Optimal. Leaf size=114 \[ -\frac{10 a^2 b^2 (a B+A b)}{3 x^3}-\frac{5 a^3 b (a B+2 A b)}{6 x^6}-\frac{a^4 (a B+5 A b)}{9 x^9}-\frac{a^5 A}{12 x^{12}}+\frac{1}{3} b^4 x^3 (5 a B+A b)+5 a b^3 \log (x) (2 a B+A b)+\frac{1}{6} b^5 B x^6 \]
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Rubi [A] time = 0.0987126, 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} \[ -\frac{10 a^2 b^2 (a B+A b)}{3 x^3}-\frac{5 a^3 b (a B+2 A b)}{6 x^6}-\frac{a^4 (a B+5 A b)}{9 x^9}-\frac{a^5 A}{12 x^{12}}+\frac{1}{3} b^4 x^3 (5 a B+A b)+5 a b^3 \log (x) (2 a B+A b)+\frac{1}{6} b^5 B x^6 \]
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^{13}} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{(a+b x)^5 (A+B x)}{x^5} \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (b^4 (A b+5 a B)+\frac{a^5 A}{x^5}+\frac{a^4 (5 A b+a B)}{x^4}+\frac{5 a^3 b (2 A b+a B)}{x^3}+\frac{10 a^2 b^2 (A b+a B)}{x^2}+\frac{5 a b^3 (A b+2 a B)}{x}+b^5 B x\right ) \, dx,x,x^3\right )\\ &=-\frac{a^5 A}{12 x^{12}}-\frac{a^4 (5 A b+a B)}{9 x^9}-\frac{5 a^3 b (2 A b+a B)}{6 x^6}-\frac{10 a^2 b^2 (A b+a B)}{3 x^3}+\frac{1}{3} b^4 (A b+5 a B) x^3+\frac{1}{6} b^5 B x^6+5 a b^3 (A b+2 a B) \log (x)\\ \end{align*}
Mathematica [A] time = 0.0382892, size = 118, normalized size = 1.04 \[ -\frac{60 a^3 b^2 x^6 \left (A+2 B x^3\right )+120 a^2 A b^3 x^9+10 a^4 b x^3 \left (2 A+3 B x^3\right )+a^5 \left (3 A+4 B x^3\right )-180 a b^3 x^{12} \log (x) (2 a B+A b)-60 a b^4 B x^{15}-6 b^5 x^{15} \left (2 A+B x^3\right )}{36 x^{12}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 124, normalized size = 1.1 \begin{align*}{\frac{{b}^{5}B{x}^{6}}{6}}+{\frac{A{x}^{3}{b}^{5}}{3}}+{\frac{5\,B{x}^{3}a{b}^{4}}{3}}-{\frac{A{a}^{5}}{12\,{x}^{12}}}-{\frac{5\,{a}^{4}bA}{9\,{x}^{9}}}-{\frac{{a}^{5}B}{9\,{x}^{9}}}-{\frac{5\,{a}^{3}{b}^{2}A}{3\,{x}^{6}}}-{\frac{5\,{a}^{4}bB}{6\,{x}^{6}}}-{\frac{10\,{a}^{2}{b}^{3}A}{3\,{x}^{3}}}-{\frac{10\,{a}^{3}{b}^{2}B}{3\,{x}^{3}}}+5\,A\ln \left ( x \right ) a{b}^{4}+10\,B\ln \left ( x \right ){a}^{2}{b}^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.28447, size = 166, normalized size = 1.46 \begin{align*} \frac{1}{6} \, B b^{5} x^{6} + \frac{1}{3} \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{3} + \frac{5}{3} \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} \log \left (x^{3}\right ) - \frac{120 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} + 30 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} + 3 \, A a^{5} + 4 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{36 \, x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.44972, size = 274, normalized size = 2.4 \begin{align*} \frac{6 \, B b^{5} x^{18} + 12 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 180 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} \log \left (x\right ) - 120 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} - 30 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} - 3 \, A a^{5} - 4 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{36 \, x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 7.53096, size = 124, normalized size = 1.09 \begin{align*} \frac{B b^{5} x^{6}}{6} + 5 a b^{3} \left (A b + 2 B a\right ) \log{\left (x \right )} + x^{3} \left (\frac{A b^{5}}{3} + \frac{5 B a b^{4}}{3}\right ) - \frac{3 A a^{5} + x^{9} \left (120 A a^{2} b^{3} + 120 B a^{3} b^{2}\right ) + x^{6} \left (60 A a^{3} b^{2} + 30 B a^{4} b\right ) + x^{3} \left (20 A a^{4} b + 4 B a^{5}\right )}{36 x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16675, size = 201, normalized size = 1.76 \begin{align*} \frac{1}{6} \, B b^{5} x^{6} + \frac{5}{3} \, B a b^{4} x^{3} + \frac{1}{3} \, A b^{5} x^{3} + 5 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} \log \left ({\left | x \right |}\right ) - \frac{250 \, B a^{2} b^{3} x^{12} + 125 \, A a b^{4} x^{12} + 120 \, B a^{3} b^{2} x^{9} + 120 \, A a^{2} b^{3} x^{9} + 30 \, B a^{4} b x^{6} + 60 \, A a^{3} b^{2} x^{6} + 4 \, B a^{5} x^{3} + 20 \, A a^{4} b x^{3} + 3 \, A a^{5}}{36 \, x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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