Optimal. Leaf size=13 \[ 7 \sin ^5(x)-5 \sin ^7(x) \]
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Rubi [A] time = 0.0241216, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.3, Rules used = {12, 2564, 14} \[ 7 \sin ^5(x)-5 \sin ^7(x) \]
Antiderivative was successfully verified.
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Rule 12
Rule 2564
Rule 14
Rubi steps
\begin{align*} \int 35 \cos ^3(x) \sin ^4(x) \, dx &=35 \int \cos ^3(x) \sin ^4(x) \, dx\\ &=35 \operatorname{Subst}\left (\int x^4 \left (1-x^2\right ) \, dx,x,\sin (x)\right )\\ &=35 \operatorname{Subst}\left (\int \left (x^4-x^6\right ) \, dx,x,\sin (x)\right )\\ &=7 \sin ^5(x)-5 \sin ^7(x)\\ \end{align*}
Mathematica [B] time = 0.0094767, size = 33, normalized size = 2.54 \[ 35 \left (\frac{3 \sin (x)}{64}-\frac{1}{64} \sin (3 x)-\frac{1}{320} \sin (5 x)+\frac{1}{448} \sin (7 x)\right ) \]
Antiderivative was successfully verified.
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Maple [B] time = 0.005, size = 29, normalized size = 2.2 \begin{align*} -5\, \left ( \cos \left ( x \right ) \right ) ^{4} \left ( \sin \left ( x \right ) \right ) ^{3}-3\,\sin \left ( x \right ) \left ( \cos \left ( x \right ) \right ) ^{4}+ \left ( 2+ \left ( \cos \left ( x \right ) \right ) ^{2} \right ) \sin \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.979526, size = 18, normalized size = 1.38 \begin{align*} -5 \, \sin \left (x\right )^{7} + 7 \, \sin \left (x\right )^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.29107, size = 66, normalized size = 5.08 \begin{align*}{\left (5 \, \cos \left (x\right )^{6} - 8 \, \cos \left (x\right )^{4} + \cos \left (x\right )^{2} + 2\right )} \sin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.061939, size = 12, normalized size = 0.92 \begin{align*} - 5 \sin ^{7}{\left (x \right )} + 7 \sin ^{5}{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07909, size = 18, normalized size = 1.38 \begin{align*} -5 \, \sin \left (x\right )^{7} + 7 \, \sin \left (x\right )^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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