Optimal. Leaf size=7 \[ \log (x) \sin ^3(a) \]
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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}
\begin {gather*} \sin ^3(a) \log (x) \end {gather*}
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 \begin {gather*} \log (x) \sin ^3(a) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 8, normalized size = 1.14
method | result | size |
default | \(\ln \left (x \right ) \left (\sin ^{3}\left (a \right )\right )\) | \(8\) |
norman | \(\ln \left (x \right ) \left (\sin ^{3}\left (a \right )\right )\) | \(8\) |
risch | \(\ln \left (x \right ) \left (\sin ^{3}\left (a \right )\right )\) | \(8\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 7, normalized size = 1.00 \begin {gather*} \log \left (x\right ) \sin \left (a\right )^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 2.67, size = 12, normalized size = 1.71 \begin {gather*} -{\left (\cos \left (a\right )^{2} - 1\right )} \log \left (x\right ) \sin \left (a\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 7, normalized size = 1.00 \begin {gather*} \log {\left (x \right )} \sin ^{3}{\left (a \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 8, normalized size = 1.14 \begin {gather*} \log \left ({\left | x \right |}\right ) \sin \left (a\right )^{3} \end {gather*}
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 \begin {gather*} {\sin \left (a\right )}^3\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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