Optimal. Leaf size=117 \[ -\frac {a^5 A}{19 x^{19}}-\frac {a^4 (a B+5 A b)}{17 x^{17}}-\frac {a^3 b (a B+2 A b)}{3 x^{15}}-\frac {10 a^2 b^2 (a B+A b)}{13 x^{13}}-\frac {b^4 (5 a B+A b)}{9 x^9}-\frac {5 a b^3 (2 a B+A b)}{11 x^{11}}-\frac {b^5 B}{7 x^7} \]
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Rubi [A] time = 0.06, antiderivative size = 117, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, 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*}
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Mathematica [A] time = 0.04, size = 117, normalized size = 1.00 \[ -\frac {a^5 A}{19 x^{19}}-\frac {a^4 (a B+5 A b)}{17 x^{17}}-\frac {a^3 b (a B+2 A b)}{3 x^{15}}-\frac {10 a^2 b^2 (a B+A b)}{13 x^{13}}-\frac {b^4 (5 a B+A b)}{9 x^9}-\frac {5 a b^3 (2 a B+A b)}{11 x^{11}}-\frac {b^5 B}{7 x^7} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.45, size = 121, normalized size = 1.03 \[ -\frac {415701 \, B b^{5} x^{12} + 323323 \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{10} + 1322685 \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{8} + 2238390 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{6} + 153153 \, A a^{5} + 969969 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{4} + 171171 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{2}}{2909907 \, x^{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.42, size = 127, normalized size = 1.09 \[ -\frac {415701 \, B b^{5} x^{12} + 1616615 \, B a b^{4} x^{10} + 323323 \, A b^{5} x^{10} + 2645370 \, B a^{2} b^{3} x^{8} + 1322685 \, A a b^{4} x^{8} + 2238390 \, B a^{3} b^{2} x^{6} + 2238390 \, A a^{2} b^{3} x^{6} + 969969 \, B a^{4} b x^{4} + 1939938 \, A a^{3} b^{2} x^{4} + 171171 \, B a^{5} x^{2} + 855855 \, A a^{4} b x^{2} + 153153 \, A a^{5}}{2909907 \, x^{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 104, normalized size = 0.89 \[ -\frac {B \,b^{5}}{7 x^{7}}-\frac {\left (A b +5 B a \right ) b^{4}}{9 x^{9}}-\frac {5 \left (A b +2 B a \right ) a \,b^{3}}{11 x^{11}}-\frac {10 \left (A b +B a \right ) a^{2} b^{2}}{13 x^{13}}-\frac {\left (2 A b +B a \right ) a^{3} b}{3 x^{15}}-\frac {A \,a^{5}}{19 x^{19}}-\frac {\left (5 A b +B a \right ) a^{4}}{17 x^{17}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.04, size = 121, normalized size = 1.03 \[ -\frac {415701 \, B b^{5} x^{12} + 323323 \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{10} + 1322685 \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{8} + 2238390 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{6} + 153153 \, A a^{5} + 969969 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{4} + 171171 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{2}}{2909907 \, x^{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 122, normalized size = 1.04 \[ -\frac {\frac {A\,a^5}{19}+x^4\,\left (\frac {B\,a^4\,b}{3}+\frac {2\,A\,a^3\,b^2}{3}\right )+x^8\,\left (\frac {10\,B\,a^2\,b^3}{11}+\frac {5\,A\,a\,b^4}{11}\right )+x^2\,\left (\frac {B\,a^5}{17}+\frac {5\,A\,b\,a^4}{17}\right )+x^{10}\,\left (\frac {A\,b^5}{9}+\frac {5\,B\,a\,b^4}{9}\right )+x^6\,\left (\frac {10\,B\,a^3\,b^2}{13}+\frac {10\,A\,a^2\,b^3}{13}\right )+\frac {B\,b^5\,x^{12}}{7}}{x^{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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