Optimal. Leaf size=47 \[ -\frac{9 a^2 b}{8 x^{8/3}}-\frac{a^3}{3 x^3}-\frac{9 a b^2}{7 x^{7/3}}-\frac{b^3}{2 x^2} \]
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Rubi [A] time = 0.0207683, antiderivative size = 47, 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} \[ -\frac{9 a^2 b}{8 x^{8/3}}-\frac{a^3}{3 x^3}-\frac{9 a b^2}{7 x^{7/3}}-\frac{b^3}{2 x^2} \]
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 )^3}{x^4} \, dx &=3 \operatorname{Subst}\left (\int \frac{(a+b x)^3}{x^{10}} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname{Subst}\left (\int \left (\frac{a^3}{x^{10}}+\frac{3 a^2 b}{x^9}+\frac{3 a b^2}{x^8}+\frac{b^3}{x^7}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=-\frac{a^3}{3 x^3}-\frac{9 a^2 b}{8 x^{8/3}}-\frac{9 a b^2}{7 x^{7/3}}-\frac{b^3}{2 x^2}\\ \end{align*}
Mathematica [A] time = 0.0159951, size = 41, normalized size = 0.87 \[ -\frac{189 a^2 b \sqrt [3]{x}+56 a^3+216 a b^2 x^{2/3}+84 b^3 x}{168 x^3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 36, normalized size = 0.8 \begin{align*} -{\frac{{a}^{3}}{3\,{x}^{3}}}-{\frac{9\,b{a}^{2}}{8}{x}^{-{\frac{8}{3}}}}-{\frac{9\,{b}^{2}a}{7}{x}^{-{\frac{7}{3}}}}-{\frac{{b}^{3}}{2\,{x}^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.973747, size = 47, normalized size = 1. \begin{align*} -\frac{84 \, b^{3} x + 216 \, a b^{2} x^{\frac{2}{3}} + 189 \, a^{2} b x^{\frac{1}{3}} + 56 \, a^{3}}{168 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.45132, size = 97, normalized size = 2.06 \begin{align*} -\frac{84 \, b^{3} x + 216 \, a b^{2} x^{\frac{2}{3}} + 189 \, a^{2} b x^{\frac{1}{3}} + 56 \, a^{3}}{168 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.90831, size = 44, normalized size = 0.94 \begin{align*} - \frac{a^{3}}{3 x^{3}} - \frac{9 a^{2} b}{8 x^{\frac{8}{3}}} - \frac{9 a b^{2}}{7 x^{\frac{7}{3}}} - \frac{b^{3}}{2 x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.23682, size = 47, normalized size = 1. \begin{align*} -\frac{84 \, b^{3} x + 216 \, a b^{2} x^{\frac{2}{3}} + 189 \, a^{2} b x^{\frac{1}{3}} + 56 \, a^{3}}{168 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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