3.74.95 \(\int \frac {-18 x+9 x \log (3 x)-e^{3-\frac {1}{3} e^{\frac {e^3 x}{3}}+\frac {e^3 x}{3}} x \log ^3(3 x)+(-9 x \log (3 x)-9 e^{-\frac {1}{3} e^{\frac {e^3 x}{3}}} \log ^3(3 x)) \log (\frac {x+e^{-\frac {1}{3} e^{\frac {e^3 x}{3}}} \log ^2(3 x)}{\log ^2(3 x)})}{9 x^3 \log (3 x)+9 e^{-\frac {1}{3} e^{\frac {e^3 x}{3}}} x^2 \log ^3(3 x)} \, dx\)

Optimal. Leaf size=30 \[ \frac {\log \left (e^{-\frac {1}{3} e^{\frac {e^3 x}{3}}}+\frac {x}{\log ^2(3 x)}\right )}{x} \]

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Rubi [F]  time = 7.23, 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 {-18 x+9 x \log (3 x)-e^{3-\frac {1}{3} e^{\frac {e^3 x}{3}}+\frac {e^3 x}{3}} x \log ^3(3 x)+\left (-9 x \log (3 x)-9 e^{-\frac {1}{3} e^{\frac {e^3 x}{3}}} \log ^3(3 x)\right ) \log \left (\frac {x+e^{-\frac {1}{3} e^{\frac {e^3 x}{3}}} \log ^2(3 x)}{\log ^2(3 x)}\right )}{9 x^3 \log (3 x)+9 e^{-\frac {1}{3} e^{\frac {e^3 x}{3}}} x^2 \log ^3(3 x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-18*x + 9*x*Log[3*x] - E^(3 - E^((E^3*x)/3)/3 + (E^3*x)/3)*x*Log[3*x]^3 + (-9*x*Log[3*x] - (9*Log[3*x]^3)
/E^(E^((E^3*x)/3)/3))*Log[(x + Log[3*x]^2/E^(E^((E^3*x)/3)/3))/Log[3*x]^2])/(9*x^3*Log[3*x] + (9*x^2*Log[3*x]^
3)/E^(E^((E^3*x)/3)/3)),x]

[Out]

-x^(-1) - 3*ExpIntegralEi[-Log[3*x]]*(2 - Log[3*x]) - 3*ExpIntegralEi[-Log[3*x]]*Log[3*x] + 2*Defer[Int][Log[3
*x]/(x^2*(E^(E^((E^3*x)/3)/3)*x + Log[3*x]^2)), x] - Defer[Int][Log[3*x]^2/(x^2*(E^(E^((E^3*x)/3)/3)*x + Log[3
*x]^2)), x] - Defer[Int][(E^(3 + (E^3*x)/3)*Log[3*x]^2)/(x*(E^(E^((E^3*x)/3)/3)*x + Log[3*x]^2)), x]/9 - Defer
[Int][Log[E^(-1/3*E^((E^3*x)/3)) + x/Log[3*x]^2]/x^2, x]

Rubi steps

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

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Mathematica [A]  time = 0.32, size = 30, normalized size = 1.00 \begin {gather*} \frac {\log \left (e^{-\frac {1}{3} e^{\frac {e^3 x}{3}}}+\frac {x}{\log ^2(3 x)}\right )}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-18*x + 9*x*Log[3*x] - E^(3 - E^((E^3*x)/3)/3 + (E^3*x)/3)*x*Log[3*x]^3 + (-9*x*Log[3*x] - (9*Log[3
*x]^3)/E^(E^((E^3*x)/3)/3))*Log[(x + Log[3*x]^2/E^(E^((E^3*x)/3)/3))/Log[3*x]^2])/(9*x^3*Log[3*x] + (9*x^2*Log
[3*x]^3)/E^(E^((E^3*x)/3)/3)),x]

[Out]

