Optimal. Leaf size=8 \[ \sin ^2\left (\sqrt {x}\right ) \]
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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 = {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*}
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Mathematica [A] time = 0.01, size = 12, normalized size = 1.50 \[ -\frac {1}{2} \cos \left (2 \sqrt {x}\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.73, size = 8, normalized size = 1.00 \[ -\cos \left (\sqrt {x}\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 6, normalized size = 0.75 \[ \sin \left (\sqrt {x}\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 9, normalized size = 1.12 \[ -\left (\cos ^{2}\left (\sqrt {x}\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.31, size = 8, normalized size = 1.00 \[ -\cos \left (\sqrt {x}\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.05, size = 8, normalized size = 1.00 \[ -{\cos \left (\sqrt {x}\right )}^2 \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.27, size = 8, normalized size = 1.00 \[ - \cos ^{2}{\left (\sqrt {x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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