\(\int \frac {e^x}{e^x+x} \, dx\) [760]

Optimal result

Integrand size = 11, antiderivative size = 11 \[ \int \frac {e^x}{e^x+x} \, dx=\text {Int}\left (\frac {e^x}{e^x+x},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.03 (sec) , antiderivative size = 11, 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 = {} \[ \int \frac {e^x}{e^x+x} \, dx=\int \frac {e^x}{e^x+x} \, dx \]

[In]

Int[E^x/(E^x + x),x]

[Out]

Defer[Int][E^x/(E^x + x), x]

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

Mathematica [N/A]

Not integrable

Time = 0.01 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.18 \[ \int \frac {e^x}{e^x+x} \, dx=\int \frac {e^x}{e^x+x} \, dx \]

[In]

Integrate[E^x/(E^x + x),x]

[Out]

Integrate[E^x/(E^x + x), x]

Maple [N/A]

Not integrable

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82

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

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.35 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \frac {e^x}{e^x+x} \, dx=\int { \frac {e^{x}}{x + e^{x}} \,d x } \]

[In]

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

[Out]

integral(e^x/(x + e^x), x)

Sympy [N/A]

Not integrable

Time = 0.21 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int \frac {e^x}{e^x+x} \, dx=\int \frac {e^{x}}{x + e^{x}}\, dx \]

[In]

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

[Out]

Integral(exp(x)/(x + exp(x)), x)

Maxima [N/A]

Not integrable

Time = 0.22 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.27 \[ \int \frac {e^x}{e^x+x} \, dx=\int { \frac {e^{x}}{x + e^{x}} \,d x } \]

[In]

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

[Out]

x - integrate(x/(x + e^x), x)

Giac [N/A]

Not integrable

Time = 0.30 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \frac {e^x}{e^x+x} \, dx=\int { \frac {e^{x}}{x + e^{x}} \,d x } \]

[In]

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

[Out]

integrate(e^x/(x + e^x), x)

Mupad [N/A]

Not integrable

Time = 0.21 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \frac {e^x}{e^x+x} \, dx=\int \frac {{\mathrm {e}}^x}{x+{\mathrm {e}}^x} \,d x \]

[In]

int(exp(x)/(x + exp(x)),x)

[Out]

int(exp(x)/(x + exp(x)), x)