Optimal. Leaf size=117 \[ -\frac{10 a^2 b^2 (a B+A b)}{9 x^9}-\frac{a^4 (a B+5 A b)}{13 x^{13}}-\frac{5 a^3 b (a B+2 A b)}{11 x^{11}}-\frac{a^5 A}{15 x^{15}}-\frac{5 a b^3 (2 a B+A b)}{7 x^7}-\frac{b^4 (5 a B+A b)}{5 x^5}-\frac{b^5 B}{3 x^3} \]
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Rubi [A] time = 0.058662, 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} \[ -\frac{10 a^2 b^2 (a B+A b)}{9 x^9}-\frac{a^4 (a B+5 A b)}{13 x^{13}}-\frac{5 a^3 b (a B+2 A b)}{11 x^{11}}-\frac{a^5 A}{15 x^{15}}-\frac{5 a b^3 (2 a B+A b)}{7 x^7}-\frac{b^4 (5 a B+A b)}{5 x^5}-\frac{b^5 B}{3 x^3} \]
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^{16}} \, dx &=\int \left (\frac{a^5 A}{x^{16}}+\frac{a^4 (5 A b+a B)}{x^{14}}+\frac{5 a^3 b (2 A b+a B)}{x^{12}}+\frac{10 a^2 b^2 (A b+a B)}{x^{10}}+\frac{5 a b^3 (A b+2 a B)}{x^8}+\frac{b^4 (A b+5 a B)}{x^6}+\frac{b^5 B}{x^4}\right ) \, dx\\ &=-\frac{a^5 A}{15 x^{15}}-\frac{a^4 (5 A b+a B)}{13 x^{13}}-\frac{5 a^3 b (2 A b+a B)}{11 x^{11}}-\frac{10 a^2 b^2 (A b+a B)}{9 x^9}-\frac{5 a b^3 (A b+2 a B)}{7 x^7}-\frac{b^4 (A b+5 a B)}{5 x^5}-\frac{b^5 B}{3 x^3}\\ \end{align*}
Mathematica [A] time = 0.0335061, size = 121, normalized size = 1.03 \[ -\frac{7150 a^2 b^3 x^6 \left (7 A+9 B x^2\right )+4550 a^3 b^2 x^4 \left (9 A+11 B x^2\right )+1575 a^4 b x^2 \left (11 A+13 B x^2\right )+231 a^5 \left (13 A+15 B x^2\right )+6435 a b^4 x^8 \left (5 A+7 B x^2\right )+3003 b^5 x^{10} \left (3 A+5 B x^2\right )}{45045 x^{15}} \]
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}}{15\,{x}^{15}}}-{\frac{{a}^{4} \left ( 5\,Ab+Ba \right ) }{13\,{x}^{13}}}-{\frac{5\,{a}^{3}b \left ( 2\,Ab+Ba \right ) }{11\,{x}^{11}}}-{\frac{10\,{b}^{2}{a}^{2} \left ( Ab+Ba \right ) }{9\,{x}^{9}}}-{\frac{5\,a{b}^{3} \left ( Ab+2\,Ba \right ) }{7\,{x}^{7}}}-{\frac{{b}^{4} \left ( Ab+5\,Ba \right ) }{5\,{x}^{5}}}-{\frac{B{b}^{5}}{3\,{x}^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03946, size = 163, normalized size = 1.39 \begin{align*} -\frac{15015 \, B b^{5} x^{12} + 9009 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{10} + 32175 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{8} + 50050 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{6} + 3003 \, A a^{5} + 20475 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{4} + 3465 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{2}}{45045 \, x^{15}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.49205, size = 294, normalized size = 2.51 \begin{align*} -\frac{15015 \, B b^{5} x^{12} + 9009 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{10} + 32175 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{8} + 50050 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{6} + 3003 \, A a^{5} + 20475 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{4} + 3465 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{2}}{45045 \, x^{15}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 37.3983, size = 128, normalized size = 1.09 \begin{align*} - \frac{3003 A a^{5} + 15015 B b^{5} x^{12} + x^{10} \left (9009 A b^{5} + 45045 B a b^{4}\right ) + x^{8} \left (32175 A a b^{4} + 64350 B a^{2} b^{3}\right ) + x^{6} \left (50050 A a^{2} b^{3} + 50050 B a^{3} b^{2}\right ) + x^{4} \left (40950 A a^{3} b^{2} + 20475 B a^{4} b\right ) + x^{2} \left (17325 A a^{4} b + 3465 B a^{5}\right )}{45045 x^{15}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13318, size = 171, normalized size = 1.46 \begin{align*} -\frac{15015 \, B b^{5} x^{12} + 45045 \, B a b^{4} x^{10} + 9009 \, A b^{5} x^{10} + 64350 \, B a^{2} b^{3} x^{8} + 32175 \, A a b^{4} x^{8} + 50050 \, B a^{3} b^{2} x^{6} + 50050 \, A a^{2} b^{3} x^{6} + 20475 \, B a^{4} b x^{4} + 40950 \, A a^{3} b^{2} x^{4} + 3465 \, B a^{5} x^{2} + 17325 \, A a^{4} b x^{2} + 3003 \, A a^{5}}{45045 \, x^{15}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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