Optimal. Leaf size=8 \[ 2 \cosh \left (\sqrt {x}\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 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 2638
Rule 5320
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*}
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Mathematica [A] time = 0.00, size = 8, normalized size = 1.00 \[ 2 \cosh \left (\sqrt {x}\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.56, size = 6, normalized size = 0.75 \[ 2 \, \cosh \left (\sqrt {x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 11, normalized size = 1.38 \[ e^{\left (-\sqrt {x}\right )} + e^{\sqrt {x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 7, normalized size = 0.88 \[ 2 \cosh \left (\sqrt {x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 6, normalized size = 0.75 \[ 2 \, \cosh \left (\sqrt {x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.40, size = 6, normalized size = 0.75 \[ 2\,\mathrm {cosh}\left (\sqrt {x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.26, size = 7, normalized size = 0.88 \[ 2 \cosh {\left (\sqrt {x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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