Optimal. Leaf size=16 \[ -\frac{1}{5} \sin ^{\frac{5}{2}}(2 x) \csc ^5(x) \]
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Rubi [A] time = 0.0224134, 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 = {4292} \[ -\frac{1}{5} \sin ^{\frac{5}{2}}(2 x) \csc ^5(x) \]
Antiderivative was successfully verified.
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Rule 4292
Rubi steps
\begin{align*} \int \csc ^5(x) \sin ^{\frac{3}{2}}(2 x) \, dx &=-\frac{1}{5} \csc ^5(x) \sin ^{\frac{5}{2}}(2 x)\\ \end{align*}
Mathematica [A] time = 0.0322744, size = 16, normalized size = 1. \[ -\frac{1}{5} \sin ^{\frac{5}{2}}(2 x) \csc ^5(x) \]
Antiderivative was successfully verified.
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Maple [C] time = 0.049, size = 508, normalized size = 31.8 \begin{align*} \text{result too large to display} \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{\sin \left (2 \, x\right )^{\frac{3}{2}}}{\sin \left (x\right )^{5}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.93462, size = 124, normalized size = 7.75 \begin{align*} \frac{4 \,{\left (\sqrt{2} \sqrt{\cos \left (x\right ) \sin \left (x\right )} \cos \left (x\right )^{2} +{\left (\cos \left (x\right )^{2} - 1\right )} \sin \left (x\right )\right )}}{5 \,{\left (\cos \left (x\right )^{2} - 1\right )} \sin \left (x\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{\sin \left (2 \, x\right )^{\frac{3}{2}}}{\sin \left (x\right )^{5}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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