Optimal. Leaf size=7 \[ e^{x^2} x \]
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Rubi [A] time = 0.0199511, antiderivative size = 7, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125, Rules used = {2204, 2212} \[ e^{x^2} x \]
Antiderivative was successfully verified.
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Rule 2204
Rule 2212
Rubi steps
\begin{align*} \int \left (e^{x^2}+2 e^{x^2} x^2\right ) \, dx &=2 \int e^{x^2} x^2 \, dx+\int e^{x^2} \, dx\\ &=e^{x^2} x+\frac{1}{2} \sqrt{\pi } \text{erfi}(x)-\int e^{x^2} \, dx\\ &=e^{x^2} x\\ \end{align*}
Mathematica [A] time = 0.0052759, size = 7, normalized size = 1. \[ e^{x^2} x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 7, normalized size = 1. \begin{align*}{{\rm e}^{{x}^{2}}}x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.935104, size = 8, normalized size = 1.14 \begin{align*} x e^{\left (x^{2}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.88616, size = 15, normalized size = 2.14 \begin{align*} x e^{\left (x^{2}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.079765, size = 5, normalized size = 0.71 \begin{align*} x e^{x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06987, size = 8, normalized size = 1.14 \begin{align*} x e^{\left (x^{2}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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