3.60.8 \(\int \frac {-e+6 e^{2 x} x \log ^2(5 e^x)+(6-6 e^x x) \log (x)+\log (5 e^x) (-6 e^x+6 e^{2 x} x-6 e^x x \log (x))}{3 e^{2 x} x \log ^2(5 e^x)-e x \log (x)-6 e^x x \log (5 e^x) \log (x)+3 x \log ^2(x)} \, dx\)

Optimal. Leaf size=25 \[ \log \left (\log (x)-\frac {3 \left (-e^x \log \left (5 e^x\right )+\log (x)\right )^2}{e}\right ) \]

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Rubi [F]  time = 8.48, 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 {-e+6 e^{2 x} x \log ^2\left (5 e^x\right )+\left (6-6 e^x x\right ) \log (x)+\log \left (5 e^x\right ) \left (-6 e^x+6 e^{2 x} x-6 e^x x \log (x)\right )}{3 e^{2 x} x \log ^2\left (5 e^x\right )-e x \log (x)-6 e^x x \log \left (5 e^x\right ) \log (x)+3 x \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-E + 6*E^(2*x)*x*Log[5*E^x]^2 + (6 - 6*E^x*x)*Log[x] + Log[5*E^x]*(-6*E^x + 6*E^(2*x)*x - 6*E^x*x*Log[x])
)/(3*E^(2*x)*x*Log[5*E^x]^2 - E*x*Log[x] - 6*E^x*x*Log[5*E^x]*Log[x] + 3*x*Log[x]^2),x]

[Out]

