Optimal. Leaf size=56 \[ -\frac {a^4}{9 x^9}-\frac {a^3 b}{2 x^8}-\frac {6 a^2 b^2}{7 x^7}-\frac {2 a b^3}{3 x^6}-\frac {b^4}{5 x^5} \]
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Rubi [A] time = 0.02, antiderivative size = 56, 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} \[ -\frac {6 a^2 b^2}{7 x^7}-\frac {a^3 b}{2 x^8}-\frac {a^4}{9 x^9}-\frac {2 a b^3}{3 x^6}-\frac {b^4}{5 x^5} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {(a+b x)^4}{x^{10}} \, dx &=\int \left (\frac {a^4}{x^{10}}+\frac {4 a^3 b}{x^9}+\frac {6 a^2 b^2}{x^8}+\frac {4 a b^3}{x^7}+\frac {b^4}{x^6}\right ) \, dx\\ &=-\frac {a^4}{9 x^9}-\frac {a^3 b}{2 x^8}-\frac {6 a^2 b^2}{7 x^7}-\frac {2 a b^3}{3 x^6}-\frac {b^4}{5 x^5}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 56, normalized size = 1.00 \[ -\frac {a^4}{9 x^9}-\frac {a^3 b}{2 x^8}-\frac {6 a^2 b^2}{7 x^7}-\frac {2 a b^3}{3 x^6}-\frac {b^4}{5 x^5} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 46, normalized size = 0.82 \[ -\frac {126 \, b^{4} x^{4} + 420 \, a b^{3} x^{3} + 540 \, a^{2} b^{2} x^{2} + 315 \, a^{3} b x + 70 \, a^{4}}{630 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.25, size = 46, normalized size = 0.82 \[ -\frac {126 \, b^{4} x^{4} + 420 \, a b^{3} x^{3} + 540 \, a^{2} b^{2} x^{2} + 315 \, a^{3} b x + 70 \, a^{4}}{630 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 47, normalized size = 0.84 \[ -\frac {b^{4}}{5 x^{5}}-\frac {2 a \,b^{3}}{3 x^{6}}-\frac {6 a^{2} b^{2}}{7 x^{7}}-\frac {a^{3} b}{2 x^{8}}-\frac {a^{4}}{9 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.34, size = 46, normalized size = 0.82 \[ -\frac {126 \, b^{4} x^{4} + 420 \, a b^{3} x^{3} + 540 \, a^{2} b^{2} x^{2} + 315 \, a^{3} b x + 70 \, a^{4}}{630 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 46, normalized size = 0.82 \[ -\frac {\frac {a^4}{9}+\frac {a^3\,b\,x}{2}+\frac {6\,a^2\,b^2\,x^2}{7}+\frac {2\,a\,b^3\,x^3}{3}+\frac {b^4\,x^4}{5}}{x^9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.50, size = 49, normalized size = 0.88 \[ \frac {- 70 a^{4} - 315 a^{3} b x - 540 a^{2} b^{2} x^{2} - 420 a b^{3} x^{3} - 126 b^{4} x^{4}}{630 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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