Optimal. Leaf size=5 \[ \log (x) \sin (x) \]
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Rubi [A]
time = 0.02, antiderivative size = 5, normalized size of antiderivative = 1.00, number of steps
used = 4, number of rules used = 3, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {2717, 2634,
3380} \begin {gather*} \log (x) \sin (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 2634
Rule 2717
Rule 3380
Rubi steps
\begin {gather*} \begin {aligned} \text {Integral} &=\int \cos (x) \log (x) \, dx+\int \frac {\sin (x)}{x} \, dx\\ &=\log (x) \sin (x)+\text {Si}(x)-\int \frac {\sin (x)}{x} \, dx\\ &=\log (x) \sin (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 5, normalized size = 1.00 \begin {gather*} \log (x) \sin (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 6, normalized size = 1.20
method | result | size |
risch | \(\ln \left (x \right ) \sin \left (x \right )\) | \(6\) |
parallelrisch | \(\ln \left (x \right ) \sin \left (x \right )\) | \(6\) |
norman | \(\frac {2 \ln \left (x \right ) \tan \left (\frac {x}{2}\right )}{1+\tan ^{2}\left (\frac {x}{2}\right )}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.38, size = 5, normalized size = 1.00 \begin {gather*} \log \left (x\right ) \sin \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.60, size = 5, normalized size = 1.00 \begin {gather*} \log \left (x\right ) \sin \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 4.35, size = 5, normalized size = 1.00 \begin {gather*} \log {\left (x \right )} \sin {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.47, size = 5, normalized size = 1.00 \begin {gather*} \log \left (x\right ) \sin \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.21, size = 5, normalized size = 1.00 \begin {gather*} \ln \left (x\right )\,\sin \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Chatgpt [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {not solved} \end {gather*}
Warning: Unable to verify antiderivative.
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