Optimal. Leaf size=43 \[ -\frac {a^3}{9 x^9}-\frac {3 a^2 b}{8 x^8}-\frac {3 a b^2}{7 x^7}-\frac {b^3}{6 x^6} \]
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Rubi [A] time = 0.01, antiderivative size = 43, 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} \[ -\frac {3 a^2 b}{8 x^8}-\frac {a^3}{9 x^9}-\frac {3 a b^2}{7 x^7}-\frac {b^3}{6 x^6} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {(a+b x)^3}{x^{10}} \, dx &=\int \left (\frac {a^3}{x^{10}}+\frac {3 a^2 b}{x^9}+\frac {3 a b^2}{x^8}+\frac {b^3}{x^7}\right ) \, dx\\ &=-\frac {a^3}{9 x^9}-\frac {3 a^2 b}{8 x^8}-\frac {3 a b^2}{7 x^7}-\frac {b^3}{6 x^6}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 43, normalized size = 1.00 \[ -\frac {a^3}{9 x^9}-\frac {3 a^2 b}{8 x^8}-\frac {3 a b^2}{7 x^7}-\frac {b^3}{6 x^6} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.47, size = 35, normalized size = 0.81 \[ -\frac {84 \, b^{3} x^{3} + 216 \, a b^{2} x^{2} + 189 \, a^{2} b x + 56 \, a^{3}}{504 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.09, size = 35, normalized size = 0.81 \[ -\frac {84 \, b^{3} x^{3} + 216 \, a b^{2} x^{2} + 189 \, a^{2} b x + 56 \, a^{3}}{504 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 36, normalized size = 0.84 \[ -\frac {b^{3}}{6 x^{6}}-\frac {3 a \,b^{2}}{7 x^{7}}-\frac {3 a^{2} b}{8 x^{8}}-\frac {a^{3}}{9 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.35, size = 35, normalized size = 0.81 \[ -\frac {84 \, b^{3} x^{3} + 216 \, a b^{2} x^{2} + 189 \, a^{2} b x + 56 \, a^{3}}{504 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 35, normalized size = 0.81 \[ -\frac {\frac {a^3}{9}+\frac {3\,a^2\,b\,x}{8}+\frac {3\,a\,b^2\,x^2}{7}+\frac {b^3\,x^3}{6}}{x^9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.38, size = 37, normalized size = 0.86 \[ \frac {- 56 a^{3} - 189 a^{2} b x - 216 a b^{2} x^{2} - 84 b^{3} x^{3}}{504 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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