Optimal. Leaf size=23 \[ \frac {\sin (x)}{2}-\frac {1}{44} \sin (11 x)-\frac {1}{52} \sin (13 x) \]
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Rubi [A] time = 0.03, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {4354, 2637} \[ \frac {\sin (x)}{2}-\frac {1}{44} \sin (11 x)-\frac {1}{52} \sin (13 x) \]
Antiderivative was successfully verified.
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Rule 2637
Rule 4354
Rubi steps
\begin {align*} \int \cos (x) \sin ^2(6 x) \, dx &=\int \left (\frac {\cos (x)}{2}-\frac {1}{4} \cos (11 x)-\frac {1}{4} \cos (13 x)\right ) \, dx\\ &=-\left (\frac {1}{4} \int \cos (11 x) \, dx\right )-\frac {1}{4} \int \cos (13 x) \, dx+\frac {1}{2} \int \cos (x) \, dx\\ &=\frac {\sin (x)}{2}-\frac {1}{44} \sin (11 x)-\frac {1}{52} \sin (13 x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 23, normalized size = 1.00 \[ \frac {\sin (x)}{2}-\frac {1}{44} \sin (11 x)-\frac {1}{52} \sin (13 x) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.60, size = 42, normalized size = 1.83 \[ -\frac {4}{143} \, {\left (2816 \, \cos \relax (x)^{12} - 6912 \, \cos \relax (x)^{10} + 6048 \, \cos \relax (x)^{8} - 2240 \, \cos \relax (x)^{6} + 315 \, \cos \relax (x)^{4} - 9 \, \cos \relax (x)^{2} - 18\right )} \sin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 17, normalized size = 0.74 \[ -\frac {1}{52} \, \sin \left (13 \, x\right ) - \frac {1}{44} \, \sin \left (11 \, x\right ) + \frac {1}{2} \, \sin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.13, size = 18, normalized size = 0.78 \[ \frac {\sin \relax (x )}{2}-\frac {\sin \left (11 x \right )}{44}-\frac {\sin \left (13 x \right )}{52} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.31, size = 17, normalized size = 0.74 \[ -\frac {1}{52} \, \sin \left (13 \, x\right ) - \frac {1}{44} \, \sin \left (11 \, x\right ) + \frac {1}{2} \, \sin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.49, size = 17, normalized size = 0.74 \[ \frac {\sin \relax (x)}{2}-\frac {\sin \left (13\,x\right )}{52}-\frac {\sin \left (11\,x\right )}{44} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.64, size = 42, normalized size = 1.83 \[ \frac {71 \sin {\relax (x )} \sin ^{2}{\left (6 x \right )}}{143} + \frac {72 \sin {\relax (x )} \cos ^{2}{\left (6 x \right )}}{143} - \frac {12 \sin {\left (6 x \right )} \cos {\relax (x )} \cos {\left (6 x \right )}}{143} \]
Verification of antiderivative is not currently implemented for this CAS.
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