Optimal. Leaf size=117 \[ \frac{10}{19} a^2 b^2 x^{19} (a B+A b)+\frac{5}{16} a^3 b x^{16} (a B+2 A b)+\frac{1}{13} a^4 x^{13} (a B+5 A b)+\frac{1}{10} a^5 A x^{10}+\frac{1}{25} b^4 x^{25} (5 a B+A b)+\frac{5}{22} a b^3 x^{22} (2 a B+A b)+\frac{1}{28} b^5 B x^{28} \]
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Rubi [A] time = 0.0975507, antiderivative size = 117, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {448} \[ \frac{10}{19} a^2 b^2 x^{19} (a B+A b)+\frac{5}{16} a^3 b x^{16} (a B+2 A b)+\frac{1}{13} a^4 x^{13} (a B+5 A b)+\frac{1}{10} a^5 A x^{10}+\frac{1}{25} b^4 x^{25} (5 a B+A b)+\frac{5}{22} a b^3 x^{22} (2 a B+A b)+\frac{1}{28} b^5 B x^{28} \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin{align*} \int x^9 \left (a+b x^3\right )^5 \left (A+B x^3\right ) \, dx &=\int \left (a^5 A x^9+a^4 (5 A b+a B) x^{12}+5 a^3 b (2 A b+a B) x^{15}+10 a^2 b^2 (A b+a B) x^{18}+5 a b^3 (A b+2 a B) x^{21}+b^4 (A b+5 a B) x^{24}+b^5 B x^{27}\right ) \, dx\\ &=\frac{1}{10} a^5 A x^{10}+\frac{1}{13} a^4 (5 A b+a B) x^{13}+\frac{5}{16} a^3 b (2 A b+a B) x^{16}+\frac{10}{19} a^2 b^2 (A b+a B) x^{19}+\frac{5}{22} a b^3 (A b+2 a B) x^{22}+\frac{1}{25} b^4 (A b+5 a B) x^{25}+\frac{1}{28} b^5 B x^{28}\\ \end{align*}
Mathematica [A] time = 0.0204761, size = 117, normalized size = 1. \[ \frac{10}{19} a^2 b^2 x^{19} (a B+A b)+\frac{5}{16} a^3 b x^{16} (a B+2 A b)+\frac{1}{13} a^4 x^{13} (a B+5 A b)+\frac{1}{10} a^5 A x^{10}+\frac{1}{25} b^4 x^{25} (5 a B+A b)+\frac{5}{22} a b^3 x^{22} (2 a B+A b)+\frac{1}{28} b^5 B x^{28} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 124, normalized size = 1.1 \begin{align*}{\frac{{b}^{5}B{x}^{28}}{28}}+{\frac{ \left ({b}^{5}A+5\,a{b}^{4}B \right ){x}^{25}}{25}}+{\frac{ \left ( 5\,a{b}^{4}A+10\,{a}^{2}{b}^{3}B \right ){x}^{22}}{22}}+{\frac{ \left ( 10\,{a}^{2}{b}^{3}A+10\,{a}^{3}{b}^{2}B \right ){x}^{19}}{19}}+{\frac{ \left ( 10\,{a}^{3}{b}^{2}A+5\,{a}^{4}bB \right ){x}^{16}}{16}}+{\frac{ \left ( 5\,{a}^{4}bA+{a}^{5}B \right ){x}^{13}}{13}}+{\frac{{a}^{5}A{x}^{10}}{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.12747, size = 161, normalized size = 1.38 \begin{align*} \frac{1}{28} \, B b^{5} x^{28} + \frac{1}{25} \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{25} + \frac{5}{22} \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{22} + \frac{10}{19} \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{19} + \frac{5}{16} \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{16} + \frac{1}{10} \, A a^{5} x^{10} + \frac{1}{13} \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{13} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.24066, size = 323, normalized size = 2.76 \begin{align*} \frac{1}{28} x^{28} b^{5} B + \frac{1}{5} x^{25} b^{4} a B + \frac{1}{25} x^{25} b^{5} A + \frac{5}{11} x^{22} b^{3} a^{2} B + \frac{5}{22} x^{22} b^{4} a A + \frac{10}{19} x^{19} b^{2} a^{3} B + \frac{10}{19} x^{19} b^{3} a^{2} A + \frac{5}{16} x^{16} b a^{4} B + \frac{5}{8} x^{16} b^{2} a^{3} A + \frac{1}{13} x^{13} a^{5} B + \frac{5}{13} x^{13} b a^{4} A + \frac{1}{10} x^{10} a^{5} A \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.084399, size = 136, normalized size = 1.16 \begin{align*} \frac{A a^{5} x^{10}}{10} + \frac{B b^{5} x^{28}}{28} + x^{25} \left (\frac{A b^{5}}{25} + \frac{B a b^{4}}{5}\right ) + x^{22} \left (\frac{5 A a b^{4}}{22} + \frac{5 B a^{2} b^{3}}{11}\right ) + x^{19} \left (\frac{10 A a^{2} b^{3}}{19} + \frac{10 B a^{3} b^{2}}{19}\right ) + x^{16} \left (\frac{5 A a^{3} b^{2}}{8} + \frac{5 B a^{4} b}{16}\right ) + x^{13} \left (\frac{5 A a^{4} b}{13} + \frac{B a^{5}}{13}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16651, size = 169, normalized size = 1.44 \begin{align*} \frac{1}{28} \, B b^{5} x^{28} + \frac{1}{5} \, B a b^{4} x^{25} + \frac{1}{25} \, A b^{5} x^{25} + \frac{5}{11} \, B a^{2} b^{3} x^{22} + \frac{5}{22} \, A a b^{4} x^{22} + \frac{10}{19} \, B a^{3} b^{2} x^{19} + \frac{10}{19} \, A a^{2} b^{3} x^{19} + \frac{5}{16} \, B a^{4} b x^{16} + \frac{5}{8} \, A a^{3} b^{2} x^{16} + \frac{1}{13} \, B a^{5} x^{13} + \frac{5}{13} \, A a^{4} b x^{13} + \frac{1}{10} \, A a^{5} x^{10} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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