3.761 \(\int \frac{e^x}{e^x+x^2} \, dx\)

Optimal. Leaf size=15 \[ \text{CannotIntegrate}\left (\frac{e^x}{x^2+e^x},x\right ) \]

[Out]

CannotIntegrate[E^x/(E^x + x^2), x]

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Rubi [A]  time = 0.0392725, 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 = {} \[ \int \frac{e^x}{e^x+x^2} \, dx \]

Verification is Not applicable to the result.

[In]

Int[E^x/(E^x + x^2),x]

[Out]

Defer[Int][E^x/(E^x + x^2), x]

Rubi steps

\begin{align*} \int \frac{e^x}{e^x+x^2} \, dx &=\int \frac{e^x}{e^x+x^2} \, dx\\ \end{align*}

Mathematica [A]  time = 0.0333633, size = 0, normalized size = 0. \[ \int \frac{e^x}{e^x+x^2} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[E^x/(E^x + x^2),x]

[Out]

Integrate[E^x/(E^x + x^2), x]

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Maple [A]  time = 0.028, size = 0, normalized size = 0. \begin{align*} \int{\frac{{{\rm e}^{x}}}{{{\rm e}^{x}}+{x}^{2}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x)/(exp(x)+x^2),x)

[Out]

int(exp(x)/(exp(x)+x^2),x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} x - \int \frac{x^{2}}{x^{2} + e^{x}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)/(exp(x)+x^2),x, algorithm="maxima")

[Out]

x - integrate(x^2/(x^2 + e^x), x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{e^{x}}{x^{2} + e^{x}}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)/(exp(x)+x^2),x, algorithm="fricas")

[Out]

integral(e^x/(x^2 + e^x), x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{e^{x}}{x^{2} + e^{x}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)/(exp(x)+x**2),x)

[Out]

Integral(exp(x)/(x**2 + exp(x)), x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{e^{x}}{x^{2} + e^{x}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)/(exp(x)+x^2),x, algorithm="giac")

[Out]

integrate(e^x/(x^2 + e^x), x)