Optimal. Leaf size=8 \[ 2 \cosh \left (\sqrt{x}\right ) \]
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Rubi [A] time = 0.0119936, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167, Rules used = {5320, 2638} \[ 2 \cosh \left (\sqrt{x}\right ) \]
Antiderivative was successfully verified.
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Rule 5320
Rule 2638
Rubi steps
\begin{align*} \int \frac{\sinh \left (\sqrt{x}\right )}{\sqrt{x}} \, dx &=2 \operatorname{Subst}\left (\int \sinh (x) \, dx,x,\sqrt{x}\right )\\ &=2 \cosh \left (\sqrt{x}\right )\\ \end{align*}
Mathematica [A] time = 0.0028366, size = 8, normalized size = 1. \[ 2 \cosh \left (\sqrt{x}\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 7, normalized size = 0.9 \begin{align*} 2\,\cosh \left ( \sqrt{x} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04629, size = 8, normalized size = 1. \begin{align*} 2 \, \cosh \left (\sqrt{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.84414, size = 23, normalized size = 2.88 \begin{align*} 2 \, \cosh \left (\sqrt{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.388617, size = 7, normalized size = 0.88 \begin{align*} 2 \cosh{\left (\sqrt{x} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16501, size = 15, normalized size = 1.88 \begin{align*} e^{\left (-\sqrt{x}\right )} + e^{\sqrt{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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