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 = 0.0263351, antiderivative size = 23, normalized size of antiderivative = 1., 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 4354
Rule 2637
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*}
Mathematica [A] time = 0.0119901, size = 23, normalized size = 1. \[ \frac{\sin (x)}{2}-\frac{1}{44} \sin (11 x)-\frac{1}{52} \sin (13 x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.051, size = 18, normalized size = 0.8 \begin{align*}{\frac{\sin \left ( x \right ) }{2}}-{\frac{\sin \left ( 11\,x \right ) }{44}}-{\frac{\sin \left ( 13\,x \right ) }{52}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00829, size = 23, normalized size = 1. \begin{align*} -\frac{1}{52} \, \sin \left (13 \, x\right ) - \frac{1}{44} \, \sin \left (11 \, x\right ) + \frac{1}{2} \, \sin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 2.48903, size = 154, normalized size = 6.7 \begin{align*} -\frac{4}{143} \,{\left (2816 \, \cos \left (x\right )^{12} - 6912 \, \cos \left (x\right )^{10} + 6048 \, \cos \left (x\right )^{8} - 2240 \, \cos \left (x\right )^{6} + 315 \, \cos \left (x\right )^{4} - 9 \, \cos \left (x\right )^{2} - 18\right )} \sin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 12.8496, size = 42, normalized size = 1.83 \begin{align*} \frac{71 \sin{\left (x \right )} \sin ^{2}{\left (6 x \right )}}{143} + \frac{72 \sin{\left (x \right )} \cos ^{2}{\left (6 x \right )}}{143} - \frac{12 \sin{\left (6 x \right )} \cos{\left (x \right )} \cos{\left (6 x \right )}}{143} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11927, size = 23, normalized size = 1. \begin{align*} -\frac{1}{52} \, \sin \left (13 \, x\right ) - \frac{1}{44} \, \sin \left (11 \, x\right ) + \frac{1}{2} \, \sin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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