Optimal. Leaf size=34 \[ -\frac{a^2}{3 x^3}-\frac{3 a b}{4 x^{8/3}}-\frac{3 b^2}{7 x^{7/3}} \]
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Rubi [A] time = 0.0139323, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {266, 43} \[ -\frac{a^2}{3 x^3}-\frac{3 a b}{4 x^{8/3}}-\frac{3 b^2}{7 x^{7/3}} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{\left (a+b \sqrt [3]{x}\right )^2}{x^4} \, dx &=3 \operatorname{Subst}\left (\int \frac{(a+b x)^2}{x^{10}} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname{Subst}\left (\int \left (\frac{a^2}{x^{10}}+\frac{2 a b}{x^9}+\frac{b^2}{x^8}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=-\frac{a^2}{3 x^3}-\frac{3 a b}{4 x^{8/3}}-\frac{3 b^2}{7 x^{7/3}}\\ \end{align*}
Mathematica [A] time = 0.0127383, size = 34, normalized size = 1. \[ -\frac{a^2}{3 x^3}-\frac{3 a b}{4 x^{8/3}}-\frac{3 b^2}{7 x^{7/3}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 25, normalized size = 0.7 \begin{align*} -{\frac{{a}^{2}}{3\,{x}^{3}}}-{\frac{3\,ab}{4}{x}^{-{\frac{8}{3}}}}-{\frac{3\,{b}^{2}}{7}{x}^{-{\frac{7}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.963596, size = 35, normalized size = 1.03 \begin{align*} -\frac{36 \, b^{2} x^{\frac{2}{3}} + 63 \, a b x^{\frac{1}{3}} + 28 \, a^{2}}{84 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.42874, size = 73, normalized size = 2.15 \begin{align*} -\frac{36 \, b^{2} x^{\frac{2}{3}} + 63 \, a b x^{\frac{1}{3}} + 28 \, a^{2}}{84 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.52527, size = 32, normalized size = 0.94 \begin{align*} - \frac{a^{2}}{3 x^{3}} - \frac{3 a b}{4 x^{\frac{8}{3}}} - \frac{3 b^{2}}{7 x^{\frac{7}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10746, size = 35, normalized size = 1.03 \begin{align*} -\frac{36 \, b^{2} x^{\frac{2}{3}} + 63 \, a b x^{\frac{1}{3}} + 28 \, a^{2}}{84 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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