\(\int \frac {1}{x+\log (x)} \, dx\) [288]

Optimal result

Integrand size = 6, antiderivative size = 6 \[ \int \frac {1}{x+\log (x)} \, dx=\text {Int}\left (\frac {1}{x+\log (x)},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.01 (sec) , antiderivative size = 6, 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 = {} \[ \int \frac {1}{x+\log (x)} \, dx=\int \frac {1}{x+\log (x)} \, dx \]

[In]

Int[(x + Log[x])^(-1),x]

[Out]

Defer[Int][(x + Log[x])^(-1), x]

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

Mathematica [N/A]

Not integrable

Time = 0.01 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.33 \[ \int \frac {1}{x+\log (x)} \, dx=\int \frac {1}{x+\log (x)} \, dx \]

[In]

Integrate[(x + Log[x])^(-1),x]

[Out]

Integrate[(x + Log[x])^(-1), x]

Maple [N/A]

Not integrable

Time = 0.47 (sec) , antiderivative size = 6, normalized size of antiderivative = 1.00

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

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.27 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.33 \[ \int \frac {1}{x+\log (x)} \, dx=\int { \frac {1}{x + \log \left (x\right )} \,d x } \]

[In]

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

[Out]

integral(1/(x + log(x)), x)

Sympy [N/A]

Not integrable

Time = 0.22 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.17 \[ \int \frac {1}{x+\log (x)} \, dx=\int \frac {1}{x + \log {\left (x \right )}}\, dx \]

[In]

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

[Out]

Integral(1/(x + log(x)), x)

Maxima [N/A]

Not integrable

Time = 0.24 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.33 \[ \int \frac {1}{x+\log (x)} \, dx=\int { \frac {1}{x + \log \left (x\right )} \,d x } \]

[In]

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

[Out]

integrate(1/(x + log(x)), x)

Giac [N/A]

Not integrable

Time = 0.31 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.33 \[ \int \frac {1}{x+\log (x)} \, dx=\int { \frac {1}{x + \log \left (x\right )} \,d x } \]

[In]

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

[Out]

integrate(1/(x + log(x)), x)

Mupad [N/A]

Not integrable

Time = 1.49 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.33 \[ \int \frac {1}{x+\log (x)} \, dx=\int \frac {1}{x+\ln \left (x\right )} \,d x \]

[In]

int(1/(x + log(x)),x)

[Out]

int(1/(x + log(x)), x)