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

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fricas [B]  time = 0.73, size = 54, normalized size = 1.80 \begin {gather*} \frac {\log \left (\frac {{\left (e^{\left (\frac {1}{3} \, x e^{3} - \frac {1}{3} \, e^{\left (\frac {1}{3} \, x e^{3}\right )} + 3\right )} \log \left (3 \, x\right )^{2} + x e^{\left (\frac {1}{3} \, x e^{3} + 3\right )}\right )} e^{\left (-\frac {1}{3} \, x e^{3} - 3\right )}}{\log \left (3 \, x\right )^{2}}\right )}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-9*log(3*x)^3*exp(-1/3*exp(1/3*x*exp(3)))-9*x*log(3*x))*log((log(3*x)^2*exp(-1/3*exp(1/3*x*exp(3))
)+x)/log(3*x)^2)-x*exp(3)*exp(1/3*x*exp(3))*log(3*x)^3*exp(-1/3*exp(1/3*x*exp(3)))+9*x*log(3*x)-18*x)/(9*x^2*l
og(3*x)^3*exp(-1/3*exp(1/3*x*exp(3)))+9*x^3*log(3*x)),x, algorithm="fricas")

[Out]

log((e^(1/3*x*e^3 - 1/3*e^(1/3*x*e^3) + 3)*log(3*x)^2 + x*e^(1/3*x*e^3 + 3))*e^(-1/3*x*e^3 - 3)/log(3*x)^2)/x

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giac [B]  time = 16.78, size = 53, normalized size = 1.77 \begin {gather*} \frac {\log \left ({\left (e^{\left (\frac {1}{3} \, x e^{3} - \frac {1}{3} \, e^{\left (\frac {1}{3} \, x e^{3}\right )}\right )} \log \left (3 \, x\right )^{2} + x e^{\left (\frac {1}{3} \, x e^{3}\right )}\right )} e^{\left (-\frac {1}{3} \, x e^{3}\right )}\right ) - \log \left (\log \left (3 \, x\right )^{2}\right )}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-9*log(3*x)^3*exp(-1/3*exp(1/3*x*exp(3)))-9*x*log(3*x))*log((log(3*x)^2*exp(-1/3*exp(1/3*x*exp(3))
)+x)/log(3*x)^2)-x*exp(3)*exp(1/3*x*exp(3))*log(3*x)^3*exp(-1/3*exp(1/3*x*exp(3)))+9*x*log(3*x)-18*x)/(9*x^2*l
og(3*x)^3*exp(-1/3*exp(1/3*x*exp(3)))+9*x^3*log(3*x)),x, algorithm="giac")

[Out]

(log((e^(1/3*x*e^3 - 1/3*e^(1/3*x*e^3))*log(3*x)^2 + x*e^(1/3*x*e^3))*e^(-1/3*x*e^3)) - log(log(3*x)^2))/x

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maple [C]  time = 0.49, size = 300, normalized size = 10.00

