3.760 \(\int \frac{e^x}{e^x+x} \, dx\)

Optimal. Leaf size=13 \[ \text{CannotIntegrate}\left (\frac{e^x}{x+e^x},x\right ) \]

[Out]

CannotIntegrate[E^x/(E^x + x), x]

________________________________________________________________________________________

Rubi [A]  time = 0.0341178, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{e^x}{e^x+x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[E^x/(E^x + x),x]

[Out]

Defer[Int][E^x/(E^x + x), x]

Rubi steps

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

Mathematica [A]  time = 0.0178615, size = 0, normalized size = 0. \[ \int \frac{e^x}{e^x+x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[E^x/(E^x + x),x]

[Out]

Integrate[E^x/(E^x + x), x]

________________________________________________________________________________________

Maple [A]  time = 0.029, size = 0, normalized size = 0. \begin{align*} \int{\frac{{{\rm e}^{x}}}{{{\rm e}^{x}}+x}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} x - \int \frac{x}{x + e^{x}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x - integrate(x/(x + e^x), x)

________________________________________________________________________________________

Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{e^{x}}{x + e^{x}}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(e^x/(x + e^x), x)

________________________________________________________________________________________

Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{e^{x}}{x + e^{x}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(exp(x)/(x + exp(x)), x)

________________________________________________________________________________________

Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{e^{x}}{x + e^{x}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(e^x/(x + e^x), x)