3.289 \(\int \frac {1}{x (x+\log (x))} \, dx\)

Optimal. Leaf size=13 \[ \text {Int}\left (\frac {1}{x (x+\log (x))},x\right ) \]

[Out]

CannotIntegrate(1/x/(x+ln(x)),x)

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Rubi [A]  time = 0.03, 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 = {} \[ \int \frac {1}{x (x+\log (x))} \, dx \]

Verification is Not applicable to the result.

[In]

Int[1/(x*(x + Log[x])),x]

[Out]

Defer[Int][1/(x*(x + Log[x])), x]

Rubi steps

\begin {align*} \int \frac {1}{x (x+\log (x))} \, dx &=\int \frac {1}{x (x+\log (x))} \, dx\\ \end {align*}

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Mathematica [A]  time = 0.04, size = 0, normalized size = 0.00 \[ \int \frac {1}{x (x+\log (x))} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/(x*(x + Log[x])),x]

[Out]

Integrate[1/(x*(x + Log[x])), x]

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fricas [A]  time = 0.44, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{x^{2} + x \log \relax (x)}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/(x+log(x)),x, algorithm="fricas")

[Out]

integral(1/(x^2 + x*log(x)), x)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (x + \log \relax (x)\right )} x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/(x+log(x)),x, algorithm="giac")

[Out]

integrate(1/((x + log(x))*x), x)

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maple [A]  time = 0.07, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (x +\ln \relax (x )\right ) x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x/(x+ln(x)),x)

[Out]

int(1/x/(x+ln(x)),x)

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (x + \log \relax (x)\right )} x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/(x+log(x)),x, algorithm="maxima")

[Out]

integrate(1/((x + log(x))*x), x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.08 \[ \int \frac {1}{x\,\left (x+\ln \relax (x)\right )} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x*(x + log(x))),x)

[Out]

int(1/(x*(x + log(x))), x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \left (x + \log {\relax (x )}\right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/(x+ln(x)),x)

[Out]

Integral(1/(x*(x + log(x))), x)

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