Optimal. Leaf size=32 \[ \frac{a^2 x^5}{5}+\frac{4}{11} a b x^{11/2}+\frac{b^2 x^6}{6} \]
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Rubi [A] time = 0.0261072, antiderivative size = 32, 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} \[ \frac{a^2 x^5}{5}+\frac{4}{11} a b x^{11/2}+\frac{b^2 x^6}{6} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \left (a+b \sqrt{x}\right )^2 x^4 \, dx &=2 \operatorname{Subst}\left (\int x^9 (a+b x)^2 \, dx,x,\sqrt{x}\right )\\ &=2 \operatorname{Subst}\left (\int \left (a^2 x^9+2 a b x^{10}+b^2 x^{11}\right ) \, dx,x,\sqrt{x}\right )\\ &=\frac{a^2 x^5}{5}+\frac{4}{11} a b x^{11/2}+\frac{b^2 x^6}{6}\\ \end{align*}
Mathematica [A] time = 0.0212138, size = 28, normalized size = 0.88 \[ \frac{1}{330} x^5 \left (66 a^2+120 a b \sqrt{x}+55 b^2 x\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 25, normalized size = 0.8 \begin{align*}{\frac{{x}^{5}{a}^{2}}{5}}+{\frac{4\,ab}{11}{x}^{{\frac{11}{2}}}}+{\frac{{b}^{2}{x}^{6}}{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.959784, size = 224, normalized size = 7. \begin{align*} \frac{{\left (b \sqrt{x} + a\right )}^{12}}{6 \, b^{10}} - \frac{18 \,{\left (b \sqrt{x} + a\right )}^{11} a}{11 \, b^{10}} + \frac{36 \,{\left (b \sqrt{x} + a\right )}^{10} a^{2}}{5 \, b^{10}} - \frac{56 \,{\left (b \sqrt{x} + a\right )}^{9} a^{3}}{3 \, b^{10}} + \frac{63 \,{\left (b \sqrt{x} + a\right )}^{8} a^{4}}{2 \, b^{10}} - \frac{36 \,{\left (b \sqrt{x} + a\right )}^{7} a^{5}}{b^{10}} + \frac{28 \,{\left (b \sqrt{x} + a\right )}^{6} a^{6}}{b^{10}} - \frac{72 \,{\left (b \sqrt{x} + a\right )}^{5} a^{7}}{5 \, b^{10}} + \frac{9 \,{\left (b \sqrt{x} + a\right )}^{4} a^{8}}{2 \, b^{10}} - \frac{2 \,{\left (b \sqrt{x} + a\right )}^{3} a^{9}}{3 \, b^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.45465, size = 63, normalized size = 1.97 \begin{align*} \frac{1}{6} \, b^{2} x^{6} + \frac{4}{11} \, a b x^{\frac{11}{2}} + \frac{1}{5} \, a^{2} x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.25027, size = 27, normalized size = 0.84 \begin{align*} \frac{a^{2} x^{5}}{5} + \frac{4 a b x^{\frac{11}{2}}}{11} + \frac{b^{2} x^{6}}{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10114, size = 32, normalized size = 1. \begin{align*} \frac{1}{6} \, b^{2} x^{6} + \frac{4}{11} \, a b x^{\frac{11}{2}} + \frac{1}{5} \, a^{2} x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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