \left(\frac{\log (3x)}{\log (x)}\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 (3x)}{\log (x)}\right)}{-x^2+\log \left(\frac{\log (3x)}{\log (x)}\right)}\right)}{x\log (x)(x^2-\log \left(\frac{\log (3x)}{\log (x)}\right))}dx-4\int \frac{\exp \left(\frac{-x^3+\log \left(\frac{x^4}{{\log }^2(x)}\right)+x\log \left(\frac{\log (3x)}{\log (x)}\right)}{-x^2+\log \left(\frac{\log (3x)}{\log (x)}\right)}\right)}{x(x^2-\log \left(\frac{\log (3x)}{\log (x)}\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 (3x)}{\log (x)}\right)}{-x^2+\log \left(\frac{\log (3x)}{\log (x)}\right)}\right)\log \left(\frac{x^4}{{\log }^2(x)}\right)}{x\log (x)\log (3x){(x^2-\log \left(\frac{\log (3x)}{\log (x)}\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 (3x)}{\log (x)}\right)}{-x^2+\log \left(\frac{\log (3x)}{\log (x)}\right)}\right)x\log \left(\frac{x^4}{{\log }^2(x)}\right)}{\log (3x){(x^2-\log \left(\frac{\log (3x)}{\log (x)}\right))}^2}dx+\int \exp \left(\frac{-x^3+\log \left(\frac{x^4}{{\log }^2(x)}\right)+x\log \left(\frac{\log (3x)}{\log (x)}\right)}{-x^2+\log \left(\frac{\log (3x)}{\log (x)}\right)}\right)dx\end{array}\end{array}$$

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

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 $$\begin{array}{c}{e}^{\left(\frac{x^3-x\log \left(\frac{\log (3)+\log (x)}{\log (x)}\right)-\log \left(\frac{x^4}{\log (x{)}^2}\right)}{x^2-\log \left(\frac{\log (3)+\log (x)}{\log (x)}\right)}\right)}\end{array}$$

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 $$\begin{array}{c}\mathit{undef}\end{array}$$

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 $$\int \frac{(x\ln (x)\ln \left(3x\right)\ln {\left(\frac{\ln \left(3x\right)}{\ln (x)}\right)}^2+((-2x^3+4)\ln (x)-2)\ln \left(3x\right)\ln \left(\frac{\ln \left(3x\right)}{\ln (x)}\right)+((2x^2\ln (x)+1)\ln \left(3x\right)-\ln (x))\ln \left(\frac{x^4}{\ln (x{)}^2}\right)+((x^5-4x^2)\ln (x)+2x^2)\ln \left(3x\right)){\mathrm{e}}^{\frac{x\ln \left(\frac{\ln \left(3x\right)}{\ln (x)}\right)+\ln \left(\frac{x^4}{\ln (x{)}^2}\right)-x^3}{\ln \left(\frac{\ln \left(3x\right)}{\ln (x)}\right)-x^2}}}{x\ln (x)\ln \left(3x\right)\ln {\left(\frac{\ln \left(3x\right)}{\ln (x)}\right)}^2-2x^3\ln (x)\ln \left(3x\right)\ln \left(\frac{\ln \left(3x\right)}{\ln (x)}\right)+x^5\ln (x)\ln \left(3x\right)}dx$$

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 $$\begin{array}{c}\int \frac{(x\log \left(3x\right)\log (x)\log {\left(\frac{\log \left(3x\right)}{\log (x)}\right)}^2-2((x^3-2)\log (x)+1)\log \left(3x\right)\log \left(\frac{\log \left(3x\right)}{\log (x)}\right)+((2x^2\log (x)+1)\log \left(3x\right)-\log (x))\log \left(\frac{x^4}{\log (x{)}^2}\right)+(2x^2+(x^5-4x^2)\log (x))\log \left(3x\right))e^{\left(\frac{x^3-x\log \left(\frac{\log \left(3x\right)}{\log (x)}\right)-\log \left(\frac{x^4}{\log (x{)}^2}\right)}{x^2-\log \left(\frac{\log \left(3x\right)}{\log (x)}\right)}\right)}}{x^5\log \left(3x\right)\log (x)-2x^3\log \left(3x\right)\log (x)\log \left(\frac{\log \left(3x\right)}{\log (x)}\right)+x\log \left(3x\right)\log (x)\log {\left(\frac{\log \left(3x\right)}{\log (x)}\right)}^2}dx\end{array}$$

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 $$\begin{array}{c}{\mathrm{e}}^{-\frac{x^3}{\ln \left(\frac{\ln \left(3x\right)}{\ln (x)}\right)-x^2}}{\left(\frac{1}{{\ln (x)}^2}\right)}^{\frac{1}{\ln \left(\frac{\ln \left(3x\right)}{\ln (x)}\right)-x^2}}{\left(x^4\right)}^{\frac{1}{\ln \left(\frac{\ln \left(3x\right)}{\ln (x)}\right)-x^2}}{\left(\frac{\ln \left(3x\right)}{\ln (x)}\right)}^{\frac{x}{\ln \left(\frac{\ln \left(3x\right)}{\ln (x)}\right)-x^2}}\end{array}$$

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 $$\begin{array}{c}{e}^{\frac{-x^3+x\log \left(\frac{\log (x)+\log (3)}{\log (x)}\right)+\log \left(\frac{x^4}{\log {(x)}^2}\right)}{-x^2+\log \left(\frac{\log (x)+\log (3)}{\log (x)}\right)}}\end{array}$$

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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