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

Optimal. Leaf size=14 \[ \text{Int}\left (\frac{e^x}{x+e^x},x\right ) \]

[Out]

CannotIntegrate[E^x/(E^x + x), x]

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Rubi [A]  time = 0.0516472, 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. \[ \text{Int}\left (\frac{e^x}{e^x+x},x\right ) \]

Verification is Not applicable to the result.

[In]  Int[E^x/(E^x + x),x]

[Out]

Defer[Int][E^x/(E^x + x), x]

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(exp(x)/(exp(x)+x),x)

[Out]

Integral(exp(x)/(x + exp(x)), x)

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Mathematica [A]  time = 0.0186384, 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]

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Maple [A]  time = 0.016, size = 0, normalized size = 0. \[ \int{\frac{{{\rm e}^{x}}}{{{\rm e}^{x}}+x}}\, dx \]

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)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(e^x/(x + e^x),x, algorithm="maxima")

[Out]

x - integrate(x/(x + e^x), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(e^x/(x + e^x),x, algorithm="fricas")

[Out]

integral(e^x/(x + e^x), x)

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

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)

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GIAC/XCAS [A]  time = 0., size = 0, normalized size = 0. \[ \int \frac{e^{x}}{x + e^{x}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(e^x/(x + e^x),x, algorithm="giac")

[Out]

integrate(e^x/(x + e^x), x)