Optimal. Leaf size=19 \[ e^x x^2-2 e^x x+2 e^x \]
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Rubi [A] time = 0.01, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {2176, 2194} \[ e^x x^2-2 e^x x+2 e^x \]
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rubi steps
\begin {align*} \int e^x x^2 \, dx &=e^x x^2-2 \int e^x x \, dx\\ &=-2 e^x x+e^x x^2+2 \int e^x \, dx\\ &=2 e^x-2 e^x x+e^x x^2\\ \end {align*}
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Mathematica [A] time = 0.01, size = 12, normalized size = 0.63 \[ e^x \left (x^2-2 x+2\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 11, normalized size = 0.58 \[ {\left (x^{2} - 2 \, x + 2\right )} e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.01, size = 11, normalized size = 0.58 \[ {\left (x^{2} - 2 \, x + 2\right )} e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 12, normalized size = 0.63 \[ \left (x^{2}-2 x +2\right ) {\mathrm e}^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 11, normalized size = 0.58 \[ {\left (x^{2} - 2 \, x + 2\right )} e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 11, normalized size = 0.58 \[ {\mathrm {e}}^x\,\left (x^2-2\,x+2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 10, normalized size = 0.53 \[ \left (x^{2} - 2 x + 2\right ) e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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