Optimal. Leaf size=47 \[ \frac{9}{10} a^2 b x^{10/3}+\frac{a^3 x^3}{3}+\frac{9}{11} a b^2 x^{11/3}+\frac{b^3 x^4}{4} \]
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Rubi [A] time = 0.0300415, 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} \[ \frac{9}{10} a^2 b x^{10/3}+\frac{a^3 x^3}{3}+\frac{9}{11} a b^2 x^{11/3}+\frac{b^3 x^4}{4} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \left (a+b \sqrt [3]{x}\right )^3 x^2 \, dx &=3 \operatorname{Subst}\left (\int x^8 (a+b x)^3 \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname{Subst}\left (\int \left (a^3 x^8+3 a^2 b x^9+3 a b^2 x^{10}+b^3 x^{11}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=\frac{a^3 x^3}{3}+\frac{9}{10} a^2 b x^{10/3}+\frac{9}{11} a b^2 x^{11/3}+\frac{b^3 x^4}{4}\\ \end{align*}
Mathematica [A] time = 0.021129, size = 41, normalized size = 0.87 \[ \frac{1}{660} x^3 \left (594 a^2 b \sqrt [3]{x}+220 a^3+540 a b^2 x^{2/3}+165 b^3 x\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 36, normalized size = 0.8 \begin{align*}{\frac{{a}^{3}{x}^{3}}{3}}+{\frac{9\,b{a}^{2}}{10}{x}^{{\frac{10}{3}}}}+{\frac{9\,{b}^{2}a}{11}{x}^{{\frac{11}{3}}}}+{\frac{{b}^{3}{x}^{4}}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.03543, size = 201, normalized size = 4.28 \begin{align*} \frac{{\left (b x^{\frac{1}{3}} + a\right )}^{12}}{4 \, b^{9}} - \frac{24 \,{\left (b x^{\frac{1}{3}} + a\right )}^{11} a}{11 \, b^{9}} + \frac{42 \,{\left (b x^{\frac{1}{3}} + a\right )}^{10} a^{2}}{5 \, b^{9}} - \frac{56 \,{\left (b x^{\frac{1}{3}} + a\right )}^{9} a^{3}}{3 \, b^{9}} + \frac{105 \,{\left (b x^{\frac{1}{3}} + a\right )}^{8} a^{4}}{4 \, b^{9}} - \frac{24 \,{\left (b x^{\frac{1}{3}} + a\right )}^{7} a^{5}}{b^{9}} + \frac{14 \,{\left (b x^{\frac{1}{3}} + a\right )}^{6} a^{6}}{b^{9}} - \frac{24 \,{\left (b x^{\frac{1}{3}} + a\right )}^{5} a^{7}}{5 \, b^{9}} + \frac{3 \,{\left (b x^{\frac{1}{3}} + a\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 = 1.45876, size = 96, normalized size = 2.04 \begin{align*} \frac{1}{4} \, b^{3} x^{4} + \frac{9}{11} \, a b^{2} x^{\frac{11}{3}} + \frac{9}{10} \, a^{2} b x^{\frac{10}{3}} + \frac{1}{3} \, a^{3} x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.09301, size = 42, normalized size = 0.89 \begin{align*} \frac{a^{3} x^{3}}{3} + \frac{9 a^{2} b x^{\frac{10}{3}}}{10} + \frac{9 a b^{2} x^{\frac{11}{3}}}{11} + \frac{b^{3} x^{4}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1069, size = 47, normalized size = 1. \begin{align*} \frac{1}{4} \, b^{3} x^{4} + \frac{9}{11} \, a b^{2} x^{\frac{11}{3}} + \frac{9}{10} \, a^{2} b x^{\frac{10}{3}} + \frac{1}{3} \, a^{3} x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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