Optimal. Leaf size=31 \[ \frac{3 \cos (x)}{8}+\frac{1}{88} \cos (11 x)-\frac{3}{104} \cos (13 x)+\frac{1}{200} \cos (25 x) \]
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Rubi [A] time = 0.0299518, antiderivative size = 31, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182, Rules used = {4354, 2638} \[ \frac{3 \cos (x)}{8}+\frac{1}{88} \cos (11 x)-\frac{3}{104} \cos (13 x)+\frac{1}{200} \cos (25 x) \]
Antiderivative was successfully verified.
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Rule 4354
Rule 2638
Rubi steps
\begin{align*} \int \cos (7 x) \sin ^3(6 x) \, dx &=\int \left (-\frac{3 \sin (x)}{8}-\frac{1}{8} \sin (11 x)+\frac{3}{8} \sin (13 x)-\frac{1}{8} \sin (25 x)\right ) \, dx\\ &=-\left (\frac{1}{8} \int \sin (11 x) \, dx\right )-\frac{1}{8} \int \sin (25 x) \, dx-\frac{3}{8} \int \sin (x) \, dx+\frac{3}{8} \int \sin (13 x) \, dx\\ &=\frac{3 \cos (x)}{8}+\frac{1}{88} \cos (11 x)-\frac{3}{104} \cos (13 x)+\frac{1}{200} \cos (25 x)\\ \end{align*}
Mathematica [A] time = 0.0153507, size = 31, normalized size = 1. \[ \frac{3 \cos (x)}{8}+\frac{1}{88} \cos (11 x)-\frac{3}{104} \cos (13 x)+\frac{1}{200} \cos (25 x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.18, size = 24, normalized size = 0.8 \begin{align*}{\frac{3\,\cos \left ( x \right ) }{8}}+{\frac{\cos \left ( 11\,x \right ) }{88}}-{\frac{3\,\cos \left ( 13\,x \right ) }{104}}+{\frac{\cos \left ( 25\,x \right ) }{200}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00676, size = 31, normalized size = 1. \begin{align*} \frac{1}{200} \, \cos \left (25 \, x\right ) - \frac{3}{104} \, \cos \left (13 \, x\right ) + \frac{1}{88} \, \cos \left (11 \, x\right ) + \frac{3}{8} \, \cos \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 3.11891, size = 297, normalized size = 9.58 \begin{align*} \frac{2097152}{25} \, \cos \left (x\right )^{25} - 524288 \, \cos \left (x\right )^{23} + 1441792 \, \cos \left (x\right )^{21} - 2293760 \, \cos \left (x\right )^{19} + 2334720 \, \cos \left (x\right )^{17} - \frac{7938048}{5} \, \cos \left (x\right )^{15} + \frac{9503232}{13} \, \cos \left (x\right )^{13} - \frac{2484992}{11} \, \cos \left (x\right )^{11} + 45248 \, \cos \left (x\right )^{9} - 5400 \, \cos \left (x\right )^{7} + \frac{1512}{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 = 11.8116, size = 70, normalized size = 2.26 \begin{align*} \frac{1421 \sin ^{3}{\left (6 x \right )} \sin{\left (7 x \right )}}{3575} + \frac{1062 \sin ^{2}{\left (6 x \right )} \cos{\left (6 x \right )} \cos{\left (7 x \right )}}{3575} + \frac{1512 \sin{\left (6 x \right )} \sin{\left (7 x \right )} \cos ^{2}{\left (6 x \right )}}{3575} + \frac{1296 \cos ^{3}{\left (6 x \right )} \cos{\left (7 x \right )}}{3575} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1035, size = 31, normalized size = 1. \begin{align*} \frac{1}{200} \, \cos \left (25 \, x\right ) - \frac{3}{104} \, \cos \left (13 \, x\right ) + \frac{1}{88} \, \cos \left (11 \, x\right ) + \frac{3}{8} \, \cos \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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