Optimal. Leaf size=47 \[ \frac{9}{14} a^2 b x^{14/3}+\frac{a^3 x^5}{5}+\frac{9}{13} a b^2 x^{13/3}+\frac{b^3 x^4}{4} \]
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Rubi [A] time = 0.0371428, 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} \[ \frac{9}{14} a^2 b x^{14/3}+\frac{a^3 x^5}{5}+\frac{9}{13} a b^2 x^{13/3}+\frac{b^3 x^4}{4} \]
Antiderivative was successfully verified.
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Rule 263
Rule 266
Rule 43
Rubi steps
\begin{align*} \int \left (a+\frac{b}{\sqrt [3]{x}}\right )^3 x^4 \, dx &=\int \left (b+a \sqrt [3]{x}\right )^3 x^3 \, dx\\ &=3 \operatorname{Subst}\left (\int x^{11} (b+a x)^3 \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname{Subst}\left (\int \left (b^3 x^{11}+3 a b^2 x^{12}+3 a^2 b x^{13}+a^3 x^{14}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=\frac{b^3 x^4}{4}+\frac{9}{13} a b^2 x^{13/3}+\frac{9}{14} a^2 b x^{14/3}+\frac{a^3 x^5}{5}\\ \end{align*}
Mathematica [A] time = 0.0278343, size = 47, normalized size = 1. \[ \frac{9}{14} a^2 b x^{14/3}+\frac{a^3 x^5}{5}+\frac{9}{13} a b^2 x^{13/3}+\frac{b^3 x^4}{4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 36, normalized size = 0.8 \begin{align*}{\frac{{b}^{3}{x}^{4}}{4}}+{\frac{9\,{b}^{2}a}{13}{x}^{{\frac{13}{3}}}}+{\frac{9\,b{a}^{2}}{14}{x}^{{\frac{14}{3}}}}+{\frac{{a}^{3}{x}^{5}}{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.9572, size = 50, normalized size = 1.06 \begin{align*} \frac{1}{1820} \,{\left (364 \, a^{3} + \frac{1170 \, a^{2} b}{x^{\frac{1}{3}}} + \frac{1260 \, a b^{2}}{x^{\frac{2}{3}}} + \frac{455 \, b^{3}}{x}\right )} x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.53258, size = 96, normalized size = 2.04 \begin{align*} \frac{1}{5} \, a^{3} x^{5} + \frac{9}{14} \, a^{2} b x^{\frac{14}{3}} + \frac{9}{13} \, a b^{2} x^{\frac{13}{3}} + \frac{1}{4} \, b^{3} x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 4.31274, size = 42, normalized size = 0.89 \begin{align*} \frac{a^{3} x^{5}}{5} + \frac{9 a^{2} b x^{\frac{14}{3}}}{14} + \frac{9 a b^{2} x^{\frac{13}{3}}}{13} + \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 = 1.14833, size = 47, normalized size = 1. \begin{align*} \frac{1}{5} \, a^{3} x^{5} + \frac{9}{14} \, a^{2} b x^{\frac{14}{3}} + \frac{9}{13} \, a b^{2} x^{\frac{13}{3}} + \frac{1}{4} \, b^{3} x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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