method	result	size
risch	\(\frac {\ln \left (\ln \left (3 x \right )^{2} {\mathrm e}^{-\frac {{\mathrm e}^{\frac {x \,{\mathrm e}^{3}}{3}}}{3}}+x \right )}{x}-\frac {i \pi \,\mathrm {csgn}\left (i \left (\ln \left (3 x \right )^{2} {\mathrm e}^{-\frac {{\mathrm e}^{\frac {x \,{\mathrm e}^{3}}{3}}}{3}}+x \right )\right ) \mathrm {csgn}\left (\frac {i}{\ln \left (3 x \right )^{2}}\right ) \mathrm {csgn}\left (\frac {i \left (\ln \left (3 x \right )^{2} {\mathrm e}^{-\frac {{\mathrm e}^{\frac {x \,{\mathrm e}^{3}}{3}}}{3}}+x \right )}{\ln \left (3 x \right )^{2}}\right )-i \pi \,\mathrm {csgn}\left (i \left (\ln \left (3 x \right )^{2} {\mathrm e}^{-\frac {{\mathrm e}^{\frac {x \,{\mathrm e}^{3}}{3}}}{3}}+x \right )\right ) \mathrm {csgn}\left (\frac {i \left (\ln \left (3 x \right )^{2} {\mathrm e}^{-\frac {{\mathrm e}^{\frac {x \,{\mathrm e}^{3}}{3}}}{3}}+x \right )}{\ln \left (3 x \right )^{2}}\right )^{2}-i \pi \,\mathrm {csgn}\left (\frac {i}{\ln \left (3 x \right )^{2}}\right ) \mathrm {csgn}\left (\frac {i \left (\ln \left (3 x \right )^{2} {\mathrm e}^{-\frac {{\mathrm e}^{\frac {x \,{\mathrm e}^{3}}{3}}}{3}}+x \right )}{\ln \left (3 x \right )^{2}}\right )^{2}-i \pi \mathrm {csgn}\left (i \ln \left (3 x \right )\right )^{2} \mathrm {csgn}\left (i \ln \left (3 x \right )^{2}\right )+2 i \pi \,\mathrm {csgn}\left (i \ln \left (3 x \right )\right ) \mathrm {csgn}\left (i \ln \left (3 x \right )^{2}\right )^{2}-i \pi \mathrm {csgn}\left (i \ln \left (3 x \right )^{2}\right )^{3}+i \pi \mathrm {csgn}\left (\frac {i \left (\ln \left (3 x \right )^{2} {\mathrm e}^{-\frac {{\mathrm e}^{\frac {x \,{\mathrm e}^{3}}{3}}}{3}}+x \right )}{\ln \left (3 x \right )^{2}}\right )^{3}+4 \ln \left (\ln \left (3 x \right )\right )}{2 x}\)	\(300\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-9*ln(3*x)^3*exp(-1/3*exp(1/3*x*exp(3)))-9*x*ln(3*x))*ln((ln(3*x)^2*exp(-1/3*exp(1/3*x*exp(3)))+x)/ln(3*
x)^2)-x*exp(3)*exp(1/3*x*exp(3))*ln(3*x)^3*exp(-1/3*exp(1/3*x*exp(3)))+9*x*ln(3*x)-18*x)/(9*x^2*ln(3*x)^3*exp(
-1/3*exp(1/3*x*exp(3)))+9*x^3*ln(3*x)),x,method=_RETURNVERBOSE)

[Out]

1/x*ln(ln(3*x)^2*exp(-1/3*exp(1/3*x*exp(3)))+x)-1/2*(I*Pi*csgn(I*(ln(3*x)^2*exp(-1/3*exp(1/3*x*exp(3)))+x))*cs
gn(I/ln(3*x)^2)*csgn(I/ln(3*x)^2*(ln(3*x)^2*exp(-1/3*exp(1/3*x*exp(3)))+x))-I*Pi*csgn(I*(ln(3*x)^2*exp(-1/3*ex
p(1/3*x*exp(3)))+x))*csgn(I/ln(3*x)^2*(ln(3*x)^2*exp(-1/3*exp(1/3*x*exp(3)))+x))^2-I*Pi*csgn(I/ln(3*x)^2)*csgn
(I/ln(3*x)^2*(ln(3*x)^2*exp(-1/3*exp(1/3*x*exp(3)))+x))^2-I*Pi*csgn(I*ln(3*x))^2*csgn(I*ln(3*x)^2)+2*I*Pi*csgn
(I*ln(3*x))*csgn(I*ln(3*x)^2)^2-I*Pi*csgn(I*ln(3*x)^2)^3+I*Pi*csgn(I/ln(3*x)^2*(ln(3*x)^2*exp(-1/3*exp(1/3*x*e
xp(3)))+x))^3+4*ln(ln(3*x)))/x

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maxima [B]  time = 0.53, size = 49, normalized size = 1.63 \begin {gather*} -\frac {e^{\left (\frac {1}{3} \, x e^{3}\right )} - 3 \, \log \left (x e^{\left (\frac {1}{3} \, e^{\left (\frac {1}{3} \, x e^{3}\right )}\right )} + \log \relax (3)^{2} + 2 \, \log \relax (3) \log \relax (x) + \log \relax (x)^{2}\right ) + 6 \, \log \left (\log \relax (3) + \log \relax (x)\right )}{3 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-9*log(3*x)^3*exp(-1/3*exp(1/3*x*exp(3)))-9*x*log(3*x))*log((log(3*x)^2*exp(-1/3*exp(1/3*x*exp(3))
)+x)/log(3*x)^2)-x*exp(3)*exp(1/3*x*exp(3))*log(3*x)^3*exp(-1/3*exp(1/3*x*exp(3)))+9*x*log(3*x)-18*x)/(9*x^2*l
og(3*x)^3*exp(-1/3*exp(1/3*x*exp(3)))+9*x^3*log(3*x)),x, algorithm="maxima")

