Optimal. Leaf size=15 \[ \frac{\sin (x)}{2}+\frac{1}{6} \sin (3 x) \]
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Rubi [A] time = 0.008827, antiderivative size = 15, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0048753, size = 15, normalized size = 1. \[ \frac{\sin (x)}{2}+\frac{1}{6} \sin (3 x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.018, size = 12, normalized size = 0.8 \begin{align*}{\frac{\sin \left ( x \right ) }{2}}+{\frac{\sin \left ( 3\,x \right ) }{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.979609, size = 15, normalized size = 1. \begin{align*} \frac{1}{6} \, \sin \left (3 \, x\right ) + \frac{1}{2} \, \sin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.33741, size = 39, normalized size = 2.6 \begin{align*} \frac{1}{3} \,{\left (2 \, \cos \left (x\right )^{2} + 1\right )} \sin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.786458, size = 20, normalized size = 1.33 \begin{align*} - \frac{\sin{\left (x \right )} \cos{\left (2 x \right )}}{3} + \frac{2 \sin{\left (2 x \right )} \cos{\left (x \right )}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10561, size = 15, normalized size = 1. \begin{align*} \frac{1}{6} \, \sin \left (3 \, x\right ) + \frac{1}{2} \, \sin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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