Optimal. Leaf size=15 \[ \frac {\sin (x)}{2}+\frac {1}{6} \sin (3 x) \]
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Rubi [A] time = 0.01, antiderivative size = 15, 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 = {4283} \[ \frac {\sin (x)}{2}+\frac {1}{6} \sin (3 x) \]
Antiderivative was successfully verified.
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Rule 4283
Rubi steps
\begin {align*} \int \cos (x) \cos (2 x) \, dx &=\frac {\sin (x)}{2}+\frac {1}{6} \sin (3 x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 15, normalized size = 1.00 \[ \frac {\sin (x)}{2}+\frac {1}{6} \sin (3 x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 12, normalized size = 0.80 \[ \frac {1}{3} \, {\left (2 \, \cos \relax (x)^{2} + 1\right )} \sin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.97, size = 11, normalized size = 0.73 \[ \frac {1}{6} \, \sin \left (3 \, x\right ) + \frac {1}{2} \, \sin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 12, normalized size = 0.80 \[ \frac {\sin \relax (x )}{2}+\frac {\sin \left (3 x \right )}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 11, normalized size = 0.73 \[ \frac {1}{6} \, \sin \left (3 \, x\right ) + \frac {1}{2} \, \sin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 9, normalized size = 0.60 \[ \sin \relax (x)-\frac {2\,{\sin \relax (x)}^3}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.56, size = 20, normalized size = 1.33 \[ - \frac {\sin {\relax (x )} \cos {\left (2 x \right )}}{3} + \frac {2 \sin {\left (2 x \right )} \cos {\relax (x )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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