Optimal. Leaf size=67 \[ -\frac {a^5}{9 x^9}-\frac {5 a^4 b}{8 x^8}-\frac {10 a^3 b^2}{7 x^7}-\frac {5 a^2 b^3}{3 x^6}-\frac {a b^4}{x^5}-\frac {b^5}{4 x^4} \]
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Rubi [A] time = 0.02, antiderivative size = 67, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {43} \[ -\frac {10 a^3 b^2}{7 x^7}-\frac {5 a^2 b^3}{3 x^6}-\frac {5 a^4 b}{8 x^8}-\frac {a^5}{9 x^9}-\frac {a b^4}{x^5}-\frac {b^5}{4 x^4} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {(a+b x)^5}{x^{10}} \, dx &=\int \left (\frac {a^5}{x^{10}}+\frac {5 a^4 b}{x^9}+\frac {10 a^3 b^2}{x^8}+\frac {10 a^2 b^3}{x^7}+\frac {5 a b^4}{x^6}+\frac {b^5}{x^5}\right ) \, dx\\ &=-\frac {a^5}{9 x^9}-\frac {5 a^4 b}{8 x^8}-\frac {10 a^3 b^2}{7 x^7}-\frac {5 a^2 b^3}{3 x^6}-\frac {a b^4}{x^5}-\frac {b^5}{4 x^4}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 67, normalized size = 1.00 \[ -\frac {a^5}{9 x^9}-\frac {5 a^4 b}{8 x^8}-\frac {10 a^3 b^2}{7 x^7}-\frac {5 a^2 b^3}{3 x^6}-\frac {a b^4}{x^5}-\frac {b^5}{4 x^4} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 57, normalized size = 0.85 \[ -\frac {126 \, b^{5} x^{5} + 504 \, a b^{4} x^{4} + 840 \, a^{2} b^{3} x^{3} + 720 \, a^{3} b^{2} x^{2} + 315 \, a^{4} b x + 56 \, a^{5}}{504 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.01, size = 57, normalized size = 0.85 \[ -\frac {126 \, b^{5} x^{5} + 504 \, a b^{4} x^{4} + 840 \, a^{2} b^{3} x^{3} + 720 \, a^{3} b^{2} x^{2} + 315 \, a^{4} b x + 56 \, a^{5}}{504 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 58, normalized size = 0.87 \[ -\frac {b^{5}}{4 x^{4}}-\frac {a \,b^{4}}{x^{5}}-\frac {5 a^{2} b^{3}}{3 x^{6}}-\frac {10 a^{3} b^{2}}{7 x^{7}}-\frac {5 a^{4} b}{8 x^{8}}-\frac {a^{5}}{9 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.36, size = 57, normalized size = 0.85 \[ -\frac {126 \, b^{5} x^{5} + 504 \, a b^{4} x^{4} + 840 \, a^{2} b^{3} x^{3} + 720 \, a^{3} b^{2} x^{2} + 315 \, a^{4} b x + 56 \, a^{5}}{504 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.00, size = 56, normalized size = 0.84 \[ -\frac {\frac {a^5}{9}+\frac {5\,a^4\,b\,x}{8}+\frac {10\,a^3\,b^2\,x^2}{7}+\frac {5\,a^2\,b^3\,x^3}{3}+a\,b^4\,x^4+\frac {b^5\,x^5}{4}}{x^9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.49, size = 61, normalized size = 0.91 \[ \frac {- 56 a^{5} - 315 a^{4} b x - 720 a^{3} b^{2} x^{2} - 840 a^{2} b^{3} x^{3} - 504 a b^{4} x^{4} - 126 b^{5} x^{5}}{504 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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