Optimal. Leaf size=69 \[ \frac{5}{8} a^2 b^3 x^{16}+\frac{5}{7} a^3 b^2 x^{14}+\frac{5}{12} a^4 b x^{12}+\frac{a^5 x^{10}}{10}+\frac{5}{18} a b^4 x^{18}+\frac{b^5 x^{20}}{20} \]
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Rubi [A] time = 0.0431, antiderivative size = 69, 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} \[ \frac{5}{8} a^2 b^3 x^{16}+\frac{5}{7} a^3 b^2 x^{14}+\frac{5}{12} a^4 b x^{12}+\frac{a^5 x^{10}}{10}+\frac{5}{18} a b^4 x^{18}+\frac{b^5 x^{20}}{20} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int x^9 \left (a+b x^2\right )^5 \, dx &=\frac{1}{2} \operatorname{Subst}\left (\int x^4 (a+b x)^5 \, dx,x,x^2\right )\\ &=\frac{1}{2} \operatorname{Subst}\left (\int \left (a^5 x^4+5 a^4 b x^5+10 a^3 b^2 x^6+10 a^2 b^3 x^7+5 a b^4 x^8+b^5 x^9\right ) \, dx,x,x^2\right )\\ &=\frac{a^5 x^{10}}{10}+\frac{5}{12} a^4 b x^{12}+\frac{5}{7} a^3 b^2 x^{14}+\frac{5}{8} a^2 b^3 x^{16}+\frac{5}{18} a b^4 x^{18}+\frac{b^5 x^{20}}{20}\\ \end{align*}
Mathematica [A] time = 0.0021335, size = 69, normalized size = 1. \[ \frac{5}{8} a^2 b^3 x^{16}+\frac{5}{7} a^3 b^2 x^{14}+\frac{5}{12} a^4 b x^{12}+\frac{a^5 x^{10}}{10}+\frac{5}{18} a b^4 x^{18}+\frac{b^5 x^{20}}{20} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 58, normalized size = 0.8 \begin{align*}{\frac{{a}^{5}{x}^{10}}{10}}+{\frac{5\,{a}^{4}b{x}^{12}}{12}}+{\frac{5\,{a}^{3}{b}^{2}{x}^{14}}{7}}+{\frac{5\,{a}^{2}{b}^{3}{x}^{16}}{8}}+{\frac{5\,a{b}^{4}{x}^{18}}{18}}+{\frac{{b}^{5}{x}^{20}}{20}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.35845, size = 77, normalized size = 1.12 \begin{align*} \frac{1}{20} \, b^{5} x^{20} + \frac{5}{18} \, a b^{4} x^{18} + \frac{5}{8} \, a^{2} b^{3} x^{16} + \frac{5}{7} \, a^{3} b^{2} x^{14} + \frac{5}{12} \, a^{4} b x^{12} + \frac{1}{10} \, a^{5} x^{10} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.10531, size = 142, normalized size = 2.06 \begin{align*} \frac{1}{20} x^{20} b^{5} + \frac{5}{18} x^{18} b^{4} a + \frac{5}{8} x^{16} b^{3} a^{2} + \frac{5}{7} x^{14} b^{2} a^{3} + \frac{5}{12} x^{12} b a^{4} + \frac{1}{10} x^{10} a^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.07128, size = 66, normalized size = 0.96 \begin{align*} \frac{a^{5} x^{10}}{10} + \frac{5 a^{4} b x^{12}}{12} + \frac{5 a^{3} b^{2} x^{14}}{7} + \frac{5 a^{2} b^{3} x^{16}}{8} + \frac{5 a b^{4} x^{18}}{18} + \frac{b^{5} x^{20}}{20} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.61746, size = 77, normalized size = 1.12 \begin{align*} \frac{1}{20} \, b^{5} x^{20} + \frac{5}{18} \, a b^{4} x^{18} + \frac{5}{8} \, a^{2} b^{3} x^{16} + \frac{5}{7} \, a^{3} b^{2} x^{14} + \frac{5}{12} \, a^{4} b x^{12} + \frac{1}{10} \, a^{5} x^{10} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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