Optimal. Leaf size=17 \[ \frac{1}{6} \sin (3 x)+\frac{1}{10} \sin (5 x) \]
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Rubi [A] time = 0.0082524, 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} \[ \frac{1}{6} \sin (3 x)+\frac{1}{10} \sin (5 x) \]
Antiderivative was successfully verified.
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Rule 4283
Rubi steps
\begin{align*} \int \cos (x) \cos (4 x) \, dx &=\frac{1}{6} \sin (3 x)+\frac{1}{10} \sin (5 x)\\ \end{align*}
Mathematica [A] time = 0.0058287, size = 17, normalized size = 1. \[ \frac{1}{6} \sin (3 x)+\frac{1}{10} \sin (5 x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.046, size = 14, normalized size = 0.8 \begin{align*}{\frac{\sin \left ( 3\,x \right ) }{6}}+{\frac{\sin \left ( 5\,x \right ) }{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.924469, size = 18, normalized size = 1.06 \begin{align*} \frac{1}{10} \, \sin \left (5 \, x\right ) + \frac{1}{6} \, \sin \left (3 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.20529, size = 59, normalized size = 3.47 \begin{align*} \frac{1}{15} \,{\left (24 \, \cos \left (x\right )^{4} - 8 \, \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 = 0.51626, size = 20, normalized size = 1.18 \begin{align*} - \frac{\sin{\left (x \right )} \cos{\left (4 x \right )}}{15} + \frac{4 \sin{\left (4 x \right )} \cos{\left (x \right )}}{15} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11297, size = 18, normalized size = 1.06 \begin{align*} \frac{1}{10} \, \sin \left (5 \, x\right ) + \frac{1}{6} \, \sin \left (3 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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