Optimal. Leaf size=23 \[ -\frac{\sqrt [3]{a x^3+b x^6}}{a x^2} \]
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Rubi [A] time = 0.0049352, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {2000} \[ -\frac{\sqrt [3]{a x^3+b x^6}}{a x^2} \]
Antiderivative was successfully verified.
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Rule 2000
Rubi steps
\begin{align*} \int \frac{1}{\left (a x^3+b x^6\right )^{2/3}} \, dx &=-\frac{\sqrt [3]{a x^3+b x^6}}{a x^2}\\ \end{align*}
Mathematica [A] time = 0.0081178, size = 23, normalized size = 1. \[ -\frac{\sqrt [3]{x^3 \left (a+b x^3\right )}}{a x^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 27, normalized size = 1.2 \begin{align*} -{\frac{x \left ( b{x}^{3}+a \right ) }{a} \left ( b{x}^{6}+a{x}^{3} \right ) ^{-{\frac{2}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.09956, size = 23, normalized size = 1. \begin{align*} -\frac{{\left (b x^{3} + a\right )}^{\frac{1}{3}}}{a x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.99811, size = 43, normalized size = 1.87 \begin{align*} -\frac{{\left (b x^{6} + a x^{3}\right )}^{\frac{1}{3}}}{a x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\left (a x^{3} + b x^{6}\right )^{\frac{2}{3}}}\, dx \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{1}{{\left (b x^{6} + a x^{3}\right )}^{\frac{2}{3}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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