Optimal. Leaf size=10 \[ -2 \cos \left (\sqrt{x-7}\right ) \]
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Rubi [A] time = 0.0179978, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.188, Rules used = {3431, 15, 2638} \[ -2 \cos \left (\sqrt{x-7}\right ) \]
Antiderivative was successfully verified.
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Rule 3431
Rule 15
Rule 2638
Rubi steps
\begin{align*} \int \frac{\sin \left (\sqrt{-7+x}\right )}{\sqrt{-7+x}} \, dx &=2 \operatorname{Subst}\left (\int \frac{x \sin (x)}{\sqrt{x^2}} \, dx,x,\sqrt{-7+x}\right )\\ &=2 \operatorname{Subst}\left (\int \sin (x) \, dx,x,\sqrt{-7+x}\right )\\ &=-2 \cos \left (\sqrt{-7+x}\right )\\ \end{align*}
Mathematica [A] time = 0.0233957, size = 10, normalized size = 1. \[ -2 \cos \left (\sqrt{x-7}\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.011, size = 9, normalized size = 0.9 \begin{align*} -2\,\cos \left ( \sqrt{-7+x} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.09476, size = 11, normalized size = 1.1 \begin{align*} -2 \, \cos \left (\sqrt{x - 7}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.99068, size = 28, normalized size = 2.8 \begin{align*} -2 \, \cos \left (\sqrt{x - 7}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.334359, size = 10, normalized size = 1. \begin{align*} - 2 \cos{\left (\sqrt{x - 7} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14195, size = 11, normalized size = 1.1 \begin{align*} -2 \, \cos \left (\sqrt{x - 7}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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