Optimal. Leaf size=28 \[ -\frac{3 \left (a+b x^2\right )^{4/3}}{8 a c (c x)^{8/3}} \]
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Rubi [A] time = 0.0056703, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053, Rules used = {264} \[ -\frac{3 \left (a+b x^2\right )^{4/3}}{8 a c (c x)^{8/3}} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{\sqrt [3]{a+b x^2}}{(c x)^{11/3}} \, dx &=-\frac{3 \left (a+b x^2\right )^{4/3}}{8 a c (c x)^{8/3}}\\ \end{align*}
Mathematica [A] time = 0.0086013, size = 26, normalized size = 0.93 \[ -\frac{3 x \left (a+b x^2\right )^{4/3}}{8 a (c x)^{11/3}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 21, normalized size = 0.8 \begin{align*} -{\frac{3\,x}{8\,a} \left ( b{x}^{2}+a \right ) ^{{\frac{4}{3}}} \left ( cx \right ) ^{-{\frac{11}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.92746, size = 47, normalized size = 1.68 \begin{align*} -\frac{3 \,{\left (b c^{\frac{1}{3}} x^{3} + a c^{\frac{1}{3}} x\right )}{\left (b x^{2} + a\right )}^{\frac{1}{3}}}{8 \, a c^{4} x^{\frac{11}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.50888, size = 65, normalized size = 2.32 \begin{align*} -\frac{3 \,{\left (b x^{2} + a\right )}^{\frac{4}{3}} \left (c x\right )^{\frac{1}{3}}}{8 \, a c^{4} x^{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 [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (b x^{2} + a\right )}^{\frac{1}{3}}}{\left (c x\right )^{\frac{11}{3}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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