Optimal. Leaf size=17 \[ \frac {1}{6} \sin (3 x)+\frac {1}{10} \sin (5 x) \]
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Rubi [A] time = 0.01, antiderivative size = 17, 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} \[ \frac {1}{6} \sin (3 x)+\frac {1}{10} \sin (5 x) \]
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*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 1.00 \[ \frac {1}{6} \sin (3 x)+\frac {1}{10} \sin (5 x) \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \cos (x) \cos (4 x) \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.59, size = 18, normalized size = 1.06 \[ \frac {1}{15} \, {\left (24 \, \cos \relax (x)^{4} - 8 \, \cos \relax (x)^{2} - 1\right )} \sin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.61, size = 13, normalized size = 0.76 \[ \frac {1}{10} \, \sin \left (5 \, x\right ) + \frac {1}{6} \, \sin \left (3 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 14, normalized size = 0.82
method | result | size |
default | \(\frac {\sin \left (3 x \right )}{6}+\frac {\sin \left (5 x \right )}{10}\) | \(14\) |
risch | \(\frac {\sin \left (3 x \right )}{6}+\frac {\sin \left (5 x \right )}{10}\) | \(14\) |
norman | \(\frac {-\frac {8 \tan \left (2 x \right ) \left (\tan ^{2}\left (\frac {x}{2}\right )\right )}{15}+\frac {2 \left (\tan ^{2}\left (2 x \right )\right ) \tan \left (\frac {x}{2}\right )}{15}+\frac {8 \tan \left (2 x \right )}{15}-\frac {2 \tan \left (\frac {x}{2}\right )}{15}}{\left (1+\tan ^{2}\left (\frac {x}{2}\right )\right ) \left (1+\tan ^{2}\left (2 x \right )\right )}\) | \(59\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 13, normalized size = 0.76 \[ \frac {1}{10} \, \sin \left (5 \, x\right ) + \frac {1}{6} \, \sin \left (3 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.19, size = 13, normalized size = 0.76 \[ \frac {\sin \left (3\,x\right )}{6}+\frac {\sin \left (5\,x\right )}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.55, size = 20, normalized size = 1.18 \[ - \frac {\sin {\relax (x )} \cos {\left (4 x \right )}}{15} + \frac {4 \sin {\left (4 x \right )} \cos {\relax (x )}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
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