Optimal. Leaf size=7 \[ -\frac{\cosh (x)}{a} \]
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Rubi [A] time = 0.0439769, antiderivative size = 7, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125, Rules used = {3175, 2638} \[ -\frac{\cosh (x)}{a} \]
Antiderivative was successfully verified.
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Rule 3175
Rule 2638
Rubi steps
\begin{align*} \int \frac{\sinh ^3(x)}{a-a \cosh ^2(x)} \, dx &=-\frac{\int \sinh (x) \, dx}{a}\\ &=-\frac{\cosh (x)}{a}\\ \end{align*}
Mathematica [A] time = 0.0027154, size = 7, normalized size = 1. \[ -\frac{\cosh (x)}{a} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.01, size = 8, normalized size = 1.1 \begin{align*} -{\frac{\cosh \left ( x \right ) }{a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.07952, size = 23, normalized size = 3.29 \begin{align*} -\frac{e^{\left (-x\right )}}{2 \, a} - \frac{e^{x}}{2 \, a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.60763, size = 16, normalized size = 2.29 \begin{align*} -\frac{\cosh \left (x\right )}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.9182, size = 17, normalized size = 2.43 \begin{align*} \frac{2 \tanh ^{2}{\left (\frac{x}{2} \right )}}{a \tanh ^{2}{\left (\frac{x}{2} \right )} - a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.22879, size = 16, normalized size = 2.29 \begin{align*} -\frac{e^{\left (-x\right )} + e^{x}}{2 \, a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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