Optimal. Leaf size=7 \[ e^{x^2} x \]
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Rubi [A] time = 0.03, antiderivative size = 7, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 3, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.231, Rules used = {2226, 2204, 2212} \[ e^{x^2} x \]
Antiderivative was successfully verified.
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Rule 2204
Rule 2212
Rule 2226
Rubi steps
\begin {align*} \int e^{x^2} \left (1+2 x^2\right ) \, dx &=\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*}
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Mathematica [A] time = 0.01, size = 7, normalized size = 1.00 \[ e^{x^2} x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 6, normalized size = 0.86 \[ x e^{\left (x^{2}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.83, size = 6, normalized size = 0.86 \[ x e^{\left (x^{2}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 7, normalized size = 1.00 \[ x \,{\mathrm e}^{x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 6, normalized size = 0.86 \[ x e^{\left (x^{2}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.15, size = 6, normalized size = 0.86 \[ x\,{\mathrm {e}}^{x^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 5, normalized size = 0.71 \[ x e^{x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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