Optimal. Leaf size=8 \[ \sinh ^2\left (\sqrt {x}\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 8, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 1.50 \[ \frac {1}{2} \cosh \left (2 \sqrt {x}\right ) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.46, size = 17, normalized size = 2.12 \[ \frac {1}{2} \, \cosh \left (\sqrt {x}\right )^{2} + \frac {1}{2} \, \sinh \left (\sqrt {x}\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.12, size = 17, normalized size = 2.12 \[ \frac {1}{4} \, e^{\left (2 \, \sqrt {x}\right )} + \frac {1}{4} \, e^{\left (-2 \, \sqrt {x}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 7, normalized size = 0.88 \[ \cosh ^{2}\left (\sqrt {x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.31, size = 6, normalized size = 0.75 \[ \cosh \left (\sqrt {x}\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.78, size = 6, normalized size = 0.75 \[ {\mathrm {cosh}\left (\sqrt {x}\right )}^2 \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.27, size = 7, normalized size = 0.88 \[ \sinh ^{2}{\left (\sqrt {x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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