Optimal. Leaf size=6 \[ \frac{\sinh (x)}{a} \]
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Rubi [A] time = 0.0439533, antiderivative size = 6, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {3175, 2637} \[ \frac{\sinh (x)}{a} \]
Antiderivative was successfully verified.
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Rule 3175
Rule 2637
Rubi steps
\begin{align*} \int \frac{\cosh ^3(x)}{a+a \sinh ^2(x)} \, dx &=\frac{\int \cosh (x) \, dx}{a}\\ &=\frac{\sinh (x)}{a}\\ \end{align*}
Mathematica [A] time = 0.0016884, size = 6, normalized size = 1. \[ \frac{\sinh (x)}{a} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.012, size = 7, normalized size = 1.2 \begin{align*}{\frac{\sinh \left ( x \right ) }{a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.17094, size = 23, normalized size = 3.83 \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 = 1.44102, size = 15, normalized size = 2.5 \begin{align*} \frac{\sinh \left (x\right )}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 3.29542, size = 17, normalized size = 2.83 \begin{align*} - \frac{2 \tanh{\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 [B] time = 1.10998, size = 19, normalized size = 3.17 \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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