Optimal. Leaf size=6 \[ -\frac{x}{a} \]
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Rubi [A] time = 0.039005, antiderivative size = 6, 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, 8} \[ -\frac{x}{a} \]
Antiderivative was successfully verified.
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Rule 3175
Rule 8
Rubi steps
\begin{align*} \int \frac{\sinh ^2(x)}{a-a \cosh ^2(x)} \, dx &=-\frac{\int 1 \, dx}{a}\\ &=-\frac{x}{a}\\ \end{align*}
Mathematica [A] time = 0.0003662, size = 6, normalized size = 1. \[ -\frac{x}{a} \]
Antiderivative was successfully verified.
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Maple [C] time = 0.013, size = 11, normalized size = 1.8 \begin{align*} -2\,{\frac{{\it Artanh} \left ( \tanh \left ( x/2 \right ) \right ) }{a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06931, size = 8, normalized size = 1.33 \begin{align*} -\frac{x}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.83426, size = 8, normalized size = 1.33 \begin{align*} -\frac{x}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.01685, size = 3, normalized size = 0.5 \begin{align*} - \frac{x}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.34469, size = 8, normalized size = 1.33 \begin{align*} -\frac{x}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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