Optimal. Leaf size=15 \[ e^x (2 x+3)-2 e^x \]
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Rubi [A] time = 0.0083929, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222, Rules used = {2176, 2194} \[ e^x (2 x+3)-2 e^x \]
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rubi steps
\begin{align*} \int e^x (3+2 x) \, dx &=e^x (3+2 x)-2 \int e^x \, dx\\ &=-2 e^x+e^x (3+2 x)\\ \end{align*}
Mathematica [A] time = 0.009235, size = 9, normalized size = 0.6 \[ e^x (2 x+1) \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 9, normalized size = 0.6 \begin{align*} \left ( 1+2\,x \right ){{\rm e}^{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.944416, size = 16, normalized size = 1.07 \begin{align*} 2 \,{\left (x - 1\right )} e^{x} + 3 \, e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.2422, size = 20, normalized size = 1.33 \begin{align*}{\left (2 \, x + 1\right )} e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.074453, size = 7, normalized size = 0.47 \begin{align*} \left (2 x + 1\right ) e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05474, size = 11, normalized size = 0.73 \begin{align*}{\left (2 \, x + 1\right )} e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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