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 = 0.03, antiderivative size = 31, normalized size of antiderivative = 1.00, 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 2638
Rule 4354
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*}
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Mathematica [A] time = 0.02, size = 31, normalized size = 1.00 \[ \frac {3 \cos (x)}{8}+\frac {1}{88} \cos (11 x)-\frac {3}{104} \cos (13 x)+\frac {1}{200} \cos (25 x) \]
Antiderivative was successfully verified.
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fricas [B] time = 1.29, size = 67, normalized size = 2.16 \[ \frac {2097152}{25} \, \cos \relax (x)^{25} - 524288 \, \cos \relax (x)^{23} + 1441792 \, \cos \relax (x)^{21} - 2293760 \, \cos \relax (x)^{19} + 2334720 \, \cos \relax (x)^{17} - \frac {7938048}{5} \, \cos \relax (x)^{15} + \frac {9503232}{13} \, \cos \relax (x)^{13} - \frac {2484992}{11} \, \cos \relax (x)^{11} + 45248 \, \cos \relax (x)^{9} - 5400 \, \cos \relax (x)^{7} + \frac {1512}{5} \, \cos \relax (x)^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 23, normalized size = 0.74 \[ \frac {1}{200} \, \cos \left (25 \, x\right ) - \frac {3}{104} \, \cos \left (13 \, x\right ) + \frac {1}{88} \, \cos \left (11 \, x\right ) + \frac {3}{8} \, \cos \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.45, size = 24, normalized size = 0.77 \[ \frac {3 \cos \relax (x )}{8}+\frac {\cos \left (11 x \right )}{88}-\frac {3 \cos \left (13 x \right )}{104}+\frac {\cos \left (25 x \right )}{200} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.73, size = 23, normalized size = 0.74 \[ \frac {1}{200} \, \cos \left (25 \, x\right ) - \frac {3}{104} \, \cos \left (13 \, x\right ) + \frac {1}{88} \, \cos \left (11 \, x\right ) + \frac {3}{8} \, \cos \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.18, size = 198, normalized size = 6.39 \[ \frac {32\,\left (-96525\,{\mathrm {tan}\left (\frac {x}{2}\right )}^{46}+8655075\,{\mathrm {tan}\left (\frac {x}{2}\right )}^{44}-300482325\,{\mathrm {tan}\left (\frac {x}{2}\right )}^{42}+5743927475\,{\mathrm {tan}\left (\frac {x}{2}\right )}^{40}-67792485475\,{\mathrm {tan}\left (\frac {x}{2}\right )}^{38}+523868412925\,{\mathrm {tan}\left (\frac {x}{2}\right )}^{36}-2750448633075\,{\mathrm {tan}\left (\frac {x}{2}\right )}^{34}+10084506042325\,{\mathrm {tan}\left (\frac {x}{2}\right )}^{32}-26325778958050\,{\mathrm {tan}\left (\frac {x}{2}\right )}^{30}+49575817586750\,{\mathrm {tan}\left (\frac {x}{2}\right )}^{28}-67895787973650\,{\mathrm {tan}\left (\frac {x}{2}\right )}^{26}+67896209197950\,{\mathrm {tan}\left (\frac {x}{2}\right )}^{24}-49575456537350\,{\mathrm {tan}\left (\frac {x}{2}\right )}^{22}+26326043727610\,{\mathrm {tan}\left (\frac {x}{2}\right )}^{20}-10084340561350\,{\mathrm {tan}\left (\frac {x}{2}\right )}^{18}+2750536240650\,{\mathrm {tan}\left (\frac {x}{2}\right )}^{16}-523829476225\,{\mathrm {tan}\left (\frac {x}{2}\right )}^{14}+67806830575\,{\mathrm {tan}\left (\frac {x}{2}\right )}^{12}-5739623945\,{\mathrm {tan}\left (\frac {x}{2}\right )}^{10}+301506975\,{\mathrm {tan}\left (\frac {x}{2}\right )}^8-8468775\,{\mathrm {tan}\left (\frac {x}{2}\right )}^6+120825\,{\mathrm {tan}\left (\frac {x}{2}\right )}^4+2025\,{\mathrm {tan}\left (\frac {x}{2}\right )}^2+81\right )}{3575\,{\left ({\mathrm {tan}\left (\frac {x}{2}\right )}^2+1\right )}^{25}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 5.27, size = 70, normalized size = 2.26 \[ \frac {1421 \sin ^{3}{\left (6 x \right )} \sin {\left (7 x \right )}}{3575} + \frac {1062 \sin ^{2}{\left (6 x \right )} \cos {\left (6 x \right )} \cos {\left (7 x \right )}}{3575} + \frac {1512 \sin {\left (6 x \right )} \sin {\left (7 x \right )} \cos ^{2}{\left (6 x \right )}}{3575} + \frac {1296 \cos ^{3}{\left (6 x \right )} \cos {\left (7 x \right )}}{3575} \]
Verification of antiderivative is not currently implemented for this CAS.
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