Optimal. Leaf size=7 \[ \sin ^3(a) \log (x) \]
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Rubi [A] time = 0.0047063, antiderivative size = 7, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25, Rules used = {12, 29} \[ \sin ^3(a) \log (x) \]
Antiderivative was successfully verified.
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Rule 12
Rule 29
Rubi steps
\begin{align*} \int \frac{\sin ^3(a)}{x} \, dx &=\sin ^3(a) \int \frac{1}{x} \, dx\\ &=\log (x) \sin ^3(a)\\ \end{align*}
Mathematica [A] time = 0.0007848, size = 7, normalized size = 1. \[ \sin ^3(a) \log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.013, size = 8, normalized size = 1.1 \begin{align*} \ln \left ( x \right ) \left ( \sin \left ( a \right ) \right ) ^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.994203, size = 9, normalized size = 1.29 \begin{align*} \log \left (x\right ) \sin \left (a\right )^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.432228, size = 42, normalized size = 6. \begin{align*} -{\left (\cos \left (a\right )^{2} - 1\right )} \log \left (x\right ) \sin \left (a\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.389422, size = 7, normalized size = 1. \begin{align*} \log{\left (x \right )} \sin ^{3}{\left (a \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1071, size = 11, normalized size = 1.57 \begin{align*} \log \left ({\left | x \right |}\right ) \sin \left (a\right )^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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