Optimal. Leaf size=16 \[ \frac {3 \sin ^{\frac {5}{3}}(x)}{5 \cos ^{\frac {5}{3}}(x)} \]
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Rubi [A] time = 0.02, antiderivative size = 16, normalized size of antiderivative = 1.00, 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} \[ \frac {3 \sin ^{\frac {5}{3}}(x)}{5 \cos ^{\frac {5}{3}}(x)} \]
Antiderivative was successfully verified.
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Rule 2563
Rubi steps
\begin {align*} \int \frac {\sin ^{\frac {2}{3}}(x)}{\cos ^{\frac {8}{3}}(x)} \, dx &=\frac {3 \sin ^{\frac {5}{3}}(x)}{5 \cos ^{\frac {5}{3}}(x)}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 16, normalized size = 1.00 \[ \frac {3 \sin ^{\frac {5}{3}}(x)}{5 \cos ^{\frac {5}{3}}(x)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.82, size = 10, normalized size = 0.62 \[ \frac {3 \, \sin \relax (x)^{\frac {5}{3}}}{5 \, \cos \relax (x)^{\frac {5}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\sin \relax (x)^{\frac {2}{3}}}{\cos \relax (x)^{\frac {8}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.06, size = 0, normalized size = 0.00 \[ \int \frac {\sin ^{\frac {2}{3}}\relax (x )}{\cos \relax (x )^{\frac {8}{3}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\sin \relax (x)^{\frac {2}{3}}}{\cos \relax (x)^{\frac {8}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.82, size = 94, normalized size = 5.88 \[ \frac {6\,2^{2/3}\,{\mathrm {tan}\left (\frac {x}{2}\right )}^{5/3}\,{\left (1-{\mathrm {tan}\left (\frac {x}{2}\right )}^2\right )}^{1/3}+6\,2^{2/3}\,{\mathrm {tan}\left (\frac {x}{2}\right )}^{11/3}\,{\left (1-{\mathrm {tan}\left (\frac {x}{2}\right )}^2\right )}^{1/3}}{5\,{\mathrm {tan}\left (\frac {x}{2}\right )}^2-{\mathrm {tan}\left (\frac {x}{2}\right )}^2\,\left (10\,{\mathrm {tan}\left (\frac {x}{2}\right )}^2-5\,{\mathrm {tan}\left (\frac {x}{2}\right )}^2\,\left ({\mathrm {tan}\left (\frac {x}{2}\right )}^2+1\right )+10\right )+5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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