Optimal. Leaf size=16 \[ \frac{e^{x^2}}{2 \left (x^2+1\right )} \]
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Rubi [A] time = 0.0576866, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062, Rules used = {2289} \[ \frac{e^{x^2}}{2 \left (x^2+1\right )} \]
Antiderivative was successfully verified.
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Rule 2289
Rubi steps
\begin{align*} \int \frac{e^{x^2} x^3}{\left (1+x^2\right )^2} \, dx &=\frac{e^{x^2}}{2 \left (1+x^2\right )}\\ \end{align*}
Mathematica [A] time = 0.0345679, size = 16, normalized size = 1. \[ \frac{e^{x^2}}{2 \left (x^2+1\right )} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.02, size = 14, normalized size = 0.9 \begin{align*}{\frac{{{\rm e}^{{x}^{2}}}}{2\,{x}^{2}+2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.975302, size = 18, normalized size = 1.12 \begin{align*} \frac{e^{\left (x^{2}\right )}}{2 \,{\left (x^{2} + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.883296, size = 31, normalized size = 1.94 \begin{align*} \frac{e^{\left (x^{2}\right )}}{2 \,{\left (x^{2} + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.091789, size = 10, normalized size = 0.62 \begin{align*} \frac{e^{x^{2}}}{2 x^{2} + 2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.3054, size = 18, normalized size = 1.12 \begin{align*} \frac{e^{\left (x^{2}\right )}}{2 \,{\left (x^{2} + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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