Optimal. Leaf size=19 \[ e^x x^2-2 e^x x+2 e^x \]
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Rubi [A] time = 0.0145115, antiderivative size = 19, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0039502, size = 12, normalized size = 0.63 \[ e^x \left (x^2-2 x+2\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 12, normalized size = 0.6 \begin{align*} \left ({x}^{2}-2\,x+2 \right ){{\rm e}^{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.957435, size = 15, normalized size = 0.79 \begin{align*}{\left (x^{2} - 2 \, x + 2\right )} e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.512646, size = 28, normalized size = 1.47 \begin{align*}{\left (x^{2} - 2 \, x + 2\right )} e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.075385, size = 10, normalized size = 0.53 \begin{align*} \left (x^{2} - 2 x + 2\right ) e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08273, size = 15, normalized size = 0.79 \begin{align*}{\left (x^{2} - 2 \, x + 2\right )} e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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