\(\int \frac {e^x}{e^x+x^2} \, dx\) [761]

Optimal result

Integrand size = 13, antiderivative size = 13 \[ \int \frac {e^x}{e^x+x^2} \, dx=\text {Int}\left (\frac {e^x}{e^x+x^2},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.03 (sec) , antiderivative size = 13, 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 = {} \[ \int \frac {e^x}{e^x+x^2} \, dx=\int \frac {e^x}{e^x+x^2} \, dx \]

[In]

Int[E^x/(E^x + x^2),x]

[Out]

Defer[Int][E^x/(E^x + x^2), x]

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

Mathematica [N/A]

Not integrable

Time = 0.05 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.15 \[ \int \frac {e^x}{e^x+x^2} \, dx=\int \frac {e^x}{e^x+x^2} \, dx \]

[In]

Integrate[E^x/(E^x + x^2),x]

[Out]

Integrate[E^x/(E^x + x^2), x]

Maple [N/A]

Not integrable

Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.85

\[\int \frac {{\mathrm e}^{x}}{{\mathrm e}^{x}+x^{2}}d x\]

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.32 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int \frac {e^x}{e^x+x^2} \, dx=\int { \frac {e^{x}}{x^{2} + e^{x}} \,d x } \]

[In]

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

[Out]

integral(e^x/(x^2 + e^x), x)

Sympy [N/A]

Not integrable

Time = 0.22 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77 \[ \int \frac {e^x}{e^x+x^2} \, dx=\int \frac {e^{x}}{x^{2} + e^{x}}\, dx \]

[In]

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

[Out]

Integral(exp(x)/(x**2 + exp(x)), x)

Maxima [N/A]

Not integrable

Time = 0.22 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.38 \[ \int \frac {e^x}{e^x+x^2} \, dx=\int { \frac {e^{x}}{x^{2} + e^{x}} \,d x } \]

[In]

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

[Out]

x - integrate(x^2/(x^2 + e^x), x)

Giac [N/A]

Not integrable

Time = 0.29 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int \frac {e^x}{e^x+x^2} \, dx=\int { \frac {e^{x}}{x^{2} + e^{x}} \,d x } \]

[In]

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

[Out]

integrate(e^x/(x^2 + e^x), x)

Mupad [N/A]

Not integrable

Time = 0.29 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int \frac {e^x}{e^x+x^2} \, dx=\int \frac {{\mathrm {e}}^x}{{\mathrm {e}}^x+x^2} \,d x \]

[In]

int(exp(x)/(exp(x) + x^2),x)

[Out]

int(exp(x)/(exp(x) + x^2), x)