Optimal. Leaf size=13 \[ \frac{1}{2} a c x^2+c x \]
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Rubi [C] time = 0.011943, antiderivative size = 26, normalized size of antiderivative = 2., number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062, Rules used = {2288} \[ \frac{c \left (1-a^2 x^2\right ) e^{2 \tanh ^{-1}(a x)}}{2 a} \]
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin{align*} \int e^{2 \tanh ^{-1}(a x)} (c-a c x) \, dx &=\frac{c e^{2 \tanh ^{-1}(a x)} \left (1-a^2 x^2\right )}{2 a}\\ \end{align*}
Mathematica [C] time = 0.0077832, size = 26, normalized size = 2. \[ \frac{c \left (1-a^2 x^2\right ) e^{2 \tanh ^{-1}(a x)}}{2 a} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.027, size = 11, normalized size = 0.9 \begin{align*} c \left ({\frac{a{x}^{2}}{2}}+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.943945, size = 15, normalized size = 1.15 \begin{align*} \frac{1}{2} \, a c x^{2} + c x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.51341, size = 26, normalized size = 2. \begin{align*} \frac{1}{2} \, a c x^{2} + c x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.078766, size = 10, normalized size = 0.77 \begin{align*} \frac{a c x^{2}}{2} + c x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17431, size = 15, normalized size = 1.15 \begin{align*} \frac{1}{2} \, a c x^{2} + c x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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