[Out]

-1/3*(e^(1/3*x*e^3) - 3*log(x*e^(1/3*e^(1/3*x*e^3)) + log(3)^2 + 2*log(3)*log(x) + log(x)^2) + 6*log(log(3) +
log(x)))/x

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {18\,x-9\,x\,\ln \left (3\,x\right )+\ln \left (\frac {{\mathrm {e}}^{-\frac {{\mathrm {e}}^{\frac {x\,{\mathrm {e}}^3}{3}}}{3}}\,{\ln \left (3\,x\right )}^2+x}{{\ln \left (3\,x\right )}^2}\right )\,\left (9\,{\mathrm {e}}^{-\frac {{\mathrm {e}}^{\frac {x\,{\mathrm {e}}^3}{3}}}{3}}\,{\ln \left (3\,x\right )}^3+9\,x\,\ln \left (3\,x\right )\right )+x\,{\ln \left (3\,x\right )}^3\,{\mathrm {e}}^3\,{\mathrm {e}}^{-\frac {{\mathrm {e}}^{\frac {x\,{\mathrm {e}}^3}{3}}}{3}}\,{\mathrm {e}}^{\frac {x\,{\mathrm {e}}^3}{3}}}{9\,x^3\,\ln \left (3\,x\right )+9\,x^2\,{\ln \left (3\,x\right )}^3\,{\mathrm {e}}^{-\frac {{\mathrm {e}}^{\frac {x\,{\mathrm {e}}^3}{3}}}{3}}} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(18*x - 9*x*log(3*x) + log((x + log(3*x)^2*exp(-exp((x*exp(3))/3)/3))/log(3*x)^2)*(9*x*log(3*x) + 9*log(3
*x)^3*exp(-exp((x*exp(3))/3)/3)) + x*log(3*x)^3*exp(3)*exp(-exp((x*exp(3))/3)/3)*exp((x*exp(3))/3))/(9*x^3*log
(3*x) + 9*x^2*log(3*x)^3*exp(-exp((x*exp(3))/3)/3)),x)

[Out]

int(-(18*x - 9*x*log(3*x) + log((x + log(3*x)^2*exp(-exp((x*exp(3))/3)/3))/log(3*x)^2)*(9*x*log(3*x) + 9*log(3
*x)^3*exp(-exp((x*exp(3))/3)/3)) + x*log(3*x)^3*exp(3)*exp(-exp((x*exp(3))/3)/3)*exp((x*exp(3))/3))/(9*x^3*log
(3*x) + 9*x^2*log(3*x)^3*exp(-exp((x*exp(3))/3)/3)), x)

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sympy [A]  time = 11.16, size = 29, normalized size = 0.97 \begin {gather*} \frac {\log {\left (\frac {x + e^{- \frac {e^{\frac {x e^{3}}{3}}}{3}} \log {\left (3 x \right )}^{2}}{\log {\left (3 x \right )}^{2}} \right )}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-9*ln(3*x)**3*exp(-1/3*exp(1/3*x*exp(3)))-9*x*ln(3*x))*ln((ln(3*x)**2*exp(-1/3*exp(1/3*x*exp(3)))+
x)/ln(3*x)**2)-x*exp(3)*exp(1/3*x*exp(3))*ln(3*x)**3*exp(-1/3*exp(1/3*x*exp(3)))+9*x*ln(3*x)-18*x)/(9*x**2*ln(
3*x)**3*exp(-1/3*exp(1/3*x*exp(3)))+9*x**3*ln(3*x)),x)

[Out]

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

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