Optimal. Leaf size=47 \[ -\frac{9 a^2 b}{7 x^{7/3}}-\frac{a^3}{2 x^2}-\frac{9 a b^2}{8 x^{8/3}}-\frac{b^3}{3 x^3} \]
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Rubi [A] time = 0.0218488, 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} \[ -\frac{9 a^2 b}{7 x^{7/3}}-\frac{a^3}{2 x^2}-\frac{9 a b^2}{8 x^{8/3}}-\frac{b^3}{3 x^3} \]
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^3} \, dx &=\int \frac{\left (b+a \sqrt [3]{x}\right )^3}{x^4} \, dx\\ &=3 \operatorname{Subst}\left (\int \frac{(b+a x)^3}{x^{10}} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname{Subst}\left (\int \left (\frac{b^3}{x^{10}}+\frac{3 a b^2}{x^9}+\frac{3 a^2 b}{x^8}+\frac{a^3}{x^7}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=-\frac{b^3}{3 x^3}-\frac{9 a b^2}{8 x^{8/3}}-\frac{9 a^2 b}{7 x^{7/3}}-\frac{a^3}{2 x^2}\\ \end{align*}
Mathematica [A] time = 0.0163333, size = 41, normalized size = 0.87 \[ -\frac{216 a^2 b x^{2/3}+84 a^3 x+189 a b^2 \sqrt [3]{x}+56 b^3}{168 x^3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 36, normalized size = 0.8 \begin{align*} -{\frac{{b}^{3}}{3\,{x}^{3}}}-{\frac{9\,{b}^{2}a}{8}{x}^{-{\frac{8}{3}}}}-{\frac{9\,b{a}^{2}}{7}{x}^{-{\frac{7}{3}}}}-{\frac{{a}^{3}}{2\,{x}^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.973976, size = 132, normalized size = 2.81 \begin{align*} -\frac{{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{9}}{3 \, b^{6}} + \frac{15 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{8} a}{8 \, b^{6}} - \frac{30 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{7} a^{2}}{7 \, b^{6}} + \frac{5 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{6} a^{3}}{b^{6}} - \frac{3 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{5} a^{4}}{b^{6}} + \frac{3 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}^{4} a^{5}}{4 \, b^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.48432, size = 97, normalized size = 2.06 \begin{align*} -\frac{84 \, a^{3} x + 216 \, a^{2} b x^{\frac{2}{3}} + 189 \, a b^{2} x^{\frac{1}{3}} + 56 \, b^{3}}{168 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.74207, size = 44, normalized size = 0.94 \begin{align*} - \frac{a^{3}}{2 x^{2}} - \frac{9 a^{2} b}{7 x^{\frac{7}{3}}} - \frac{9 a b^{2}}{8 x^{\frac{8}{3}}} - \frac{b^{3}}{3 x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.22113, size = 47, normalized size = 1. \begin{align*} -\frac{84 \, a^{3} x + 216 \, a^{2} b x^{\frac{2}{3}} + 189 \, a b^{2} x^{\frac{1}{3}} + 56 \, b^{3}}{168 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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