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

Optimal. Leaf size=16 \[ \text {Int}\left (\frac {e^x}{x^2+e^x},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.04, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, 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*}

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Mathematica [A]  time = 0.03, size = 0, normalized size = 0.00 \[ \int \frac {e^x}{e^x+x^2} \, dx \]

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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fricas [A]  time = 0.40, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {e^{x}}{x^{2} + e^{x}}, x\right ) \]

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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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {e^{x}}{x^{2} + e^{x}}\,{d x} \]

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)

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maple [A]  time = 0.04, size = 0, normalized size = 0.00 \[ \int \frac {{\mathrm e}^{x}}{x^{2}+{\mathrm e}^{x}}\, dx \]

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 = 0.00, size = 0, normalized size = 0.00 \[ x - \int \frac {x^{2}}{x^{2} + e^{x}}\,{d x} \]

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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mupad [A]  time = 0.00, size = -1, normalized size = -0.06 \[ \int \frac {{\mathrm {e}}^x}{{\mathrm {e}}^x+x^2} \,d x \]

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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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {e^{x}}{x^{2} + e^{x}}\, dx \]

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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