Optimal. Leaf size=22 \[ \frac{1}{2} e^{x^2} x^2-\frac{e^{x^2}}{2} \]
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Rubi [A] time = 0.019292, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222, Rules used = {2212, 2209} \[ \frac{1}{2} e^{x^2} x^2-\frac{e^{x^2}}{2} \]
Antiderivative was successfully verified.
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Rule 2212
Rule 2209
Rubi steps
\begin{align*} \int e^{x^2} x^3 \, dx &=\frac{1}{2} e^{x^2} x^2-\int e^{x^2} x \, dx\\ &=-\frac{e^{x^2}}{2}+\frac{1}{2} e^{x^2} x^2\\ \end{align*}
Mathematica [A] time = 0.0016353, size = 14, normalized size = 0.64 \[ \frac{1}{2} e^{x^2} \left (x^2-1\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 12, normalized size = 0.6 \begin{align*}{\frac{ \left ({x}^{2}-1 \right ){{\rm e}^{{x}^{2}}}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.941293, size = 15, normalized size = 0.68 \begin{align*} \frac{1}{2} \,{\left (x^{2} - 1\right )} e^{\left (x^{2}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.32601, size = 31, normalized size = 1.41 \begin{align*} \frac{1}{2} \,{\left (x^{2} - 1\right )} e^{\left (x^{2}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.077963, size = 10, normalized size = 0.45 \begin{align*} \frac{\left (x^{2} - 1\right ) e^{x^{2}}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06031, size = 15, normalized size = 0.68 \begin{align*} \frac{1}{2} \,{\left (x^{2} - 1\right )} e^{\left (x^{2}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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