Optimal. Leaf size=5 \[ \log (x) \sin (x) \]
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Rubi [A] time = 0.0332612, antiderivative size = 5, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25, Rules used = {2637, 2554, 3299} \[ \log (x) \sin (x) \]
Antiderivative was successfully verified.
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Rule 2637
Rule 2554
Rule 3299
Rubi steps
\begin{align*} \int \left (\cos (x) \log (x)+\frac{\sin (x)}{x}\right ) \, dx &=\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{align*}
Mathematica [A] time = 0.0209431, size = 5, normalized size = 1. \[ \log (x) \sin (x) \]
Antiderivative was successfully verified.
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Maple [B] time = 0.05, size = 19, normalized size = 3.8 \begin{align*} 2\,{\frac{\ln \left ( x \right ) \tan \left ( x/2 \right ) }{1+ \left ( \tan \left ( x/2 \right ) \right ) ^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.16891, size = 7, normalized size = 1.4 \begin{align*} \log \left (x\right ) \sin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.24786, size = 20, normalized size = 4. \begin{align*} \log \left (x\right ) \sin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 12.8869, size = 5, normalized size = 1. \begin{align*} \log{\left (x \right )} \sin{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19441, size = 7, normalized size = 1.4 \begin{align*} \log \left (x\right ) \sin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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