Optimal. Leaf size=47 \[ \frac{9}{11} a^2 b x^{11/3}+\frac{a^3 x^4}{4}+\frac{9}{10} a b^2 x^{10/3}+\frac{b^3 x^3}{3} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0343602, 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} \[ \frac{9}{11} a^2 b x^{11/3}+\frac{a^3 x^4}{4}+\frac{9}{10} a b^2 x^{10/3}+\frac{b^3 x^3}{3} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 263
Rule 266
Rule 43
Rubi steps
\begin{align*} \int \left (a+\frac{b}{\sqrt [3]{x}}\right )^3 x^3 \, dx &=\int \left (b+a \sqrt [3]{x}\right )^3 x^2 \, dx\\ &=3 \operatorname{Subst}\left (\int x^8 (b+a x)^3 \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname{Subst}\left (\int \left (b^3 x^8+3 a b^2 x^9+3 a^2 b x^{10}+a^3 x^{11}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=\frac{b^3 x^3}{3}+\frac{9}{10} a b^2 x^{10/3}+\frac{9}{11} a^2 b x^{11/3}+\frac{a^3 x^4}{4}\\ \end{align*}
Mathematica [A] time = 0.0234589, size = 41, normalized size = 0.87 \[ \frac{1}{660} x^3 \left (540 a^2 b x^{2/3}+165 a^3 x+594 a b^2 \sqrt [3]{x}+220 b^3\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 36, normalized size = 0.8 \begin{align*}{\frac{{b}^{3}{x}^{3}}{3}}+{\frac{9\,{b}^{2}a}{10}{x}^{{\frac{10}{3}}}}+{\frac{9\,b{a}^{2}}{11}{x}^{{\frac{11}{3}}}}+{\frac{{a}^{3}{x}^{4}}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.981474, size = 50, normalized size = 1.06 \begin{align*} \frac{1}{660} \,{\left (165 \, a^{3} + \frac{540 \, a^{2} b}{x^{\frac{1}{3}}} + \frac{594 \, a b^{2}}{x^{\frac{2}{3}}} + \frac{220 \, b^{3}}{x}\right )} x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.47566, size = 96, normalized size = 2.04 \begin{align*} \frac{1}{4} \, a^{3} x^{4} + \frac{9}{11} \, a^{2} b x^{\frac{11}{3}} + \frac{9}{10} \, a b^{2} x^{\frac{10}{3}} + \frac{1}{3} \, b^{3} x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 2.69634, size = 42, normalized size = 0.89 \begin{align*} \frac{a^{3} x^{4}}{4} + \frac{9 a^{2} b x^{\frac{11}{3}}}{11} + \frac{9 a b^{2} x^{\frac{10}{3}}}{10} + \frac{b^{3} x^{3}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.21503, size = 47, normalized size = 1. \begin{align*} \frac{1}{4} \, a^{3} x^{4} + \frac{9}{11} \, a^{2} b x^{\frac{11}{3}} + \frac{9}{10} \, a b^{2} x^{\frac{10}{3}} + \frac{1}{3} \, b^{3} x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]