2*x + 2*Log[Log[5*E^x]] + E*Defer[Int][1/(x*(-3*E^(2*x)*Log[5*E^x]^2 + E*Log[x] + 6*E^x*Log[5*E^x]*Log[x] - 3*
Log[x]^2)), x] - 2*E*Defer[Int][Log[x]/(-3*E^(2*x)*Log[5*E^x]^2 + E*Log[x] + 6*E^x*Log[5*E^x]*Log[x] - 3*Log[x
]^2), x] - 2*E*Defer[Int][Log[x]/(Log[5*E^x]*(-3*E^(2*x)*Log[5*E^x]^2 + E*Log[x] + 6*E^x*Log[5*E^x]*Log[x] - 3
*Log[x]^2)), x] - 6*Defer[Int][(E^x*Log[5*E^x])/(x*(3*E^(2*x)*Log[5*E^x]^2 - E*Log[x] - 6*E^x*Log[5*E^x]*Log[x
] + 3*Log[x]^2)), x] + 6*Defer[Int][(E^x*Log[x])/(3*E^(2*x)*Log[5*E^x]^2 - E*Log[x] - 6*E^x*Log[5*E^x]*Log[x]
+ 3*Log[x]^2), x] + 6*Defer[Int][Log[x]/(x*(3*E^(2*x)*Log[5*E^x]^2 - E*Log[x] - 6*E^x*Log[5*E^x]*Log[x] + 3*Lo
g[x]^2)), x] + 6*Defer[Int][(E^x*Log[5*E^x]*Log[x])/(3*E^(2*x)*Log[5*E^x]^2 - E*Log[x] - 6*E^x*Log[5*E^x]*Log[
x] + 3*Log[x]^2), x] - 6*Defer[Int][Log[x]^2/(3*E^(2*x)*Log[5*E^x]^2 - E*Log[x] - 6*E^x*Log[5*E^x]*Log[x] + 3*
Log[x]^2), x] - 6*Defer[Int][Log[x]^2/(Log[5*E^x]*(3*E^(2*x)*Log[5*E^x]^2 - E*Log[x] - 6*E^x*Log[5*E^x]*Log[x]
+ 3*Log[x]^2)), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {2 \left (1+\log \left (5 e^x\right )\right )}{\log \left (5 e^x\right )}+\frac {-e \log \left (5 e^x\right )-6 e^x \log ^2\left (5 e^x\right )+2 e x \log (x)+6 \log \left (5 e^x\right ) \log (x)+2 e x \log \left (5 e^x\right ) \log (x)+6 e^x x \log \left (5 e^x\right ) \log (x)+6 e^x x \log ^2\left (5 e^x\right ) \log (x)-6 x \log ^2(x)-6 x \log \left (5 e^x\right ) \log ^2(x)}{x \log \left (5 e^x\right ) \left (3 e^{2 x} \log ^2\left (5 e^x\right )-e \log (x)-6 e^x \log \left (5 e^x\right ) \log (x)+3 \log ^2(x)\right )}\right ) \, dx\\ &=2 \int \frac {1+\log \left (5 e^x\right )}{\log \left (5 e^x\right )} \, dx+\int \frac {-e \log \left (5 e^x\right )-6 e^x \log ^2\left (5 e^x\right )+2 e x \log (x)+6 \log \left (5 e^x\right ) \log (x)+2 e x \log \left (5 e^x\right ) \log (x)+6 e^x x \log \left (5 e^x\right ) \log (x)+6 e^x x \log ^2\left (5 e^x\right ) \log (x)-6 x \log ^2(x)-6 x \log \left (5 e^x\right ) \log ^2(x)}{x \log \left (5 e^x\right ) \left (3 e^{2 x} \log ^2\left (5 e^x\right )-e \log (x)-6 e^x \log \left (5 e^x\right ) \log (x)+3 \log ^2(x)\right )} \, dx\\ &=2 \operatorname {Subst}\left (\int \frac {1+\frac {1}{\log (5 x)}}{x} \, dx,x,e^x\right )+\int \frac {2 x (e-3 \log (x)) \log (x)+6 e^x \log ^2\left (5 e^x\right ) (-1+x \log (x))+\log \left (5 e^x\right ) \left (-e+2 \left (3+e x+3 e^x x\right ) \log (x)-6 x \log ^2(x)\right )}{x \log \left (5 e^x\right ) \left (3 e^{2 x} \log ^2\left (5 e^x\right )-6 e^x \log \left (5 e^x\right ) \log (x)+\log (x) (-e+3 \log (x))\right )} \, dx\\ &=2 \operatorname {Subst}\left (\int \left (\frac {1}{x}+\frac {1}{x \log (5 x)}\right ) \, dx,x,e^x\right )+\int \left (\frac {e}{x \left (-3 e^{2 x} \log ^2\left (5 e^x\right )+e \log (x)+6 e^x \log \left (5 e^x\right ) \log (x)-3 \log ^2(x)\right )}-\frac {2 e \log (x)}{-3 e^{2 x} \log ^2\left (5 e^x\right )+e \log (x)+6 e^x \log \left (5 e^x\right ) \log (x)-3 \log ^2(x)}-\frac {2 e \log (x)}{\log \left (5 e^x\right ) \left (-3 e^{2 