\(\int \frac {x}{x+\log (x)} \, dx\) [287]

Optimal result

Integrand size = 8, antiderivative size = 8 \[ \int \frac {x}{x+\log (x)} \, dx=\text {Int}\left (\frac {x}{x+\log (x)},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.02 (sec) , antiderivative size = 8, 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 = {} \[ \int \frac {x}{x+\log (x)} \, dx=\int \frac {x}{x+\log (x)} \, dx \]

[In]

Int[x/(x + Log[x]),x]

[Out]

Defer[Int][x/(x + Log[x]), x]

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

Mathematica [N/A]

Not integrable

Time = 9.10 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.25 \[ \int \frac {x}{x+\log (x)} \, dx=\int \frac {x}{x+\log (x)} \, dx \]

[In]

Integrate[x/(x + Log[x]),x]

[Out]

Integrate[x/(x + Log[x]), x]

Maple [N/A]

Not integrable

Time = 0.47 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00

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

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.27 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.25 \[ \int \frac {x}{x+\log (x)} \, dx=\int { \frac {x}{x + \log \left (x\right )} \,d x } \]

[In]

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

[Out]

integral(x/(x + log(x)), x)

Sympy [N/A]

Not integrable

Time = 0.24 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.88 \[ \int \frac {x}{x+\log (x)} \, dx=\int \frac {x}{x + \log {\left (x \right )}}\, dx \]

[In]

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

[Out]

Integral(x/(x + log(x)), x)

Maxima [N/A]

Not integrable

Time = 0.24 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.25 \[ \int \frac {x}{x+\log (x)} \, dx=\int { \frac {x}{x + \log \left (x\right )} \,d x } \]

[In]

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

[Out]

integrate(x/(x + log(x)), x)

Giac [N/A]

Not integrable

Time = 0.31 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.25 \[ \int \frac {x}{x+\log (x)} \, dx=\int { \frac {x}{x + \log \left (x\right )} \,d x } \]

[In]

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

[Out]

integrate(x/(x + log(x)), x)

Mupad [N/A]

Not integrable

Time = 1.43 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.25 \[ \int \frac {x}{x+\log (x)} \, dx=\int \frac {x}{x+\ln \left (x\right )} \,d x \]

[In]

int(x/(x + log(x)),x)

[Out]

int(x/(x + log(x)), x)