Optimal. Leaf size=21 \[ -\frac {1}{10} x^3 \cos (\log (x))+\frac {3}{10} x^3 \sin (\log (x)) \]
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Rubi [A]
time = 0.01, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {4573}
\begin {gather*} \frac {3}{10} x^3 \sin (\log (x))-\frac {1}{10} x^3 \cos (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Rule 4573
Rubi steps
\begin {gather*} \begin {aligned} \text {Integral} &=-\frac {1}{10} x^3 \cos (\log (x))+\frac {3}{10} x^3 \sin (\log (x))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 21, normalized size = 1.00 \begin {gather*} -\frac {1}{10} x^3 \cos (\log (x))+\frac {3}{10} x^3 \sin (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains complex when optimal does not.
time = 0.14, size = 26, normalized size = 1.24
method | result | size |
risch | \(\left (-\frac {1}{20}-\frac {3 i}{20}\right ) x^{3} x^{i}+\left (-\frac {1}{20}+\frac {3 i}{20}\right ) x^{3} x^{-i}\) | \(26\) |
norman | \(\frac {-\frac {x^{3}}{10}+\frac {3 x^{3} \tan \left (\frac {\ln \left (x \right )}{2}\right )}{5}+\frac {x^{3} \left (\tan ^{2}\left (\frac {\ln \left (x \right )}{2}\right )\right )}{10}}{1+\tan ^{2}\left (\frac {\ln \left (x \right )}{2}\right )}\) | \(41\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.34, size = 14, normalized size = 0.67 \begin {gather*} -\frac {1}{10} \, x^{3} {\left (\cos \left (\log \left (x\right )\right ) - 3 \, \sin \left (\log \left (x\right )\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.60, size = 17, normalized size = 0.81 \begin {gather*} -\frac {1}{10} \, x^{3} \cos \left (\log \left (x\right )\right ) + \frac {3}{10} \, x^{3} \sin \left (\log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.40, size = 20, normalized size = 0.95 \begin {gather*} \frac {3 x^{3} \sin {\left (\log {\left (x \right )} \right )}}{10} - \frac {x^{3} \cos {\left (\log {\left (x \right )} \right )}}{10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.49, size = 17, normalized size = 0.81 \begin {gather*} -\frac {1}{10} \, x^{3} \cos \left (\log \left (x\right )\right ) + \frac {3}{10} \, x^{3} \sin \left (\log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.14, size = 14, normalized size = 0.67 \begin {gather*} -\frac {\sqrt {10}\,x^3\,\cos \left (\mathrm {atan}\left (3\right )+\ln \left (x\right )\right )}{10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Chatgpt [F] Failed to verify
time = 1.00, size = 17, normalized size = 0.81 \begin {gather*} -\frac {x^{2} \cos \left (\ln \left (x \right )\right )}{2}-\frac {x^{2} \sin \left (\ln \left (x \right )\right )}{4} \end {gather*}
Warning: Unable to verify antiderivative.
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