Optimal. Leaf size=8 \[ \sinh ^2\left (\sqrt{x}\right ) \]
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Rubi [A] time = 0.0140994, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {5370} \[ \sinh ^2\left (\sqrt{x}\right ) \]
Antiderivative was successfully verified.
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Rule 5370
Rubi steps
\begin{align*} \int \frac{\cosh \left (\sqrt{x}\right ) \sinh \left (\sqrt{x}\right )}{\sqrt{x}} \, dx &=\sinh ^2\left (\sqrt{x}\right )\\ \end{align*}
Mathematica [A] time = 0.0040892, size = 12, normalized size = 1.5 \[ \frac{1}{2} \cosh \left (2 \sqrt{x}\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 7, normalized size = 0.9 \begin{align*} \left ( \cosh \left ( \sqrt{x} \right ) \right ) ^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.17754, size = 8, normalized size = 1. \begin{align*} \cosh \left (\sqrt{x}\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.95028, size = 58, normalized size = 7.25 \begin{align*} \frac{1}{2} \, \cosh \left (\sqrt{x}\right )^{2} + \frac{1}{2} \, \sinh \left (\sqrt{x}\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.362589, size = 7, normalized size = 0.88 \begin{align*} \cosh ^{2}{\left (\sqrt{x} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.11933, size = 23, normalized size = 2.88 \begin{align*} \frac{1}{4} \, e^{\left (2 \, \sqrt{x}\right )} + \frac{1}{4} \, e^{\left (-2 \, \sqrt{x}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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