Optimal. Leaf size=29 \[ a^2 x+\frac{3}{2} a b x^{4/3}+\frac{3}{5} b^2 x^{5/3} \]
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Rubi [A] time = 0.0155383, antiderivative size = 29, 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} \[ a^2 x+\frac{3}{2} a b x^{4/3}+\frac{3}{5} b^2 x^{5/3} \]
Antiderivative was successfully verified.
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Rule 190
Rule 43
Rubi steps
\begin{align*} \int \left (a+b \sqrt [3]{x}\right )^2 \, dx &=3 \operatorname{Subst}\left (\int x^2 (a+b x)^2 \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname{Subst}\left (\int \left (a^2 x^2+2 a b x^3+b^2 x^4\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=a^2 x+\frac{3}{2} a b x^{4/3}+\frac{3}{5} b^2 x^{5/3}\\ \end{align*}
Mathematica [A] time = 0.0126745, size = 29, normalized size = 1. \[ a^2 x+\frac{3}{2} a b x^{4/3}+\frac{3}{5} b^2 x^{5/3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 22, normalized size = 0.8 \begin{align*}{a}^{2}x+{\frac{3\,ab}{2}{x}^{{\frac{4}{3}}}}+{\frac{3\,{b}^{2}}{5}{x}^{{\frac{5}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00659, size = 28, normalized size = 0.97 \begin{align*} \frac{3}{5} \, b^{2} x^{\frac{5}{3}} + \frac{3}{2} \, a b x^{\frac{4}{3}} + a^{2} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.51137, size = 58, normalized size = 2. \begin{align*} \frac{3}{5} \, b^{2} x^{\frac{5}{3}} + \frac{3}{2} \, a b x^{\frac{4}{3}} + a^{2} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.35243, size = 27, normalized size = 0.93 \begin{align*} a^{2} x + \frac{3 a b x^{\frac{4}{3}}}{2} + \frac{3 b^{2} x^{\frac{5}{3}}}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09883, size = 28, normalized size = 0.97 \begin{align*} \frac{3}{5} \, b^{2} x^{\frac{5}{3}} + \frac{3}{2} \, a b x^{\frac{4}{3}} + a^{2} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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