Optimal. Leaf size=17 \[ -\frac {(a+b x)^9}{9 a x^9} \]
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Rubi [A] time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {37} \[ -\frac {(a+b x)^9}{9 a x^9} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin {align*} \int \frac {(a+b x)^8}{x^{10}} \, dx &=-\frac {(a+b x)^9}{9 a x^9}\\ \end {align*}
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Mathematica [B] time = 0.01, size = 96, normalized size = 5.65 \[ -\frac {a^8}{9 x^9}-\frac {a^7 b}{x^8}-\frac {4 a^6 b^2}{x^7}-\frac {28 a^5 b^3}{3 x^6}-\frac {14 a^4 b^4}{x^5}-\frac {14 a^3 b^5}{x^4}-\frac {28 a^2 b^6}{3 x^3}-\frac {4 a b^7}{x^2}-\frac {b^8}{x} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.53, size = 88, normalized size = 5.18 \[ -\frac {9 \, b^{8} x^{8} + 36 \, a b^{7} x^{7} + 84 \, a^{2} b^{6} x^{6} + 126 \, a^{3} b^{5} x^{5} + 126 \, a^{4} b^{4} x^{4} + 84 \, a^{5} b^{3} x^{3} + 36 \, a^{6} b^{2} x^{2} + 9 \, a^{7} b x + a^{8}}{9 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.17, size = 88, normalized size = 5.18 \[ -\frac {9 \, b^{8} x^{8} + 36 \, a b^{7} x^{7} + 84 \, a^{2} b^{6} x^{6} + 126 \, a^{3} b^{5} x^{5} + 126 \, a^{4} b^{4} x^{4} + 84 \, a^{5} b^{3} x^{3} + 36 \, a^{6} b^{2} x^{2} + 9 \, a^{7} b x + a^{8}}{9 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.01, size = 91, normalized size = 5.35 \[ -\frac {b^{8}}{x}-\frac {4 a \,b^{7}}{x^{2}}-\frac {28 a^{2} b^{6}}{3 x^{3}}-\frac {14 a^{3} b^{5}}{x^{4}}-\frac {14 a^{4} b^{4}}{x^{5}}-\frac {28 a^{5} b^{3}}{3 x^{6}}-\frac {4 a^{6} b^{2}}{x^{7}}-\frac {a^{7} b}{x^{8}}-\frac {a^{8}}{9 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.34, size = 88, normalized size = 5.18 \[ -\frac {9 \, b^{8} x^{8} + 36 \, a b^{7} x^{7} + 84 \, a^{2} b^{6} x^{6} + 126 \, a^{3} b^{5} x^{5} + 126 \, a^{4} b^{4} x^{4} + 84 \, a^{5} b^{3} x^{3} + 36 \, a^{6} b^{2} x^{2} + 9 \, a^{7} b x + a^{8}}{9 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 88, normalized size = 5.18 \[ -\frac {\frac {a^8}{9}+a^7\,b\,x+4\,a^6\,b^2\,x^2+\frac {28\,a^5\,b^3\,x^3}{3}+14\,a^4\,b^4\,x^4+14\,a^3\,b^5\,x^5+\frac {28\,a^2\,b^6\,x^6}{3}+4\,a\,b^7\,x^7+b^8\,x^8}{x^9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.73, size = 95, normalized size = 5.59 \[ \frac {- a^{8} - 9 a^{7} b x - 36 a^{6} b^{2} x^{2} - 84 a^{5} b^{3} x^{3} - 126 a^{4} b^{4} x^{4} - 126 a^{3} b^{5} x^{5} - 84 a^{2} b^{6} x^{6} - 36 a b^{7} x^{7} - 9 b^{8} x^{8}}{9 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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