Optimal. Leaf size=115 \[ -\frac{10 a^2 b^2 (a B+A b)}{x}-\frac{5 a^3 b (a B+2 A b)}{4 x^4}-\frac{a^4 (a B+5 A b)}{7 x^7}-\frac{a^5 A}{10 x^{10}}+\frac{1}{5} b^4 x^5 (5 a B+A b)+\frac{5}{2} a b^3 x^2 (2 a B+A b)+\frac{1}{8} b^5 B x^8 \]
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Rubi [A] time = 0.0631634, antiderivative size = 115, 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} \[ -\frac{10 a^2 b^2 (a B+A b)}{x}-\frac{5 a^3 b (a B+2 A b)}{4 x^4}-\frac{a^4 (a B+5 A b)}{7 x^7}-\frac{a^5 A}{10 x^{10}}+\frac{1}{5} b^4 x^5 (5 a B+A b)+\frac{5}{2} a b^3 x^2 (2 a B+A b)+\frac{1}{8} b^5 B x^8 \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^5 \left (A+B x^3\right )}{x^{11}} \, dx &=\int \left (\frac{a^5 A}{x^{11}}+\frac{a^4 (5 A b+a B)}{x^8}+\frac{5 a^3 b (2 A b+a B)}{x^5}+\frac{10 a^2 b^2 (A b+a B)}{x^2}+5 a b^3 (A b+2 a B) x+b^4 (A b+5 a B) x^4+b^5 B x^7\right ) \, dx\\ &=-\frac{a^5 A}{10 x^{10}}-\frac{a^4 (5 A b+a B)}{7 x^7}-\frac{5 a^3 b (2 A b+a B)}{4 x^4}-\frac{10 a^2 b^2 (A b+a B)}{x}+\frac{5}{2} a b^3 (A b+2 a B) x^2+\frac{1}{5} b^4 (A b+5 a B) x^5+\frac{1}{8} b^5 B x^8\\ \end{align*}
Mathematica [A] time = 0.0231462, size = 118, normalized size = 1.03 \[ \frac{1400 a^2 b^3 x^9 \left (B x^3-2 A\right )-700 a^3 b^2 x^6 \left (A+4 B x^3\right )-50 a^4 b x^3 \left (4 A+7 B x^3\right )-4 a^5 \left (7 A+10 B x^3\right )+140 a b^4 x^{12} \left (5 A+2 B x^3\right )+7 b^5 x^{15} \left (8 A+5 B x^3\right )}{280 x^{10}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 111, normalized size = 1. \begin{align*}{\frac{{b}^{5}B{x}^{8}}{8}}+{\frac{A{x}^{5}{b}^{5}}{5}}+B{x}^{5}a{b}^{4}+{\frac{5\,A{x}^{2}a{b}^{4}}{2}}+5\,B{x}^{2}{a}^{2}{b}^{3}-{\frac{5\,{a}^{3}b \left ( 2\,Ab+Ba \right ) }{4\,{x}^{4}}}-{\frac{A{a}^{5}}{10\,{x}^{10}}}-10\,{\frac{{a}^{2}{b}^{2} \left ( Ab+Ba \right ) }{x}}-{\frac{{a}^{4} \left ( 5\,Ab+Ba \right ) }{7\,{x}^{7}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.14326, size = 165, normalized size = 1.43 \begin{align*} \frac{1}{8} \, B b^{5} x^{8} + \frac{1}{5} \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{5} + \frac{5}{2} \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{2} - \frac{1400 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} + 175 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} + 14 \, A a^{5} + 20 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{140 \, x^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.41073, size = 273, normalized size = 2.37 \begin{align*} \frac{35 \, B b^{5} x^{18} + 56 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 700 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} - 2800 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} - 350 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} - 28 \, A a^{5} - 40 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{280 \, x^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 3.31842, size = 126, normalized size = 1.1 \begin{align*} \frac{B b^{5} x^{8}}{8} + x^{5} \left (\frac{A b^{5}}{5} + B a b^{4}\right ) + x^{2} \left (\frac{5 A a b^{4}}{2} + 5 B a^{2} b^{3}\right ) - \frac{14 A a^{5} + x^{9} \left (1400 A a^{2} b^{3} + 1400 B a^{3} b^{2}\right ) + x^{6} \left (350 A a^{3} b^{2} + 175 B a^{4} b\right ) + x^{3} \left (100 A a^{4} b + 20 B a^{5}\right )}{140 x^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.2071, size = 171, normalized size = 1.49 \begin{align*} \frac{1}{8} \, B b^{5} x^{8} + B a b^{4} x^{5} + \frac{1}{5} \, A b^{5} x^{5} + 5 \, B a^{2} b^{3} x^{2} + \frac{5}{2} \, A a b^{4} x^{2} - \frac{1400 \, B a^{3} b^{2} x^{9} + 1400 \, A a^{2} b^{3} x^{9} + 175 \, B a^{4} b x^{6} + 350 \, A a^{3} b^{2} x^{6} + 20 \, B a^{5} x^{3} + 100 \, A a^{4} b x^{3} + 14 \, A a^{5}}{140 \, x^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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