Optimal. Leaf size=117 \[ -\frac{10 a^2 b^2 (a B+A b)}{13 x^{13}}-\frac{a^4 (a B+5 A b)}{17 x^{17}}-\frac{a^3 b (a B+2 A b)}{3 x^{15}}-\frac{a^5 A}{19 x^{19}}-\frac{5 a b^3 (2 a B+A b)}{11 x^{11}}-\frac{b^4 (5 a B+A b)}{9 x^9}-\frac{b^5 B}{7 x^7} \]
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Rubi [A] time = 0.0586581, 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} \[ -\frac{10 a^2 b^2 (a B+A b)}{13 x^{13}}-\frac{a^4 (a B+5 A b)}{17 x^{17}}-\frac{a^3 b (a B+2 A b)}{3 x^{15}}-\frac{a^5 A}{19 x^{19}}-\frac{5 a b^3 (2 a B+A b)}{11 x^{11}}-\frac{b^4 (5 a B+A b)}{9 x^9}-\frac{b^5 B}{7 x^7} \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin{align*} \int \frac{\left (a+b x^2\right )^5 \left (A+B x^2\right )}{x^{20}} \, dx &=\int \left (\frac{a^5 A}{x^{20}}+\frac{a^4 (5 A b+a B)}{x^{18}}+\frac{5 a^3 b (2 A b+a B)}{x^{16}}+\frac{10 a^2 b^2 (A b+a B)}{x^{14}}+\frac{5 a b^3 (A b+2 a B)}{x^{12}}+\frac{b^4 (A b+5 a B)}{x^{10}}+\frac{b^5 B}{x^8}\right ) \, dx\\ &=-\frac{a^5 A}{19 x^{19}}-\frac{a^4 (5 A b+a B)}{17 x^{17}}-\frac{a^3 b (2 A b+a B)}{3 x^{15}}-\frac{10 a^2 b^2 (A b+a B)}{13 x^{13}}-\frac{5 a b^3 (A b+2 a B)}{11 x^{11}}-\frac{b^4 (A b+5 a B)}{9 x^9}-\frac{b^5 B}{7 x^7}\\ \end{align*}
Mathematica [A] time = 0.0425499, size = 117, normalized size = 1. \[ -\frac{10 a^2 b^2 (a B+A b)}{13 x^{13}}-\frac{a^4 (a B+5 A b)}{17 x^{17}}-\frac{a^3 b (a B+2 A b)}{3 x^{15}}-\frac{a^5 A}{19 x^{19}}-\frac{5 a b^3 (2 a B+A b)}{11 x^{11}}-\frac{b^4 (5 a B+A b)}{9 x^9}-\frac{b^5 B}{7 x^7} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 104, normalized size = 0.9 \begin{align*} -{\frac{A{a}^{5}}{19\,{x}^{19}}}-{\frac{{a}^{4} \left ( 5\,Ab+Ba \right ) }{17\,{x}^{17}}}-{\frac{{a}^{3}b \left ( 2\,Ab+Ba \right ) }{3\,{x}^{15}}}-{\frac{10\,{b}^{2}{a}^{2} \left ( Ab+Ba \right ) }{13\,{x}^{13}}}-{\frac{5\,a{b}^{3} \left ( Ab+2\,Ba \right ) }{11\,{x}^{11}}}-{\frac{{b}^{4} \left ( Ab+5\,Ba \right ) }{9\,{x}^{9}}}-{\frac{B{b}^{5}}{7\,{x}^{7}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00315, size = 163, normalized size = 1.39 \begin{align*} -\frac{415701 \, B b^{5} x^{12} + 323323 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{10} + 1322685 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{8} + 2238390 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{6} + 153153 \, A a^{5} + 969969 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{4} + 171171 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{2}}{2909907 \, x^{19}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.38052, size = 313, normalized size = 2.68 \begin{align*} -\frac{415701 \, B b^{5} x^{12} + 323323 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{10} + 1322685 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{8} + 2238390 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{6} + 153153 \, A a^{5} + 969969 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{4} + 171171 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{2}}{2909907 \, x^{19}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 176.26, size = 128, normalized size = 1.09 \begin{align*} - \frac{153153 A a^{5} + 415701 B b^{5} x^{12} + x^{10} \left (323323 A b^{5} + 1616615 B a b^{4}\right ) + x^{8} \left (1322685 A a b^{4} + 2645370 B a^{2} b^{3}\right ) + x^{6} \left (2238390 A a^{2} b^{3} + 2238390 B a^{3} b^{2}\right ) + x^{4} \left (1939938 A a^{3} b^{2} + 969969 B a^{4} b\right ) + x^{2} \left (855855 A a^{4} b + 171171 B a^{5}\right )}{2909907 x^{19}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18392, size = 171, normalized size = 1.46 \begin{align*} -\frac{415701 \, B b^{5} x^{12} + 1616615 \, B a b^{4} x^{10} + 323323 \, A b^{5} x^{10} + 2645370 \, B a^{2} b^{3} x^{8} + 1322685 \, A a b^{4} x^{8} + 2238390 \, B a^{3} b^{2} x^{6} + 2238390 \, A a^{2} b^{3} x^{6} + 969969 \, B a^{4} b x^{4} + 1939938 \, A a^{3} b^{2} x^{4} + 171171 \, B a^{5} x^{2} + 855855 \, A a^{4} b x^{2} + 153153 \, A a^{5}}{2909907 \, x^{19}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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