Optimal. Leaf size=102 \[ -\frac {a^8}{9 x^9}-\frac {8 a^7 b}{7 x^7}-\frac {28 a^6 b^2}{5 x^5}-\frac {56 a^5 b^3}{3 x^3}-\frac {70 a^4 b^4}{x}+56 a^3 b^5 x+\frac {28}{3} a^2 b^6 x^3+\frac {8}{5} a b^7 x^5+\frac {b^8 x^7}{7} \]
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Rubi [A] time = 0.04, antiderivative size = 102, 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} \[ -\frac {28 a^6 b^2}{5 x^5}-\frac {56 a^5 b^3}{3 x^3}+\frac {28}{3} a^2 b^6 x^3-\frac {70 a^4 b^4}{x}+56 a^3 b^5 x-\frac {8 a^7 b}{7 x^7}-\frac {a^8}{9 x^9}+\frac {8}{5} a b^7 x^5+\frac {b^8 x^7}{7} \]
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin {align*} \int \frac {\left (a+b x^2\right )^8}{x^{10}} \, dx &=\int \left (56 a^3 b^5+\frac {a^8}{x^{10}}+\frac {8 a^7 b}{x^8}+\frac {28 a^6 b^2}{x^6}+\frac {56 a^5 b^3}{x^4}+\frac {70 a^4 b^4}{x^2}+28 a^2 b^6 x^2+8 a b^7 x^4+b^8 x^6\right ) \, dx\\ &=-\frac {a^8}{9 x^9}-\frac {8 a^7 b}{7 x^7}-\frac {28 a^6 b^2}{5 x^5}-\frac {56 a^5 b^3}{3 x^3}-\frac {70 a^4 b^4}{x}+56 a^3 b^5 x+\frac {28}{3} a^2 b^6 x^3+\frac {8}{5} a b^7 x^5+\frac {b^8 x^7}{7}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 102, normalized size = 1.00 \[ -\frac {a^8}{9 x^9}-\frac {8 a^7 b}{7 x^7}-\frac {28 a^6 b^2}{5 x^5}-\frac {56 a^5 b^3}{3 x^3}-\frac {70 a^4 b^4}{x}+56 a^3 b^5 x+\frac {28}{3} a^2 b^6 x^3+\frac {8}{5} a b^7 x^5+\frac {b^8 x^7}{7} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.90, size = 92, normalized size = 0.90 \[ \frac {45 \, b^{8} x^{16} + 504 \, a b^{7} x^{14} + 2940 \, a^{2} b^{6} x^{12} + 17640 \, a^{3} b^{5} x^{10} - 22050 \, a^{4} b^{4} x^{8} - 5880 \, a^{5} b^{3} x^{6} - 1764 \, a^{6} b^{2} x^{4} - 360 \, a^{7} b x^{2} - 35 \, a^{8}}{315 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.94, size = 91, normalized size = 0.89 \[ \frac {1}{7} \, b^{8} x^{7} + \frac {8}{5} \, a b^{7} x^{5} + \frac {28}{3} \, a^{2} b^{6} x^{3} + 56 \, a^{3} b^{5} x - \frac {22050 \, a^{4} b^{4} x^{8} + 5880 \, a^{5} b^{3} x^{6} + 1764 \, a^{6} b^{2} x^{4} + 360 \, a^{7} b x^{2} + 35 \, a^{8}}{315 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 89, normalized size = 0.87 \[ \frac {b^{8} x^{7}}{7}+\frac {8 a \,b^{7} x^{5}}{5}+\frac {28 a^{2} b^{6} x^{3}}{3}+56 a^{3} b^{5} x -\frac {70 a^{4} b^{4}}{x}-\frac {56 a^{5} b^{3}}{3 x^{3}}-\frac {28 a^{6} b^{2}}{5 x^{5}}-\frac {8 a^{7} b}{7 x^{7}}-\frac {a^{8}}{9 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.36, size = 91, normalized size = 0.89 \[ \frac {1}{7} \, b^{8} x^{7} + \frac {8}{5} \, a b^{7} x^{5} + \frac {28}{3} \, a^{2} b^{6} x^{3} + 56 \, a^{3} b^{5} x - \frac {22050 \, a^{4} b^{4} x^{8} + 5880 \, a^{5} b^{3} x^{6} + 1764 \, a^{6} b^{2} x^{4} + 360 \, a^{7} b x^{2} + 35 \, a^{8}}{315 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 91, normalized size = 0.89 \[ \frac {b^8\,x^7}{7}-\frac {\frac {a^8}{9}+\frac {8\,a^7\,b\,x^2}{7}+\frac {28\,a^6\,b^2\,x^4}{5}+\frac {56\,a^5\,b^3\,x^6}{3}+70\,a^4\,b^4\,x^8}{x^9}+56\,a^3\,b^5\,x+\frac {8\,a\,b^7\,x^5}{5}+\frac {28\,a^2\,b^6\,x^3}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.42, size = 100, normalized size = 0.98 \[ 56 a^{3} b^{5} x + \frac {28 a^{2} b^{6} x^{3}}{3} + \frac {8 a b^{7} x^{5}}{5} + \frac {b^{8} x^{7}}{7} + \frac {- 35 a^{8} - 360 a^{7} b x^{2} - 1764 a^{6} b^{2} x^{4} - 5880 a^{5} b^{3} x^{6} - 22050 a^{4} b^{4} x^{8}}{315 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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