Optimal. Leaf size=17 \[ \frac {\sin ^5(x)}{5}-\frac {\sin ^7(x)}{7} \]
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Rubi [A] time = 0.02, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {2564, 14} \[ \frac {\sin ^5(x)}{5}-\frac {\sin ^7(x)}{7} \]
Antiderivative was successfully verified.
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Rule 14
Rule 2564
Rubi steps
\begin {align*} \int \cos ^3(x) \sin ^4(x) \, dx &=\operatorname {Subst}\left (\int x^4 \left (1-x^2\right ) \, dx,x,\sin (x)\right )\\ &=\operatorname {Subst}\left (\int \left (x^4-x^6\right ) \, dx,x,\sin (x)\right )\\ &=\frac {\sin ^5(x)}{5}-\frac {\sin ^7(x)}{7}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 31, normalized size = 1.82 \[ \frac {3 \sin (x)}{64}-\frac {1}{64} \sin (3 x)-\frac {1}{320} \sin (5 x)+\frac {1}{448} \sin (7 x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 22, normalized size = 1.29 \[ \frac {1}{35} \, {\left (5 \, \cos \relax (x)^{6} - 8 \, \cos \relax (x)^{4} + \cos \relax (x)^{2} + 2\right )} \sin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.96, size = 13, normalized size = 0.76 \[ -\frac {1}{7} \, \sin \relax (x)^{7} + \frac {1}{5} \, \sin \relax (x)^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.01, size = 30, normalized size = 1.76 \[ -\frac {\left (\cos ^{4}\relax (x )\right ) \left (\sin ^{3}\relax (x )\right )}{7}-\frac {3 \left (\cos ^{4}\relax (x )\right ) \sin \relax (x )}{35}+\frac {\left (\cos ^{2}\relax (x )+2\right ) \sin \relax (x )}{35} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 13, normalized size = 0.76 \[ -\frac {1}{7} \, \sin \relax (x)^{7} + \frac {1}{5} \, \sin \relax (x)^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.15, size = 14, normalized size = 0.82 \[ -\frac {{\sin \relax (x)}^5\,\left (5\,{\sin \relax (x)}^2-7\right )}{35} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 12, normalized size = 0.71 \[ - \frac {\sin ^{7}{\relax (x )}}{7} + \frac {\sin ^{5}{\relax (x )}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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