Optimal. Leaf size=17 \[ \frac{1}{4} \sin (2 x)+\frac{1}{8} \sin (4 x) \]
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Rubi [A] time = 0.0088595, antiderivative size = 17, 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} \[ \frac{1}{4} \sin (2 x)+\frac{1}{8} \sin (4 x) \]
Antiderivative was successfully verified.
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Rule 4283
Rubi steps
\begin{align*} \int \cos (x) \cos (3 x) \, dx &=\frac{1}{4} \sin (2 x)+\frac{1}{8} \sin (4 x)\\ \end{align*}
Mathematica [A] time = 0.0057414, size = 17, normalized size = 1. \[ \frac{1}{4} \sin (2 x)+\frac{1}{8} \sin (4 x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.021, size = 14, normalized size = 0.8 \begin{align*}{\frac{\sin \left ( 2\,x \right ) }{4}}+{\frac{\sin \left ( 4\,x \right ) }{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.986717, size = 18, normalized size = 1.06 \begin{align*} \frac{1}{8} \, \sin \left (4 \, x\right ) + \frac{1}{4} \, \sin \left (2 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.36121, size = 23, normalized size = 1.35 \begin{align*} \cos \left (x\right )^{3} \sin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.813564, size = 20, normalized size = 1.18 \begin{align*} - \frac{\sin{\left (x \right )} \cos{\left (3 x \right )}}{8} + \frac{3 \sin{\left (3 x \right )} \cos{\left (x \right )}}{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10823, size = 18, normalized size = 1.06 \begin{align*} \frac{1}{8} \, \sin \left (4 \, x\right ) + \frac{1}{4} \, \sin \left (2 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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