Optimal. Leaf size=10 \[ \cos (3 x)+\log (\sin (2 x)) \]
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Rubi [A] time = 0.01, antiderivative size = 10, normalized size of antiderivative = 1.00, 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 2638
Rule 3475
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*}
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Mathematica [A] time = 0.01, size = 10, normalized size = 1.00 \[ \cos (3 x)+\log (\sin (2 x)) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.91, size = 18, normalized size = 1.80 \[ 4 \, \cos \relax (x)^{3} - 3 \, \cos \relax (x) + \log \left (-\frac {1}{2} \, \cos \relax (x) \sin \relax (x)\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 11, normalized size = 1.10 \[ \cos \left (3 \, x\right ) + \log \left ({\left | \sin \left (2 \, x\right ) \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 17, normalized size = 1.70 \[ -\frac {\ln \left (\cot ^{2}\left (2 x \right )+1\right )}{2}+\cos \left (3 x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.32, size = 10, normalized size = 1.00 \[ \cos \left (3 \, x\right ) + \log \left (\sin \left (2 \, x\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.08, size = 24, normalized size = 2.40 \[ \cos \left (3\,x\right )+\ln \left (\cos \left (\frac {x}{2}\right )\,\left (\sin \left (\frac {x}{2}\right )-2\,{\sin \left (\frac {x}{2}\right )}^3\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 10, normalized size = 1.00 \[ \log {\left (\sin {\left (2 x \right )} \right )} + \cos {\left (3 x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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