Optimal. Leaf size=42 \[ \frac{9}{4} a^2 b x^{4/3}+a^3 x+\frac{9}{5} a b^2 x^{5/3}+\frac{b^3 x^2}{2} \]
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Rubi [A] time = 0.0219194, antiderivative size = 42, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182, Rules used = {190, 43} \[ \frac{9}{4} a^2 b x^{4/3}+a^3 x+\frac{9}{5} a b^2 x^{5/3}+\frac{b^3 x^2}{2} \]
Antiderivative was successfully verified.
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Rule 190
Rule 43
Rubi steps
\begin{align*} \int \left (a+b \sqrt [3]{x}\right )^3 \, dx &=3 \operatorname{Subst}\left (\int x^2 (a+b x)^3 \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname{Subst}\left (\int \left (a^3 x^2+3 a^2 b x^3+3 a b^2 x^4+b^3 x^5\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=a^3 x+\frac{9}{4} a^2 b x^{4/3}+\frac{9}{5} a b^2 x^{5/3}+\frac{b^3 x^2}{2}\\ \end{align*}
Mathematica [A] time = 0.0150406, size = 42, normalized size = 1. \[ \frac{9}{4} a^2 b x^{4/3}+a^3 x+\frac{9}{5} a b^2 x^{5/3}+\frac{b^3 x^2}{2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 33, normalized size = 0.8 \begin{align*}{a}^{3}x+{\frac{9\,b{a}^{2}}{4}{x}^{{\frac{4}{3}}}}+{\frac{9\,{b}^{2}a}{5}{x}^{{\frac{5}{3}}}}+{\frac{{b}^{3}{x}^{2}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.969567, size = 43, normalized size = 1.02 \begin{align*} \frac{1}{2} \, b^{3} x^{2} + \frac{9}{5} \, a b^{2} x^{\frac{5}{3}} + \frac{9}{4} \, a^{2} b x^{\frac{4}{3}} + a^{3} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.42633, size = 82, normalized size = 1.95 \begin{align*} \frac{1}{2} \, b^{3} x^{2} + \frac{9}{5} \, a b^{2} x^{\frac{5}{3}} + \frac{9}{4} \, a^{2} b x^{\frac{4}{3}} + a^{3} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.69621, size = 39, normalized size = 0.93 \begin{align*} a^{3} x + \frac{9 a^{2} b x^{\frac{4}{3}}}{4} + \frac{9 a b^{2} x^{\frac{5}{3}}}{5} + \frac{b^{3} x^{2}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11134, size = 43, normalized size = 1.02 \begin{align*} \frac{1}{2} \, b^{3} x^{2} + \frac{9}{5} \, a b^{2} x^{\frac{5}{3}} + \frac{9}{4} \, a^{2} b x^{\frac{4}{3}} + a^{3} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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