Optimal. Leaf size=10 \[ \cos (3 x)+\log (\sin (2 x)) \]
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Rubi [A] time = 0.0076479, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {3475, 2638} \[ \cos (3 x)+\log (\sin (2 x)) \]
Antiderivative was successfully verified.
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Rule 3475
Rule 2638
Rubi steps
\begin{align*} \int (2 \cot (2 x)-3 \sin (3 x)) \, dx &=2 \int \cot (2 x) \, dx-3 \int \sin (3 x) \, dx\\ &=\cos (3 x)+\log (\sin (2 x))\\ \end{align*}
Mathematica [A] time = 0.0102941, size = 10, normalized size = 1. \[ \cos (3 x)+\log (\sin (2 x)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 17, normalized size = 1.7 \begin{align*} -{\frac{\ln \left ( \left ( \cot \left ( 2\,x \right ) \right ) ^{2}+1 \right ) }{2}}+\cos \left ( 3\,x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.977552, size = 14, normalized size = 1.4 \begin{align*} \cos \left (3 \, x\right ) + \log \left (\sin \left (2 \, x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.46583, size = 66, normalized size = 6.6 \begin{align*} 4 \, \cos \left (x\right )^{3} - 3 \, \cos \left (x\right ) + \log \left (-\frac{1}{2} \, \cos \left (x\right ) \sin \left (x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.065541, size = 10, normalized size = 1. \begin{align*} \log{\left (\sin{\left (2 x \right )} \right )} + \cos{\left (3 x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09397, size = 15, normalized size = 1.5 \begin{align*} \cos \left (3 \, x\right ) + \log \left ({\left | \sin \left (2 \, x\right ) \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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