x} \log ^2\left (5 e^x\right )+e \log (x)+6 e^x \log \left (5 e^x\right ) \log (x)-3 \log ^2(x)\right )}-\frac {6 e^x \log \left (5 e^x\right )}{x \left (3 e^{2 x} \log ^2\left (5 e^x\right )-e \log (x)-6 e^x \log \left (5 e^x\right ) \log (x)+3 \log ^2(x)\right )}+\frac {6 e^x \log (x)}{3 e^{2 x} \log ^2\left (5 e^x\right )-e \log (x)-6 e^x \log \left (5 e^x\right ) \log (x)+3 \log ^2(x)}+\frac {6 \log (x)}{x \left (3 e^{2 x} \log ^2\left (5 e^x\right )-e \log (x)-6 e^x \log \left (5 e^x\right ) \log (x)+3 \log ^2(x)\right )}+\frac {6 e^x \log \left (5 e^x\right ) \log (x)}{3 e^{2 x} \log ^2\left (5 e^x\right )-e \log (x)-6 e^x \log \left (5 e^x\right ) \log (x)+3 \log ^2(x)}-\frac {6 \log ^2(x)}{3 e^{2 x} \log ^2\left (5 e^x\right )-e \log (x)-6 e^x \log \left (5 e^x\right ) \log (x)+3 \log ^2(x)}-\frac {6 \log ^2(x)}{\log \left (5 e^x\right ) \left (3 e^{2 x} \log ^2\left (5 e^x\right )-e \log (x)-6 e^x \log \left (5 e^x\right ) \log (x)+3 \log ^2(x)\right )}\right ) \, dx\\ &=2 x+2 \operatorname {Subst}\left (\int \frac {1}{x \log (5 x)} \, dx,x,e^x\right )-6 \int \frac {e^x \log \left (5 e^x\right )}{x \left (3 e^{2 x} \log ^2\left (5 e^x\right )-e \log (x)-6 e^x \log \left (5 e^x\right ) \log (x)+3 \log ^2(x)\right )} \, dx+6 \int \frac {e^x \log (x)}{3 e^{2 x} \log ^2\left (5 e^x\right )-e \log (x)-6 e^x \log \left (5 e^x\right ) \log (x)+3 \log ^2(x)} \, dx+6 \int \frac {\log (x)}{x \left (3 e^{2 x} \log ^2\left (5 e^x\right )-e \log (x)-6 e^x \log \left (5 e^x\right ) \log (x)+3 \log ^2(x)\right )} \, dx+6 \int \frac {e^x \log \left (5 e^x\right ) \log (x)}{3 e^{2 x} \log ^2\left (5 e^x\right )-e \log (x)-6 e^x \log \left (5 e^x\right ) \log (x)+3 \log ^2(x)} \, dx-6 \int \frac {\log ^2(x)}{3 e^{2 x} \log ^2\left (5 e^x\right )-e \log (x)-6 e^x \log \left (5 e^x\right ) \log (x)+3 \log ^2(x)} \, dx-6 \int \frac {\log ^2(x)}{\log \left (5 e^x\right ) \left (3 e^{2 x} \log ^2\left (5 e^x\right )-e \log (x)-6 e^x \log \left (5 e^x\right ) \log (x)+3 \log ^2(x)\right )} \, dx+e \int \frac {1}{x \left (-3 e^{2 x} \log ^2\left (5 e^x\right )+e \log (x)+6 e^x \log \left (5 e^x\right ) \log (x)-3 \log ^2(x)\right )} \, dx-(2 e) \int \frac {\log (x)}{-3 e^{2 x} \log ^2\left (5 e^x\right )+e \log (x)+6 e^x \log \left (5 e^x\right ) \log (x)-3 \log ^2(x)} \, dx-(2 e) \int \frac {\log (x)}{\log \left (5 e^x\right ) \left (-3 e^{2 x} \log ^2\left (5 e^x\right )+e \log (x)+6 e^x \log \left (5 e^x\right ) \log (x)-3 \log ^2(x)\right )} \, dx\\ &=2 x+2 \operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,\log \left (5 e^x\right )\right )-6 \int \frac {e^x \log \left (5 e^x\right )}{x \left (3 e^{2 x} \log ^2\left (5 e^x\right )-e \log (x)-6 e^x \log \left (5 e^x\right ) \log (x)+3 \log ^2(x)\right )} \, dx+6 \int \frac {e^x \log (x)}{3 e^{2 x} \log ^2\left (5 e^x\right )-e \log (x)-6 e^x \log \left (5 e^x\right ) \log (x)+3 \log ^2(x)} \, dx+6 \int \frac {\log (x)}{x \left (3 e^{2 x} \log ^2\left (5 e^x\right )-e \log (x)-6 e^x \log \left (5 e^x\right ) \log (x)+3 \log ^2(x)\right )} \, dx+6 \int \frac {e^x \log \left (5 e^x\right ) \log (x)}{3 e^{2 x} \log ^2\left (5 e^x\right )-e \log (x)-6 e^x \log \left (5 e^x\right ) \log (x)+3 \log ^2(x)} \, dx-6 \int \frac {\log ^2(x)}{3 e^{2 x} \log ^2\left (5 e^x\right )-e \log (x)-6 e^x \log \left (5 e^x\right ) \log (x)+3 \log ^2(x)} \, dx-6 \int \frac {\log ^2(x)}{\log \left (5 e^x\right ) \left (3 e^{2 x} \log ^2\left (5 e^x\right )-e \log (x)-6 e^x \log \left (5 e^x\right ) \log (x)+3 \log ^2(x)\right )} \, dx+e \int \frac {1}{x \left (-3 e^{2 x} \log ^2\left (5 e^x\right )+e \log (x)+6 e^x \log \left (5 e^x\right ) \log (x)-3 \log ^2(x)\right )} \, dx-(2 e) \int \frac {\log (x)}{-3 e^{2 x} \log ^2\left (5 e^x\right )+e \log (x)+6 e^x \log \left (5 e^x\right ) \log (x)-3 \log ^2(x)} \, dx-(2 e) \int \frac {\log (x)}{\log \left (5 e^x\right ) \left (-3 e^{2 x} \log ^2\left (5 e^x\right )+e \log (x)+6 e^x \log \left (5 e^x\right ) \log (x)-3 \log ^2(x)\right )} \, dx\\ &=2 x+2 \log \left (\log \left (5 e^x\right )\right )-6 \int \frac {e^x \log \left (5 e^x\right )}{x \left (3 e^{2 x} \log ^2\left (5 e^x\right )-e \log (x)-6 e^x \log \left (5 e^x\right ) \log (x)+3 \log ^2(x)\right )} \, dx+6 \int \frac {e^x \log (x)}{3 e^{2 x} \log ^2\left (5 e^x\right )-e \log (x)-6 e^x \log \left (5 e^x\right ) \log (x)+3 \log ^2(x)} \, dx+6 \int \frac {\log (x)}{x \left (3 e^{2 x} \log ^2\left (5 e^x\right )-e \log (x)-6 e^x \log \left (5 e^x\right ) \log (x)+3 \log ^2(x)\right )} \, dx+6 \int \frac {e^x \log \left (5 e^x\right ) \log (x)}{3 e^{2 x} \log ^2\left (5 e^x\right )-e \log (x)-6 e^x \log \left (5 e^x\right ) \log (x)+3 \log ^2(x)} \, dx-6 \int \frac {\log ^2(x)}{3 e^{2 x} \log ^2\left (5 e^x\right )-e \log (x)-6 e^x \log \left (5 e^x\right ) \log (x)+3 \log ^2(x)} \, dx-6 \int \frac {\log ^2(x)}{\log \left (5 e^x\right ) \left (3 e^{2 x} \log ^2\left (5 e^x\right )-e \log (x)-6 e^x \log \left (5 e^x\right ) \log (x)+3 \log ^2(x)\right )} \, dx+e \int \frac {1}{x \left (-3 e^{2 x} \log ^2\left (5 e^x\right )+e \log (x)+6 e^x \log \left (5 e^x\right ) \log (x)-3 \log ^2(x)\right )} \, dx-(2 e) \int \frac {\log (x)}{-3 e^{2 x} \log ^2\left (5 e^x\right )+e \log (x)+6 e^x \log \left (5 e^x\right ) \log (x)-3 \log ^2(x)} \, dx-(2 e) \int \frac {\log (x)}{\log \left (5 e^x\right ) \left (-3 e^{2 x} \log ^2\left (5 e^x\right )+e \log (x)+6 e^x \log \left (5 e^x\right ) \log (x)-3 \log ^2(x)\right )} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [F]  time = 0.46, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {-e+6 e^{2 x} x \log ^2\left (5 e^x\right )+\left (6-6 e^x x\right ) \log (x)+\log \left (5 e^x\right ) \left (-6 e^x+6 e^{2 x} x-6 e^x x \log (x)\right )}{3 e^{2 x} x \log ^2\left (5 e^x\right )-e x \log (x)-6 e^x x \log \left (5 e^x\right ) \log (x)+3 x \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(-E + 6*E^(2*x)*x*Log[5*E^x]^2 + (6 - 6*E^x*x)*Log[x] + Log[5*E^x]*(-6*E^x + 6*E^(2*x)*x - 6*E^x*x*L
og[x]))/(3*E^(2*x)*x*Log[5*E^x]^2 - E*x*Log[x] - 6*E^x*x*Log[5*E^x]*Log[x] + 3*x*Log[x]^2),x]

