Optimal. Leaf size=33 \[ -\frac{3}{40} \cos (5 x)-\frac{3}{56} \cos (7 x)+\frac{1}{136} \cos (17 x)+\frac{1}{152} \cos (19 x) \]
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Rubi [A] time = 0.031273, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222, Rules used = {4354, 2638} \[ -\frac{3}{40} \cos (5 x)-\frac{3}{56} \cos (7 x)+\frac{1}{136} \cos (17 x)+\frac{1}{152} \cos (19 x) \]
Antiderivative was successfully verified.
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Rule 4354
Rule 2638
Rubi steps
\begin{align*} \int \cos (x) \sin ^3(6 x) \, dx &=\int \left (\frac{3}{8} \sin (5 x)+\frac{3}{8} \sin (7 x)-\frac{1}{8} \sin (17 x)-\frac{1}{8} \sin (19 x)\right ) \, dx\\ &=-\left (\frac{1}{8} \int \sin (17 x) \, dx\right )-\frac{1}{8} \int \sin (19 x) \, dx+\frac{3}{8} \int \sin (5 x) \, dx+\frac{3}{8} \int \sin (7 x) \, dx\\ &=-\frac{3}{40} \cos (5 x)-\frac{3}{56} \cos (7 x)+\frac{1}{136} \cos (17 x)+\frac{1}{152} \cos (19 x)\\ \end{align*}
Mathematica [A] time = 0.0145286, size = 33, normalized size = 1. \[ -\frac{3}{40} \cos (5 x)-\frac{3}{56} \cos (7 x)+\frac{1}{136} \cos (17 x)+\frac{1}{152} \cos (19 x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.059, size = 26, normalized size = 0.8 \begin{align*} -{\frac{3\,\cos \left ( 5\,x \right ) }{40}}-{\frac{3\,\cos \left ( 7\,x \right ) }{56}}+{\frac{\cos \left ( 17\,x \right ) }{136}}+{\frac{\cos \left ( 19\,x \right ) }{152}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02419, size = 34, normalized size = 1.03 \begin{align*} \frac{1}{152} \, \cos \left (19 \, x\right ) + \frac{1}{136} \, \cos \left (17 \, x\right ) - \frac{3}{56} \, \cos \left (7 \, x\right ) - \frac{3}{40} \, \cos \left (5 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.76163, size = 197, normalized size = 5.97 \begin{align*} \frac{32768}{19} \, \cos \left (x\right )^{19} - \frac{131072}{17} \, \cos \left (x\right )^{17} + 14336 \, \cos \left (x\right )^{15} - 14336 \, \cos \left (x\right )^{13} + 8320 \, \cos \left (x\right )^{11} - 2816 \, \cos \left (x\right )^{9} + \frac{3672}{7} \, \cos \left (x\right )^{7} - \frac{216}{5} \, \cos \left (x\right )^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 16.1038, size = 65, normalized size = 1.97 \begin{align*} - \frac{251 \sin{\left (x \right )} \sin ^{3}{\left (6 x \right )}}{11305} - \frac{216 \sin{\left (x \right )} \sin{\left (6 x \right )} \cos ^{2}{\left (6 x \right )}}{11305} - \frac{1926 \sin ^{2}{\left (6 x \right )} \cos{\left (x \right )} \cos{\left (6 x \right )}}{11305} - \frac{1296 \cos{\left (x \right )} \cos ^{3}{\left (6 x \right )}}{11305} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1403, size = 34, normalized size = 1.03 \begin{align*} \frac{1}{152} \, \cos \left (19 \, x\right ) + \frac{1}{136} \, \cos \left (17 \, x\right ) - \frac{3}{56} \, \cos \left (7 \, x\right ) - \frac{3}{40} \, \cos \left (5 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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