Optimal. Leaf size=113 \[ -\frac{a^2 b^2 (a B+A b)}{x^{10}}-\frac{a^4 (a B+5 A b)}{16 x^{16}}-\frac{5 a^3 b (a B+2 A b)}{13 x^{13}}-\frac{a^5 A}{19 x^{19}}-\frac{5 a b^3 (2 a B+A b)}{7 x^7}-\frac{b^4 (5 a B+A b)}{4 x^4}-\frac{b^5 B}{x} \]
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Rubi [A] time = 0.0643632, antiderivative size = 113, 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} \[ -\frac{a^2 b^2 (a B+A b)}{x^{10}}-\frac{a^4 (a B+5 A b)}{16 x^{16}}-\frac{5 a^3 b (a B+2 A b)}{13 x^{13}}-\frac{a^5 A}{19 x^{19}}-\frac{5 a b^3 (2 a B+A b)}{7 x^7}-\frac{b^4 (5 a B+A b)}{4 x^4}-\frac{b^5 B}{x} \]
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^{20}} \, dx &=\int \left (\frac{a^5 A}{x^{20}}+\frac{a^4 (5 A b+a B)}{x^{17}}+\frac{5 a^3 b (2 A b+a B)}{x^{14}}+\frac{10 a^2 b^2 (A b+a B)}{x^{11}}+\frac{5 a b^3 (A b+2 a B)}{x^8}+\frac{b^4 (A b+5 a B)}{x^5}+\frac{b^5 B}{x^2}\right ) \, dx\\ &=-\frac{a^5 A}{19 x^{19}}-\frac{a^4 (5 A b+a B)}{16 x^{16}}-\frac{5 a^3 b (2 A b+a B)}{13 x^{13}}-\frac{a^2 b^2 (A b+a B)}{x^{10}}-\frac{5 a b^3 (A b+2 a B)}{7 x^7}-\frac{b^4 (A b+5 a B)}{4 x^4}-\frac{b^5 B}{x}\\ \end{align*}
Mathematica [A] time = 0.0295196, size = 119, normalized size = 1.05 \[ -\frac{3952 a^2 b^3 x^9 \left (7 A+10 B x^3\right )+2128 a^3 b^2 x^6 \left (10 A+13 B x^3\right )+665 a^4 b x^3 \left (13 A+16 B x^3\right )+91 a^5 \left (16 A+19 B x^3\right )+4940 a b^4 x^{12} \left (4 A+7 B x^3\right )+6916 b^5 x^{15} \left (A+4 B x^3\right )}{27664 x^{19}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.008, size = 104, normalized size = 0.9 \begin{align*} -{\frac{A{a}^{5}}{19\,{x}^{19}}}-{\frac{{a}^{4} \left ( 5\,Ab+Ba \right ) }{16\,{x}^{16}}}-{\frac{5\,{a}^{3}b \left ( 2\,Ab+Ba \right ) }{13\,{x}^{13}}}-{\frac{{a}^{2}{b}^{2} \left ( Ab+Ba \right ) }{{x}^{10}}}-{\frac{5\,a{b}^{3} \left ( Ab+2\,Ba \right ) }{7\,{x}^{7}}}-{\frac{{b}^{4} \left ( Ab+5\,Ba \right ) }{4\,{x}^{4}}}-{\frac{B{b}^{5}}{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.12837, size = 163, normalized size = 1.44 \begin{align*} -\frac{27664 \, B b^{5} x^{18} + 6916 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 19760 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} + 27664 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} + 10640 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} + 1456 \, A a^{5} + 1729 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{27664 \, x^{19}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.41254, size = 296, normalized size = 2.62 \begin{align*} -\frac{27664 \, B b^{5} x^{18} + 6916 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 19760 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} + 27664 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} + 10640 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} + 1456 \, A a^{5} + 1729 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{27664 \, x^{19}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.2132, size = 171, normalized size = 1.51 \begin{align*} -\frac{27664 \, B b^{5} x^{18} + 34580 \, B a b^{4} x^{15} + 6916 \, A b^{5} x^{15} + 39520 \, B a^{2} b^{3} x^{12} + 19760 \, A a b^{4} x^{12} + 27664 \, B a^{3} b^{2} x^{9} + 27664 \, A a^{2} b^{3} x^{9} + 10640 \, B a^{4} b x^{6} + 21280 \, A a^{3} b^{2} x^{6} + 1729 \, B a^{5} x^{3} + 8645 \, A a^{4} b x^{3} + 1456 \, A a^{5}}{27664 \, x^{19}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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