Optimal. Leaf size=47 \[ -\frac{9 a^2 b}{10 x^{10/3}}-\frac{a^3}{3 x^3}-\frac{9 a b^2}{11 x^{11/3}}-\frac{b^3}{4 x^4} \]
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Rubi [A] time = 0.0214049, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2, Rules used = {263, 266, 43} \[ -\frac{9 a^2 b}{10 x^{10/3}}-\frac{a^3}{3 x^3}-\frac{9 a b^2}{11 x^{11/3}}-\frac{b^3}{4 x^4} \]
Antiderivative was successfully verified.
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Rule 263
Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{\left (a+\frac{b}{\sqrt [3]{x}}\right )^3}{x^4} \, dx &=\int \frac{\left (b+a \sqrt [3]{x}\right )^3}{x^5} \, dx\\ &=3 \operatorname{Subst}\left (\int \frac{(b+a x)^3}{x^{13}} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname{Subst}\left (\int \left (\frac{b^3}{x^{13}}+\frac{3 a b^2}{x^{12}}+\frac{3 a^2 b}{x^{11}}+\frac{a^3}{x^{10}}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=-\frac{b^3}{4 x^4}-\frac{9 a b^2}{11 x^{11/3}}-\frac{9 a^2 b}{10 x^{10/3}}-\frac{a^3}{3 x^3}\\ \end{align*}
Mathematica [A] time = 0.0161741, size = 41, normalized size = 0.87 \[ -\frac{594 a^2 b x^{2/3}+220 a^3 x+540 a b^2 \sqrt [3]{x}+165 b^3}{660 x^4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 36, normalized size = 0.8 \begin{align*} -{\frac{{b}^{3}}{4\,{x}^{4}}}-{\frac{9\,{b}^{2}a}{11}{x}^{-{\frac{11}{3}}}}-{\frac{9\,b{a}^{2}}{10}{x}^{-{\frac{10}{3}}}}-{\frac{{a}^{3}}{3\,{x}^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.956527, size = 201, normalized size = 4.28 \begin{align*} -\frac{{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{12}}{4 \, b^{9}} + \frac{24 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{11} a}{11 \, b^{9}} - \frac{42 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{10} a^{2}}{5 \, b^{9}} + \frac{56 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{9} a^{3}}{3 \, b^{9}} - \frac{105 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{8} a^{4}}{4 \, b^{9}} + \frac{24 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{7} a^{5}}{b^{9}} - \frac{14 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{6} a^{6}}{b^{9}} + \frac{24 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{5} a^{7}}{5 \, b^{9}} - \frac{3 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{4} a^{8}}{4 \, b^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.59053, size = 100, normalized size = 2.13 \begin{align*} -\frac{220 \, a^{3} x + 594 \, a^{2} b x^{\frac{2}{3}} + 540 \, a b^{2} x^{\frac{1}{3}} + 165 \, b^{3}}{660 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 5.37162, size = 44, normalized size = 0.94 \begin{align*} - \frac{a^{3}}{3 x^{3}} - \frac{9 a^{2} b}{10 x^{\frac{10}{3}}} - \frac{9 a b^{2}}{11 x^{\frac{11}{3}}} - \frac{b^{3}}{4 x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14757, size = 47, normalized size = 1. \begin{align*} -\frac{220 \, a^{3} x + 594 \, a^{2} b x^{\frac{2}{3}} + 540 \, a b^{2} x^{\frac{1}{3}} + 165 \, b^{3}}{660 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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