Optimal. Leaf size=8 \[ \sin ^2\left (\sqrt{x}\right ) \]
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Rubi [A] time = 0.0110285, 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 = {3441} \[ \sin ^2\left (\sqrt{x}\right ) \]
Antiderivative was successfully verified.
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Rule 3441
Rubi steps
\begin{align*} \int \frac{\cos \left (\sqrt{x}\right ) \sin \left (\sqrt{x}\right )}{\sqrt{x}} \, dx &=\sin ^2\left (\sqrt{x}\right )\\ \end{align*}
Mathematica [A] time = 0.0123849, size = 12, normalized size = 1.5 \[ -\frac{1}{2} \cos \left (2 \sqrt{x}\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 9, normalized size = 1.1 \begin{align*} - \left ( \cos \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 = 0.957622, size = 11, normalized size = 1.38 \begin{align*} -\cos \left (\sqrt{x}\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.89804, size = 23, normalized size = 2.88 \begin{align*} -\cos \left (\sqrt{x}\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.305078, size = 8, normalized size = 1. \begin{align*} - \cos ^{2}{\left (\sqrt{x} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06722, size = 11, normalized size = 1.38 \begin{align*} -\cos \left (\sqrt{x}\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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