Optimal. Leaf size=19 \[ e^x x^2-7 e^x x+7 e^x \]
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Rubi [A] time = 0.0429315, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 8, number of rules used = 4, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.364, Rules used = {1593, 2196, 2176, 2194} \[ e^x x^2-7 e^x x+7 e^x \]
Antiderivative was successfully verified.
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Rule 1593
Rule 2196
Rule 2176
Rule 2194
Rubi steps
\begin{align*} \int e^x \left (-5 x+x^2\right ) \, dx &=\int e^x (-5+x) x \, dx\\ &=\int \left (-5 e^x x+e^x x^2\right ) \, dx\\ &=-\left (5 \int e^x x \, dx\right )+\int e^x x^2 \, dx\\ &=-5 e^x x+e^x x^2-2 \int e^x x \, dx+5 \int e^x \, dx\\ &=5 e^x-7 e^x x+e^x x^2+2 \int e^x \, dx\\ &=7 e^x-7 e^x x+e^x x^2\\ \end{align*}
Mathematica [A] time = 0.0269181, size = 12, normalized size = 0.63 \[ e^x \left (x^2-7 x+7\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.022, size = 12, normalized size = 0.6 \begin{align*}{{\rm e}^{x}} \left ({x}^{2}-7\,x+7 \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.980786, size = 26, normalized size = 1.37 \begin{align*}{\left (x^{2} - 2 \, x + 2\right )} e^{x} - 5 \,{\left (x - 1\right )} e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.721356, size = 28, normalized size = 1.47 \begin{align*}{\left (x^{2} - 7 \, x + 7\right )} e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.0871, size = 10, normalized size = 0.53 \begin{align*} \left (x^{2} - 7 x + 7\right ) e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.26269, size = 15, normalized size = 0.79 \begin{align*}{\left (x^{2} - 7 \, x + 7\right )} e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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