Optimal. Leaf size=108 \[ -\frac{10 a^2 b^2 (a B+A b)}{3 x^3}-\frac{a^4 (a B+5 A b)}{7 x^7}-\frac{a^3 b (a B+2 A b)}{x^5}-\frac{a^5 A}{9 x^9}-\frac{5 a b^3 (2 a B+A b)}{x}+b^4 x (5 a B+A b)+\frac{1}{3} b^5 B x^3 \]
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Rubi [A] time = 0.0663631, antiderivative size = 108, 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} \[ -\frac{10 a^2 b^2 (a B+A b)}{3 x^3}-\frac{a^4 (a B+5 A b)}{7 x^7}-\frac{a^3 b (a B+2 A b)}{x^5}-\frac{a^5 A}{9 x^9}-\frac{5 a b^3 (2 a B+A b)}{x}+b^4 x (5 a B+A b)+\frac{1}{3} b^5 B x^3 \]
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^{10}} \, dx &=\int \left (b^4 (A b+5 a B)+\frac{a^5 A}{x^{10}}+\frac{a^4 (5 A b+a B)}{x^8}+\frac{5 a^3 b (2 A b+a B)}{x^6}+\frac{10 a^2 b^2 (A b+a B)}{x^4}+\frac{5 a b^3 (A b+2 a B)}{x^2}+b^5 B x^2\right ) \, dx\\ &=-\frac{a^5 A}{9 x^9}-\frac{a^4 (5 A b+a B)}{7 x^7}-\frac{a^3 b (2 A b+a B)}{x^5}-\frac{10 a^2 b^2 (A b+a B)}{3 x^3}-\frac{5 a b^3 (A b+2 a B)}{x}+b^4 (A b+5 a B) x+\frac{1}{3} b^5 B x^3\\ \end{align*}
Mathematica [A] time = 0.0321109, size = 115, normalized size = 1.06 \[ -\frac{210 a^2 b^3 x^6 \left (A+3 B x^2\right )+42 a^3 b^2 x^4 \left (3 A+5 B x^2\right )+9 a^4 b x^2 \left (5 A+7 B x^2\right )+a^5 \left (7 A+9 B x^2\right )+315 a b^4 x^8 \left (A-B x^2\right )-21 b^5 x^{10} \left (3 A+B x^2\right )}{63 x^9} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 102, normalized size = 0.9 \begin{align*}{\frac{{b}^{5}B{x}^{3}}{3}}+{b}^{5}Ax+5\,a{b}^{4}Bx-{\frac{10\,{b}^{2}{a}^{2} \left ( Ab+Ba \right ) }{3\,{x}^{3}}}-{\frac{{a}^{3}b \left ( 2\,Ab+Ba \right ) }{{x}^{5}}}-{\frac{{a}^{4} \left ( 5\,Ab+Ba \right ) }{7\,{x}^{7}}}-5\,{\frac{a{b}^{3} \left ( Ab+2\,Ba \right ) }{x}}-{\frac{A{a}^{5}}{9\,{x}^{9}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01553, size = 161, normalized size = 1.49 \begin{align*} \frac{1}{3} \, B b^{5} x^{3} +{\left (5 \, B a b^{4} + A b^{5}\right )} x - \frac{315 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{8} + 210 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{6} + 7 \, A a^{5} + 63 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{4} + 9 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{2}}{63 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.44344, size = 263, normalized size = 2.44 \begin{align*} \frac{21 \, B b^{5} x^{12} + 63 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{10} - 315 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{8} - 210 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{6} - 7 \, A a^{5} - 63 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{4} - 9 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{2}}{63 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 3.39189, size = 122, normalized size = 1.13 \begin{align*} \frac{B b^{5} x^{3}}{3} + x \left (A b^{5} + 5 B a b^{4}\right ) - \frac{7 A a^{5} + x^{8} \left (315 A a b^{4} + 630 B a^{2} b^{3}\right ) + x^{6} \left (210 A a^{2} b^{3} + 210 B a^{3} b^{2}\right ) + x^{4} \left (126 A a^{3} b^{2} + 63 B a^{4} b\right ) + x^{2} \left (45 A a^{4} b + 9 B a^{5}\right )}{63 x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15211, size = 166, normalized size = 1.54 \begin{align*} \frac{1}{3} \, B b^{5} x^{3} + 5 \, B a b^{4} x + A b^{5} x - \frac{630 \, B a^{2} b^{3} x^{8} + 315 \, A a b^{4} x^{8} + 210 \, B a^{3} b^{2} x^{6} + 210 \, A a^{2} b^{3} x^{6} + 63 \, B a^{4} b x^{4} + 126 \, A a^{3} b^{2} x^{4} + 9 \, B a^{5} x^{2} + 45 \, A a^{4} b x^{2} + 7 \, A a^{5}}{63 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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