[Out]

Integrate[(-E + 6*E^(2*x)*x*Log[5*E^x]^2 + (6 - 6*E^x*x)*Log[x] + Log[5*E^x]*(-6*E^x + 6*E^(2*x)*x - 6*E^x*x*L
og[x]))/(3*E^(2*x)*x*Log[5*E^x]^2 - E*x*Log[x] - 6*E^x*x*Log[5*E^x]*Log[x] + 3*x*Log[x]^2), x]

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fricas [A]  time = 0.76, size = 42, normalized size = 1.68 \begin {gather*} \log \left (3 \, {\left (x^{2} + 2 \, x \log \relax (5) + \log \relax (5)^{2}\right )} e^{\left (2 \, x\right )} - {\left (6 \, {\left (x + \log \relax (5)\right )} e^{x} + e\right )} \log \relax (x) + 3 \, \log \relax (x)^{2}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((6*x*exp(x)^2*log(5*exp(x))^2+(-6*x*exp(x)*log(x)+6*x*exp(x)^2-6*exp(x))*log(5*exp(x))+(-6*exp(x)*x+
6)*log(x)-exp(1))/(3*x*exp(x)^2*log(5*exp(x))^2-6*x*exp(x)*log(x)*log(5*exp(x))+3*x*log(x)^2-x*exp(1)*log(x)),
x, algorithm="fricas")

[Out]

log(3*(x^2 + 2*x*log(5) + log(5)^2)*e^(2*x) - (6*(x + log(5))*e^x + e)*log(x) + 3*log(x)^2)

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giac [B]  time = 0.47, size = 56, normalized size = 2.24 \begin {gather*} \log \left (-3 \, x^{2} e^{\left (2 \, x\right )} - 6 \, x e^{\left (2 \, x\right )} \log \relax (5) - 3 \, e^{\left (2 \, x\right )} \log \relax (5)^{2} + 6 \, x e^{x} \log \relax (x) + 6 \, e^{x} \log \relax (5) \log \relax (x) + e \log \relax (x) - 3 \, \log \relax (x)^{2}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((6*x*exp(x)^2*log(5*exp(x))^2+(-6*x*exp(x)*log(x)+6*x*exp(x)^2-6*exp(x))*log(5*exp(x))+(-6*exp(x)*x+
6)*log(x)-exp(1))/(3*x*exp(x)^2*log(5*exp(x))^2-6*x*exp(x)*log(x)*log(5*exp(x))+3*x*log(x)^2-x*exp(1)*log(x)),
x, algorithm="giac")

[Out]

log(-3*x^2*e^(2*x) - 6*x*e^(2*x)*log(5) - 3*e^(2*x)*log(5)^2 + 6*x*e^x*log(x) + 6*e^x*log(5)*log(x) + e*log(x)
- 3*log(x)^2)

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maple [B]  time = 0.28, size = 69, normalized size = 2.76

method	result	size
risch	\(2 x +\ln \left (\ln \left ({\mathrm e}^{x}\right )^{2}-{\mathrm e}^{-x} \left (-2 \,{\mathrm e}^{x} \ln \relax (5)+2 \ln \relax (x )\right ) \ln \left ({\mathrm e}^{x}\right )-\frac {\left (-12 \ln \relax (5)^{2} {\mathrm e}^{2 x}+24 \ln \relax (5) {\mathrm e}^{x} \ln \relax (x )+4 \,{\mathrm e} \ln \relax (x )-12 \ln \relax (x )^{2}\right ) {\mathrm e}^{-2 x}}{12}\right )\)	\(69\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((6*x*exp(x)^2*ln(5*exp(x))^2+(-6*x*exp(x)*ln(x)+6*x*exp(x)^2-6*exp(x))*ln(5*exp(x))+(-6*exp(x)*x+6)*ln(x)-
exp(1))/(3*x*exp(x)^2*ln(5*exp(x))^2-6*x*exp(x)*ln(x)*ln(5*exp(x))+3*x*ln(x)^2-x*exp(1)*ln(x)),x,method=_RETUR
NVERBOSE)

[Out]

2*x+ln(ln(exp(x))^2-exp(-x)*(-2*exp(x)*ln(5)+2*ln(x))*ln(exp(x))-1/12*(-12*ln(5)^2*exp(2*x)+24*ln(5)*exp(x)*ln
(x)+4*exp(1)*ln(x)-12*ln(x)^2)*exp(-2*x))

