Optimal. Leaf size=7 \[ \sin ^3(a) \log (x) \]
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Rubi [A] time = 0.00, antiderivative size = 7, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, 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*}
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Mathematica [A] time = 0.00, size = 7, normalized size = 1.00 \[ \sin ^3(a) \log (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 12, normalized size = 1.71 \[ -{\left (\cos \relax (a)^{2} - 1\right )} \log \relax (x) \sin \relax (a) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 8, normalized size = 1.14 \[ \log \left ({\left | x \right |}\right ) \sin \relax (a)^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 8, normalized size = 1.14 \[ \ln \relax (x ) \left (\sin ^{3}\relax (a )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.30, size = 7, normalized size = 1.00 \[ \log \relax (x) \sin \relax (a)^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.12, size = 7, normalized size = 1.00 \[ {\sin \relax (a)}^3\,\ln \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.05, size = 7, normalized size = 1.00 \[ \log {\relax (x )} \sin ^{3}{\relax (a )} \]
Verification of antiderivative is not currently implemented for this CAS.
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