Optimal. Leaf size=16 \[ -\frac{3 \cos ^{\frac{5}{3}}(x)}{5 \sin ^{\frac{5}{3}}(x)} \]
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Rubi [A] time = 0.0220673, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {2563} \[ -\frac{3 \cos ^{\frac{5}{3}}(x)}{5 \sin ^{\frac{5}{3}}(x)} \]
Antiderivative was successfully verified.
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Rule 2563
Rubi steps
\begin{align*} \int \frac{\cos ^{\frac{2}{3}}(x)}{\sin ^{\frac{8}{3}}(x)} \, dx &=-\frac{3 \cos ^{\frac{5}{3}}(x)}{5 \sin ^{\frac{5}{3}}(x)}\\ \end{align*}
Mathematica [A] time = 0.010515, size = 16, normalized size = 1. \[ -\frac{3 \cos ^{\frac{5}{3}}(x)}{5 \sin ^{\frac{5}{3}}(x)} \]
Antiderivative was successfully verified.
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Maple [F] time = 0.044, size = 0, normalized size = 0. \begin{align*} \int{ \left ( \cos \left ( x \right ) \right ) ^{{\frac{2}{3}}} \left ( \sin \left ( x \right ) \right ) ^{-{\frac{8}{3}}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\cos \left (x\right )^{\frac{2}{3}}}{\sin \left (x\right )^{\frac{8}{3}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.45454, size = 62, normalized size = 3.88 \begin{align*} \frac{3 \, \cos \left (x\right )^{\frac{5}{3}} \sin \left (x\right )^{\frac{1}{3}}}{5 \,{\left (\cos \left (x\right )^{2} - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\cos \left (x\right )^{\frac{2}{3}}}{\sin \left (x\right )^{\frac{8}{3}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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