Optimal. Leaf size=10 \[ -\frac{3}{4} \csc ^{\frac{4}{3}}(x) \]
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Rubi [A] time = 0.0165183, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222, Rules used = {2621, 30} \[ -\frac{3}{4} \csc ^{\frac{4}{3}}(x) \]
Antiderivative was successfully verified.
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Rule 2621
Rule 30
Rubi steps
\begin{align*} \int \cos (x) \csc ^{\frac{7}{3}}(x) \, dx &=-\operatorname{Subst}\left (\int \sqrt [3]{x} \, dx,x,\csc (x)\right )\\ &=-\frac{3}{4} \csc ^{\frac{4}{3}}(x)\\ \end{align*}
Mathematica [A] time = 0.0076398, size = 10, normalized size = 1. \[ -\frac{3}{4} \csc ^{\frac{4}{3}}(x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.026, size = 7, normalized size = 0.7 \begin{align*} -{\frac{3}{4} \left ( \csc \left ( x \right ) \right ) ^{{\frac{4}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.962924, size = 8, normalized size = 0.8 \begin{align*} -\frac{3}{4 \, \sin \left (x\right )^{\frac{4}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.04112, size = 26, normalized size = 2.6 \begin{align*} -\frac{3}{4 \, \sin \left (x\right )^{\frac{4}{3}}} \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 [A] time = 1.14886, size = 8, normalized size = 0.8 \begin{align*} -\frac{3}{4 \, \sin \left (x\right )^{\frac{4}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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