\(\int \frac {1}{x (x+\log (x))} \, dx\) [289]

Optimal result

Integrand size = 10, antiderivative size = 10 \[ \int \frac {1}{x (x+\log (x))} \, dx=\text {Int}\left (\frac {1}{x (x+\log (x))},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {1}{x (x+\log (x))} \, dx=\int \frac {1}{x (x+\log (x))} \, dx \]

[In]

Int[1/(x*(x + Log[x])),x]

[Out]

Defer[Int][1/(x*(x + Log[x])), x]

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

Mathematica [N/A]

Not integrable

Time = 0.05 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {1}{x (x+\log (x))} \, dx=\int \frac {1}{x (x+\log (x))} \, dx \]

[In]

Integrate[1/(x*(x + Log[x])),x]

[Out]

Integrate[1/(x*(x + Log[x])), x]

Maple [N/A]

Not integrable

Time = 0.44 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00

\[\int \frac {1}{x \left (x +\ln \left (x \right )\right )}d x\]

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.27 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {1}{x (x+\log (x))} \, dx=\int { \frac {1}{{\left (x + \log \left (x\right )\right )} x} \,d x } \]

[In]

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

[Out]

integral(1/(x^2 + x*log(x)), x)

Sympy [N/A]

Not integrable

Time = 0.54 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {1}{x (x+\log (x))} \, dx=\int \frac {1}{x \left (x + \log {\left (x \right )}\right )}\, dx \]

[In]

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

[Out]

Integral(1/(x*(x + log(x))), x)

Maxima [N/A]

Not integrable

Time = 0.23 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {1}{x (x+\log (x))} \, dx=\int { \frac {1}{{\left (x + \log \left (x\right )\right )} x} \,d x } \]

[In]

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

[Out]

integrate(1/((x + log(x))*x), x)

Giac [N/A]

Not integrable

Time = 0.33 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {1}{x (x+\log (x))} \, dx=\int { \frac {1}{{\left (x + \log \left (x\right )\right )} x} \,d x } \]

[In]

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

[Out]

integrate(1/((x + log(x))*x), x)

Mupad [N/A]

Not integrable

Time = 1.49 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {1}{x (x+\log (x))} \, dx=\int \frac {1}{x\,\left (x+\ln \left (x\right )\right )} \,d x \]

[In]

int(1/(x*(x + log(x))),x)

[Out]

int(1/(x*(x + log(x))), x)