Optimal. Leaf size=47 \[ \frac{2}{3} a^2 b x^{9/2}+\frac{a^3 x^4}{4}+\frac{3}{5} a b^2 x^5+\frac{2}{11} b^3 x^{11/2} \]
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Rubi [A] time = 0.0283058, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {266, 43} \[ \frac{2}{3} a^2 b x^{9/2}+\frac{a^3 x^4}{4}+\frac{3}{5} a b^2 x^5+\frac{2}{11} b^3 x^{11/2} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \left (a+b \sqrt{x}\right )^3 x^3 \, dx &=2 \operatorname{Subst}\left (\int x^7 (a+b x)^3 \, dx,x,\sqrt{x}\right )\\ &=2 \operatorname{Subst}\left (\int \left (a^3 x^7+3 a^2 b x^8+3 a b^2 x^9+b^3 x^{10}\right ) \, dx,x,\sqrt{x}\right )\\ &=\frac{a^3 x^4}{4}+\frac{2}{3} a^2 b x^{9/2}+\frac{3}{5} a b^2 x^5+\frac{2}{11} b^3 x^{11/2}\\ \end{align*}
Mathematica [A] time = 0.0188698, size = 47, normalized size = 1. \[ \frac{2}{3} a^2 b x^{9/2}+\frac{a^3 x^4}{4}+\frac{3}{5} a b^2 x^5+\frac{2}{11} b^3 x^{11/2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 36, normalized size = 0.8 \begin{align*}{\frac{{a}^{3}{x}^{4}}{4}}+{\frac{2\,b{a}^{2}}{3}{x}^{{\frac{9}{2}}}}+{\frac{3\,{x}^{5}a{b}^{2}}{5}}+{\frac{2\,{b}^{3}}{11}{x}^{{\frac{11}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.01894, size = 178, normalized size = 3.79 \begin{align*} \frac{2 \,{\left (b \sqrt{x} + a\right )}^{11}}{11 \, b^{8}} - \frac{7 \,{\left (b \sqrt{x} + a\right )}^{10} a}{5 \, b^{8}} + \frac{14 \,{\left (b \sqrt{x} + a\right )}^{9} a^{2}}{3 \, b^{8}} - \frac{35 \,{\left (b \sqrt{x} + a\right )}^{8} a^{3}}{4 \, b^{8}} + \frac{10 \,{\left (b \sqrt{x} + a\right )}^{7} a^{4}}{b^{8}} - \frac{7 \,{\left (b \sqrt{x} + a\right )}^{6} a^{5}}{b^{8}} + \frac{14 \,{\left (b \sqrt{x} + a\right )}^{5} a^{6}}{5 \, b^{8}} - \frac{{\left (b \sqrt{x} + a\right )}^{4} a^{7}}{2 \, b^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.4756, size = 96, normalized size = 2.04 \begin{align*} \frac{3}{5} \, a b^{2} x^{5} + \frac{1}{4} \, a^{3} x^{4} + \frac{2}{33} \,{\left (3 \, b^{3} x^{5} + 11 \, a^{2} b x^{4}\right )} \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.57005, size = 44, normalized size = 0.94 \begin{align*} \frac{a^{3} x^{4}}{4} + \frac{2 a^{2} b x^{\frac{9}{2}}}{3} + \frac{3 a b^{2} x^{5}}{5} + \frac{2 b^{3} x^{\frac{11}{2}}}{11} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12402, size = 47, normalized size = 1. \begin{align*} \frac{2}{11} \, b^{3} x^{\frac{11}{2}} + \frac{3}{5} \, a b^{2} x^{5} + \frac{2}{3} \, a^{2} b x^{\frac{9}{2}} + \frac{1}{4} \, a^{3} x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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