Optimal. Leaf size=10 \[ -\frac {3}{4} \csc ^{\frac {4}{3}}(x) \]
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Rubi [A] time = 0.02, antiderivative size = 10, normalized size of antiderivative = 1.00, 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 30
Rule 2621
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*}
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Mathematica [A] time = 0.01, size = 10, normalized size = 1.00 \[ -\frac {3}{4} \csc ^{\frac {4}{3}}(x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 6, normalized size = 0.60 \[ -\frac {3}{4 \, \sin \relax (x)^{\frac {4}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.37, size = 6, normalized size = 0.60 \[ -\frac {3}{4 \, \sin \relax (x)^{\frac {4}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 7, normalized size = 0.70 \[ -\frac {3 \left (\csc ^{\frac {4}{3}}\relax (x )\right )}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.13, size = 6, normalized size = 0.60 \[ -\frac {3}{4 \, \sin \relax (x)^{\frac {4}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.20, size = 8, normalized size = 0.80 \[ -\frac {3\,{\left (\frac {1}{\sin \relax (x)}\right )}^{4/3}}{4} \]
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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