Optimal. Leaf size=114 \[ 10 a^2 b^2 \log (x) (a B+A b)-\frac{5 a^3 b (a B+2 A b)}{3 x^3}-\frac{a^4 (a B+5 A b)}{6 x^6}-\frac{a^5 A}{9 x^9}+\frac{1}{6} b^4 x^6 (5 a B+A b)+\frac{5}{3} a b^3 x^3 (2 a B+A b)+\frac{1}{9} b^5 B x^9 \]
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Rubi [A] time = 0.104487, antiderivative size = 114, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1, Rules used = {446, 76} \[ 10 a^2 b^2 \log (x) (a B+A b)-\frac{5 a^3 b (a B+2 A b)}{3 x^3}-\frac{a^4 (a B+5 A b)}{6 x^6}-\frac{a^5 A}{9 x^9}+\frac{1}{6} b^4 x^6 (5 a B+A b)+\frac{5}{3} a b^3 x^3 (2 a B+A b)+\frac{1}{9} b^5 B x^9 \]
Antiderivative was successfully verified.
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Rule 446
Rule 76
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^5 \left (A+B x^3\right )}{x^{10}} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{(a+b x)^5 (A+B x)}{x^4} \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (5 a b^3 (A b+2 a B)+\frac{a^5 A}{x^4}+\frac{a^4 (5 A b+a B)}{x^3}+\frac{5 a^3 b (2 A b+a B)}{x^2}+\frac{10 a^2 b^2 (A b+a B)}{x}+b^4 (A b+5 a B) x+b^5 B x^2\right ) \, dx,x,x^3\right )\\ &=-\frac{a^5 A}{9 x^9}-\frac{a^4 (5 A b+a B)}{6 x^6}-\frac{5 a^3 b (2 A b+a B)}{3 x^3}+\frac{5}{3} a b^3 (A b+2 a B) x^3+\frac{1}{6} b^4 (A b+5 a B) x^6+\frac{1}{9} b^5 B x^9+10 a^2 b^2 (A b+a B) \log (x)\\ \end{align*}
Mathematica [A] time = 0.0509723, size = 106, normalized size = 0.93 \[ \frac{1}{18} \left (180 a^2 b^2 \log (x) (a B+A b)-\frac{30 a^3 b (a B+2 A b)}{x^3}-\frac{3 a^4 (a B+5 A b)}{x^6}-\frac{2 a^5 A}{x^9}+3 b^4 x^6 (5 a B+A b)+30 a b^3 x^3 (2 a B+A b)+2 b^5 B x^9\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.008, size = 124, normalized size = 1.1 \begin{align*}{\frac{{b}^{5}B{x}^{9}}{9}}+{\frac{A{x}^{6}{b}^{5}}{6}}+{\frac{5\,B{x}^{6}a{b}^{4}}{6}}+{\frac{5\,A{x}^{3}a{b}^{4}}{3}}+{\frac{10\,B{x}^{3}{a}^{2}{b}^{3}}{3}}-{\frac{A{a}^{5}}{9\,{x}^{9}}}-{\frac{10\,{a}^{3}{b}^{2}A}{3\,{x}^{3}}}-{\frac{5\,{a}^{4}bB}{3\,{x}^{3}}}-{\frac{5\,{a}^{4}bA}{6\,{x}^{6}}}-{\frac{{a}^{5}B}{6\,{x}^{6}}}+10\,A\ln \left ( x \right ){a}^{2}{b}^{3}+10\,B\ln \left ( x \right ){a}^{3}{b}^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.33105, size = 166, normalized size = 1.46 \begin{align*} \frac{1}{9} \, B b^{5} x^{9} + \frac{1}{6} \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{6} + \frac{5}{3} \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{3} + \frac{10}{3} \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} \log \left (x^{3}\right ) - \frac{30 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} + 2 \, A a^{5} + 3 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{18 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.49055, size = 270, normalized size = 2.37 \begin{align*} \frac{2 \, B b^{5} x^{18} + 3 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 30 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} + 180 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} \log \left (x\right ) - 30 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} - 2 \, A a^{5} - 3 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{18 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.50999, size = 126, normalized size = 1.11 \begin{align*} \frac{B b^{5} x^{9}}{9} + 10 a^{2} b^{2} \left (A b + B a\right ) \log{\left (x \right )} + x^{6} \left (\frac{A b^{5}}{6} + \frac{5 B a b^{4}}{6}\right ) + x^{3} \left (\frac{5 A a b^{4}}{3} + \frac{10 B a^{2} b^{3}}{3}\right ) - \frac{2 A a^{5} + x^{6} \left (60 A a^{3} b^{2} + 30 B a^{4} b\right ) + x^{3} \left (15 A a^{4} b + 3 B a^{5}\right )}{18 x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16011, size = 203, normalized size = 1.78 \begin{align*} \frac{1}{9} \, B b^{5} x^{9} + \frac{5}{6} \, B a b^{4} x^{6} + \frac{1}{6} \, A b^{5} x^{6} + \frac{10}{3} \, B a^{2} b^{3} x^{3} + \frac{5}{3} \, A a b^{4} x^{3} + 10 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} \log \left ({\left | x \right |}\right ) - \frac{110 \, B a^{3} b^{2} x^{9} + 110 \, A a^{2} b^{3} x^{9} + 30 \, B a^{4} b x^{6} + 60 \, A a^{3} b^{2} x^{6} + 3 \, B a^{5} x^{3} + 15 \, A a^{4} b x^{3} + 2 \, A a^{5}}{18 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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