\(\int \frac {x}{e^x+x} \, dx\) [758]

Optimal result

Integrand size = 9, antiderivative size = 9 \[ \int \frac {x}{e^x+x} \, dx=\text {Int}\left (\frac {x}{e^x+x},x\right ) \]

[Out]

CannotIntegrate(x/(exp(x)+x),x)

Rubi [N/A]

Not integrable

Time = 0.02 (sec) , antiderivative size = 9, 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 = {} \[ \int \frac {x}{e^x+x} \, dx=\int \frac {x}{e^x+x} \, dx \]

[In]

Int[x/(E^x + x),x]

[Out]

Defer[Int][x/(E^x + x), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {x}{e^x+x} \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 3.77 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.22 \[ \int \frac {x}{e^x+x} \, dx=\int \frac {x}{e^x+x} \, dx \]

[In]

Integrate[x/(E^x + x),x]

[Out]

Integrate[x/(E^x + x), x]

Maple [N/A]

Not integrable

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.89

\[\int \frac {x}{{\mathrm e}^{x}+x}d x\]

[In]

int(x/(exp(x)+x),x)

[Out]

int(x/(exp(x)+x),x)

Fricas [N/A]

Not integrable

Time = 0.34 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.11 \[ \int \frac {x}{e^x+x} \, dx=\int { \frac {x}{x + e^{x}} \,d x } \]

[In]

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

[Out]

integral(x/(x + e^x), x)

Sympy [N/A]

Not integrable

Time = 0.20 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int \frac {x}{e^x+x} \, dx=\int \frac {x}{x + e^{x}}\, dx \]

[In]

integrate(x/(exp(x)+x),x)

[Out]

Integral(x/(x + exp(x)), x)

Maxima [N/A]

Not integrable

Time = 0.22 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.11 \[ \int \frac {x}{e^x+x} \, dx=\int { \frac {x}{x + e^{x}} \,d x } \]

[In]

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

[Out]

integrate(x/(x + e^x), x)

Giac [N/A]

Not integrable

Time = 0.31 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.11 \[ \int \frac {x}{e^x+x} \, dx=\int { \frac {x}{x + e^{x}} \,d x } \]

[In]

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

[Out]

integrate(x/(x + e^x), x)

Mupad [N/A]

Not integrable

Time = 0.26 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.11 \[ \int \frac {x}{e^x+x} \, dx=\int \frac {x}{x+{\mathrm {e}}^x} \,d x \]

[In]

int(x/(x + exp(x)),x)

[Out]

int(x/(x + exp(x)), x)