Optimal. Leaf size=16 \[ \frac {3 \sin ^{\frac {5}{3}}(x)}{5 \cos ^{\frac {5}{3}}(x)} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, 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 = {2643}
\begin {gather*} \frac {3 \sin ^{\frac {5}{3}}(x)}{5 \cos ^{\frac {5}{3}}(x)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2643
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*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 16, normalized size = 1.00 \begin {gather*} \frac {3 \sin ^{\frac {5}{3}}(x)}{5 \cos ^{\frac {5}{3}}(x)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [F]
time = 0.02, size = 0, normalized size = 0.00 \[\int \frac {\sin ^{\frac {2}{3}}\left (x \right )}{\cos \left (x \right )^{\frac {8}{3}}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.39, size = 10, normalized size = 0.62 \begin {gather*} \frac {3 \, \sin \left (x\right )^{\frac {5}{3}}}{5 \, \cos \left (x\right )^{\frac {5}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: SystemError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.82, size = 94, normalized size = 5.88 \begin {gather*} \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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________