Optimal. Leaf size=20 \[ \frac{1}{2} e^{2 x} x-\frac{e^{2 x}}{4} \]
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Rubi [A] time = 0.0084638, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.286, Rules used = {2176, 2194} \[ \frac{1}{2} e^{2 x} x-\frac{e^{2 x}}{4} \]
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rubi steps
\begin{align*} \int e^{2 x} x \, dx &=\frac{1}{2} e^{2 x} x-\frac{1}{2} \int e^{2 x} \, dx\\ &=-\frac{e^{2 x}}{4}+\frac{1}{2} e^{2 x} x\\ \end{align*}
Mathematica [A] time = 0.0042397, size = 15, normalized size = 0.75 \[ e^{2 x} \left (\frac{x}{2}-\frac{1}{4}\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 12, normalized size = 0.6 \begin{align*}{\frac{ \left ( 2\,x-1 \right ){{\rm e}^{2\,x}}}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.936104, size = 15, normalized size = 0.75 \begin{align*} \frac{1}{4} \,{\left (2 \, x - 1\right )} e^{\left (2 \, x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.8314, size = 31, normalized size = 1.55 \begin{align*} \frac{1}{4} \,{\left (2 \, x - 1\right )} e^{\left (2 \, x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.075245, size = 10, normalized size = 0.5 \begin{align*} \frac{\left (2 x - 1\right ) e^{2 x}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05513, size = 15, normalized size = 0.75 \begin{align*} \frac{1}{4} \,{\left (2 \, x - 1\right )} e^{\left (2 \, x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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