Optimal. Leaf size=30 \[ \frac {x}{4}+\frac {1}{8} \sin (2 x)+\frac {1}{16} \sin (4 x)+\frac {1}{24} \sin (6 x) \]
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Rubi [A] time = 0.03, antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {4355, 2637} \[ \frac {x}{4}+\frac {1}{8} \sin (2 x)+\frac {1}{16} \sin (4 x)+\frac {1}{24} \sin (6 x) \]
Antiderivative was successfully verified.
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Rule 2637
Rule 4355
Rubi steps
\begin {align*} \int \cos (x) \cos (2 x) \cos (3 x) \, dx &=\int \left (\frac {1}{4}+\frac {1}{4} \cos (2 x)+\frac {1}{4} \cos (4 x)+\frac {1}{4} \cos (6 x)\right ) \, dx\\ &=\frac {x}{4}+\frac {1}{4} \int \cos (2 x) \, dx+\frac {1}{4} \int \cos (4 x) \, dx+\frac {1}{4} \int \cos (6 x) \, dx\\ &=\frac {x}{4}+\frac {1}{8} \sin (2 x)+\frac {1}{16} \sin (4 x)+\frac {1}{24} \sin (6 x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 30, normalized size = 1.00 \[ \frac {x}{4}+\frac {1}{8} \sin (2 x)+\frac {1}{16} \sin (4 x)+\frac {1}{24} \sin (6 x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 25, normalized size = 0.83 \[ \frac {1}{12} \, {\left (16 \, \cos \relax (x)^{5} - 10 \, \cos \relax (x)^{3} + 3 \, \cos \relax (x)\right )} \sin \relax (x) + \frac {1}{4} \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.18, size = 22, normalized size = 0.73 \[ \frac {1}{4} \, x + \frac {1}{24} \, \sin \left (6 \, x\right ) + \frac {1}{16} \, \sin \left (4 \, x\right ) + \frac {1}{8} \, \sin \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 23, normalized size = 0.77 \[ \frac {x}{4}+\frac {\sin \left (2 x \right )}{8}+\frac {\sin \left (4 x \right )}{16}+\frac {\sin \left (6 x \right )}{24} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 22, normalized size = 0.73 \[ \frac {1}{4} \, x + \frac {1}{24} \, \sin \left (6 \, x\right ) + \frac {1}{16} \, \sin \left (4 \, x\right ) + \frac {1}{8} \, \sin \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.28, size = 22, normalized size = 0.73 \[ \frac {x}{4}+\frac {\sin \left (2\,x\right )}{8}+\frac {\sin \left (4\,x\right )}{16}+\frac {\sin \left (6\,x\right )}{24} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 12.70, size = 112, normalized size = 3.73 \[ - \frac {x \sin {\relax (x )} \sin {\left (2 x \right )} \cos {\left (3 x \right )}}{4} + \frac {x \sin {\relax (x )} \sin {\left (3 x \right )} \cos {\left (2 x \right )}}{4} + \frac {x \sin {\left (2 x \right )} \sin {\left (3 x \right )} \cos {\relax (x )}}{4} + \frac {x \cos {\relax (x )} \cos {\left (2 x \right )} \cos {\left (3 x \right )}}{4} + \frac {\sin {\relax (x )} \sin {\left (2 x \right )} \sin {\left (3 x \right )}}{24} - \frac {\sin {\left (2 x \right )} \cos {\relax (x )} \cos {\left (3 x \right )}}{8} + \frac {\sin {\left (3 x \right )} \cos {\relax (x )} \cos {\left (2 x \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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