Optimal. Leaf size=30 \[ \frac {x^2}{2}+\frac {20 \sin ^9(x)}{3}-\frac {120 \sin ^7(x)}{7}+12 \sin ^5(x) \]
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Rubi [A] time = 0.03, antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 2, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {2564, 270} \[ \frac {x^2}{2}+\frac {20 \sin ^9(x)}{3}-\frac {120 \sin ^7(x)}{7}+12 \sin ^5(x) \]
Antiderivative was successfully verified.
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Rule 270
Rule 2564
Rubi steps
\begin {align*} \int \left (x+60 \cos ^5(x) \sin ^4(x)\right ) \, dx &=\frac {x^2}{2}+60 \int \cos ^5(x) \sin ^4(x) \, dx\\ &=\frac {x^2}{2}+60 \operatorname {Subst}\left (\int x^4 \left (1-x^2\right )^2 \, dx,x,\sin (x)\right )\\ &=\frac {x^2}{2}+60 \operatorname {Subst}\left (\int \left (x^4-2 x^6+x^8\right ) \, dx,x,\sin (x)\right )\\ &=\frac {x^2}{2}+12 \sin ^5(x)-\frac {120 \sin ^7(x)}{7}+\frac {20 \sin ^9(x)}{3}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 46, normalized size = 1.53 \[ \frac {x^2}{2}+\frac {45 \sin (x)}{32}-\frac {5}{16} \sin (3 x)-\frac {3}{16} \sin (5 x)+\frac {15}{448} \sin (7 x)+\frac {5}{192} \sin (9 x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 36, normalized size = 1.20 \[ \frac {1}{2} \, x^{2} + \frac {4}{21} \, {\left (35 \, \cos \relax (x)^{8} - 50 \, \cos \relax (x)^{6} + 3 \, \cos \relax (x)^{4} + 4 \, \cos \relax (x)^{2} + 8\right )} \sin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 24, normalized size = 0.80 \[ \frac {20}{3} \, \sin \relax (x)^{9} - \frac {120}{7} \, \sin \relax (x)^{7} + 12 \, \sin \relax (x)^{5} + \frac {1}{2} \, x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 41, normalized size = 1.37 \[ \frac {x^{2}}{2}-\frac {20 \left (\cos ^{6}\relax (x )\right ) \left (\sin ^{3}\relax (x )\right )}{3}-\frac {20 \sin \relax (x ) \left (\cos ^{6}\relax (x )\right )}{7}+\frac {4 \left (\frac {8}{3}+\cos ^{4}\relax (x )+\frac {4 \left (\cos ^{2}\relax (x )\right )}{3}\right ) \sin \relax (x )}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.33, size = 24, normalized size = 0.80 \[ \frac {20}{3} \, \sin \relax (x)^{9} - \frac {120}{7} \, \sin \relax (x)^{7} + 12 \, \sin \relax (x)^{5} + \frac {1}{2} \, x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.00, size = 24, normalized size = 0.80 \[ \frac {x^2}{2}+\frac {20\,{\sin \relax (x)}^9}{3}-\frac {120\,{\sin \relax (x)}^7}{7}+12\,{\sin \relax (x)}^5 \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 27, normalized size = 0.90 \[ \frac {x^{2}}{2} + \frac {20 \sin ^{9}{\relax (x )}}{3} - \frac {120 \sin ^{7}{\relax (x )}}{7} + 12 \sin ^{5}{\relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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