Optimal. Leaf size=47 \[ \frac{9}{7} a^2 b x^{7/3}+\frac{a^3 x^2}{2}+\frac{9}{8} a b^2 x^{8/3}+\frac{b^3 x^3}{3} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0255488, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {266, 43} \[ \frac{9}{7} a^2 b x^{7/3}+\frac{a^3 x^2}{2}+\frac{9}{8} a b^2 x^{8/3}+\frac{b^3 x^3}{3} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 266
Rule 43
Rubi steps
\begin{align*} \int \left (a+b \sqrt [3]{x}\right )^3 x \, dx &=3 \operatorname{Subst}\left (\int x^5 (a+b x)^3 \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname{Subst}\left (\int \left (a^3 x^5+3 a^2 b x^6+3 a b^2 x^7+b^3 x^8\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=\frac{a^3 x^2}{2}+\frac{9}{7} a^2 b x^{7/3}+\frac{9}{8} a b^2 x^{8/3}+\frac{b^3 x^3}{3}\\ \end{align*}
Mathematica [A] time = 0.0175139, size = 47, normalized size = 1. \[ \frac{9}{7} a^2 b x^{7/3}+\frac{a^3 x^2}{2}+\frac{9}{8} a b^2 x^{8/3}+\frac{b^3 x^3}{3} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 36, normalized size = 0.8 \begin{align*}{\frac{{x}^{2}{a}^{3}}{2}}+{\frac{9\,b{a}^{2}}{7}{x}^{{\frac{7}{3}}}}+{\frac{9\,{b}^{2}a}{8}{x}^{{\frac{8}{3}}}}+{\frac{{b}^{3}{x}^{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] time = 1.00595, size = 132, normalized size = 2.81 \begin{align*} \frac{{\left (b x^{\frac{1}{3}} + a\right )}^{9}}{3 \, b^{6}} - \frac{15 \,{\left (b x^{\frac{1}{3}} + a\right )}^{8} a}{8 \, b^{6}} + \frac{30 \,{\left (b x^{\frac{1}{3}} + a\right )}^{7} a^{2}}{7 \, b^{6}} - \frac{5 \,{\left (b x^{\frac{1}{3}} + a\right )}^{6} a^{3}}{b^{6}} + \frac{3 \,{\left (b x^{\frac{1}{3}} + a\right )}^{5} a^{4}}{b^{6}} - \frac{3 \,{\left (b x^{\frac{1}{3}} + a\right )}^{4} a^{5}}{4 \, b^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.44549, size = 90, normalized size = 1.91 \begin{align*} \frac{1}{3} \, b^{3} x^{3} + \frac{9}{8} \, a b^{2} x^{\frac{8}{3}} + \frac{9}{7} \, a^{2} b x^{\frac{7}{3}} + \frac{1}{2} \, a^{3} x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 1.81274, size = 42, normalized size = 0.89 \begin{align*} \frac{a^{3} x^{2}}{2} + \frac{9 a^{2} b x^{\frac{7}{3}}}{7} + \frac{9 a b^{2} x^{\frac{8}{3}}}{8} + \frac{b^{3} x^{3}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.10261, size = 47, normalized size = 1. \begin{align*} \frac{1}{3} \, b^{3} x^{3} + \frac{9}{8} \, a b^{2} x^{\frac{8}{3}} + \frac{9}{7} \, a^{2} b x^{\frac{7}{3}} + \frac{1}{2} \, a^{3} x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]