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maxima [B]  time = 0.52, size = 67, normalized size = 2.68 \begin {gather*} 2 \, \log \left (x + \log \relax (5)\right ) + \log \left (-\frac {6 \, {\left (x + \log \relax (5)\right )} e^{x} \log \relax (x) - 3 \, {\left (x^{2} + 2 \, x \log \relax (5) + \log \relax (5)^{2}\right )} e^{\left (2 \, x\right )} + e \log \relax (x) - 3 \, \log \relax (x)^{2}}{3 \, {\left (x^{2} + 2 \, x \log \relax (5) + \log \relax (5)^{2}\right )}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((6*x*exp(x)^2*log(5*exp(x))^2+(-6*x*exp(x)*log(x)+6*x*exp(x)^2-6*exp(x))*log(5*exp(x))+(-6*exp(x)*x+
6)*log(x)-exp(1))/(3*x*exp(x)^2*log(5*exp(x))^2-6*x*exp(x)*log(x)*log(5*exp(x))+3*x*log(x)^2-x*exp(1)*log(x)),
x, algorithm="maxima")

[Out]

2*log(x + log(5)) + log(-1/3*(6*(x + log(5))*e^x*log(x) - 3*(x^2 + 2*x*log(5) + log(5)^2)*e^(2*x) + e*log(x) -
3*log(x)^2)/(x^2 + 2*x*log(5) + log(5)^2))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {-6\,x\,{\mathrm {e}}^{2\,x}\,{\ln \left (5\,{\mathrm {e}}^x\right )}^2+\left (6\,{\mathrm {e}}^x-6\,x\,{\mathrm {e}}^{2\,x}+6\,x\,{\mathrm {e}}^x\,\ln \relax (x)\right )\,\ln \left (5\,{\mathrm {e}}^x\right )+\mathrm {e}+\ln \relax (x)\,\left (6\,x\,{\mathrm {e}}^x-6\right )}{3\,x\,{\mathrm {e}}^{2\,x}\,{\ln \left (5\,{\mathrm {e}}^x\right )}^2-6\,x\,{\mathrm {e}}^x\,\ln \left (5\,{\mathrm {e}}^x\right )\,\ln \relax (x)+3\,x\,{\ln \relax (x)}^2-x\,\mathrm {e}\,\ln \relax (x)} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(1) + log(5*exp(x))*(6*exp(x) - 6*x*exp(2*x) + 6*x*exp(x)*log(x)) + log(x)*(6*x*exp(x) - 6) - 6*x*exp
(2*x)*log(5*exp(x))^2)/(3*x*log(x)^2 + 3*x*exp(2*x)*log(5*exp(x))^2 - x*exp(1)*log(x) - 6*x*exp(x)*log(5*exp(x
))*log(x)),x)

[Out]

int(-(exp(1) + log(5*exp(x))*(6*exp(x) - 6*x*exp(2*x) + 6*x*exp(x)*log(x)) + log(x)*(6*x*exp(x) - 6) - 6*x*exp
(2*x)*log(5*exp(x))^2)/(3*x*log(x)^2 + 3*x*exp(2*x)*log(5*exp(x))^2 - x*exp(1)*log(x) - 6*x*exp(x)*log(5*exp(x
))*log(x)), x)

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sympy [B]  time = 3.67, size = 60, normalized size = 2.40 \begin {gather*} 2 \log {\left (x + \log {\relax (5 )} \right )} + \log {\left (\frac {3 \log {\relax (x )}^{2} - e \log {\relax (x )}}{3 x^{2} + 6 x \log {\relax (5 )} + 3 \log {\relax (5 )}^{2}} + e^{2 x} - \frac {2 e^{x} \log {\relax (x )}}{x + \log {\relax (5 )}} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((6*x*exp(x)**2*ln(5*exp(x))**2+(-6*x*exp(x)*ln(x)+6*x*exp(x)**2-6*exp(x))*ln(5*exp(x))+(-6*exp(x)*x+
6)*ln(x)-exp(1))/(3*x*exp(x)**2*ln(5*exp(x))**2-6*x*exp(x)*ln(x)*ln(5*exp(x))+3*x*ln(x)**2-x*exp(1)*ln(x)),x)

[Out]

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

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