Optimal. Leaf size=16 \[ \frac {e^{x^2}}{2 \left (x^2+1\right )} \]
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Rubi [A] time = 0.06, antiderivative size = 16, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.03, size = 16, normalized size = 1.00 \[ \frac {e^{x^2}}{2 \left (x^2+1\right )} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.37, size = 13, normalized size = 0.81 \[ \frac {e^{\left (x^{2}\right )}}{2 \, {\left (x^{2} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 13, normalized size = 0.81 \[ \frac {e^{\left (x^{2}\right )}}{2 \, {\left (x^{2} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 14, normalized size = 0.88 \[ \frac {{\mathrm e}^{x^{2}}}{2 x^{2}+2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.09, size = 13, normalized size = 0.81 \[ \frac {e^{\left (x^{2}\right )}}{2 \, {\left (x^{2} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.48, size = 14, normalized size = 0.88 \[ \frac {{\mathrm {e}}^{x^2}}{2\,\left (x^2+1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 10, normalized size = 0.62 \[ \frac {e^{x^{2}}}{2 x^{2} + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
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