Optimal. Leaf size=106 \[ -\frac {a^8}{19 x^{19}}-\frac {8 a^7 b}{17 x^{17}}-\frac {28 a^6 b^2}{15 x^{15}}-\frac {56 a^5 b^3}{13 x^{13}}-\frac {70 a^4 b^4}{11 x^{11}}-\frac {56 a^3 b^5}{9 x^9}-\frac {4 a^2 b^6}{x^7}-\frac {8 a b^7}{5 x^5}-\frac {b^8}{3 x^3} \]
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Rubi [A] time = 0.04, antiderivative size = 106, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {270} \[ -\frac {28 a^6 b^2}{15 x^{15}}-\frac {56 a^5 b^3}{13 x^{13}}-\frac {70 a^4 b^4}{11 x^{11}}-\frac {56 a^3 b^5}{9 x^9}-\frac {4 a^2 b^6}{x^7}-\frac {8 a^7 b}{17 x^{17}}-\frac {a^8}{19 x^{19}}-\frac {8 a b^7}{5 x^5}-\frac {b^8}{3 x^3} \]
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin {align*} \int \frac {\left (a+b x^2\right )^8}{x^{20}} \, dx &=\int \left (\frac {a^8}{x^{20}}+\frac {8 a^7 b}{x^{18}}+\frac {28 a^6 b^2}{x^{16}}+\frac {56 a^5 b^3}{x^{14}}+\frac {70 a^4 b^4}{x^{12}}+\frac {56 a^3 b^5}{x^{10}}+\frac {28 a^2 b^6}{x^8}+\frac {8 a b^7}{x^6}+\frac {b^8}{x^4}\right ) \, dx\\ &=-\frac {a^8}{19 x^{19}}-\frac {8 a^7 b}{17 x^{17}}-\frac {28 a^6 b^2}{15 x^{15}}-\frac {56 a^5 b^3}{13 x^{13}}-\frac {70 a^4 b^4}{11 x^{11}}-\frac {56 a^3 b^5}{9 x^9}-\frac {4 a^2 b^6}{x^7}-\frac {8 a b^7}{5 x^5}-\frac {b^8}{3 x^3}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 106, normalized size = 1.00 \[ -\frac {a^8}{19 x^{19}}-\frac {8 a^7 b}{17 x^{17}}-\frac {28 a^6 b^2}{15 x^{15}}-\frac {56 a^5 b^3}{13 x^{13}}-\frac {70 a^4 b^4}{11 x^{11}}-\frac {56 a^3 b^5}{9 x^9}-\frac {4 a^2 b^6}{x^7}-\frac {8 a b^7}{5 x^5}-\frac {b^8}{3 x^3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.85, size = 92, normalized size = 0.87 \[ -\frac {692835 \, b^{8} x^{16} + 3325608 \, a b^{7} x^{14} + 8314020 \, a^{2} b^{6} x^{12} + 12932920 \, a^{3} b^{5} x^{10} + 13226850 \, a^{4} b^{4} x^{8} + 8953560 \, a^{5} b^{3} x^{6} + 3879876 \, a^{6} b^{2} x^{4} + 978120 \, a^{7} b x^{2} + 109395 \, a^{8}}{2078505 \, x^{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.14, size = 92, normalized size = 0.87 \[ -\frac {692835 \, b^{8} x^{16} + 3325608 \, a b^{7} x^{14} + 8314020 \, a^{2} b^{6} x^{12} + 12932920 \, a^{3} b^{5} x^{10} + 13226850 \, a^{4} b^{4} x^{8} + 8953560 \, a^{5} b^{3} x^{6} + 3879876 \, a^{6} b^{2} x^{4} + 978120 \, a^{7} b x^{2} + 109395 \, a^{8}}{2078505 \, x^{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 91, normalized size = 0.86 \[ -\frac {b^{8}}{3 x^{3}}-\frac {8 a \,b^{7}}{5 x^{5}}-\frac {4 a^{2} b^{6}}{x^{7}}-\frac {56 a^{3} b^{5}}{9 x^{9}}-\frac {70 a^{4} b^{4}}{11 x^{11}}-\frac {56 a^{5} b^{3}}{13 x^{13}}-\frac {28 a^{6} b^{2}}{15 x^{15}}-\frac {8 a^{7} b}{17 x^{17}}-\frac {a^{8}}{19 x^{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.36, size = 92, normalized size = 0.87 \[ -\frac {692835 \, b^{8} x^{16} + 3325608 \, a b^{7} x^{14} + 8314020 \, a^{2} b^{6} x^{12} + 12932920 \, a^{3} b^{5} x^{10} + 13226850 \, a^{4} b^{4} x^{8} + 8953560 \, a^{5} b^{3} x^{6} + 3879876 \, a^{6} b^{2} x^{4} + 978120 \, a^{7} b x^{2} + 109395 \, a^{8}}{2078505 \, x^{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 92, normalized size = 0.87 \[ -\frac {\frac {a^8}{19}+\frac {8\,a^7\,b\,x^2}{17}+\frac {28\,a^6\,b^2\,x^4}{15}+\frac {56\,a^5\,b^3\,x^6}{13}+\frac {70\,a^4\,b^4\,x^8}{11}+\frac {56\,a^3\,b^5\,x^{10}}{9}+4\,a^2\,b^6\,x^{12}+\frac {8\,a\,b^7\,x^{14}}{5}+\frac {b^8\,x^{16}}{3}}{x^{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.84, size = 99, normalized size = 0.93 \[ \frac {- 109395 a^{8} - 978120 a^{7} b x^{2} - 3879876 a^{6} b^{2} x^{4} - 8953560 a^{5} b^{3} x^{6} - 13226850 a^{4} b^{4} x^{8} - 12932920 a^{3} b^{5} x^{10} - 8314020 a^{2} b^{6} x^{12} - 3325608 a b^{7} x^{14} - 692835 b^{8} x^{16}}{2078505 x^{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
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