Optimal. Leaf size=67 \[ -\frac{10 a^3 b^2}{7 x^7}-\frac{5 a^2 b^3}{3 x^6}-\frac{5 a^4 b}{8 x^8}-\frac{a^5}{9 x^9}-\frac{a b^4}{x^5}-\frac{b^5}{4 x^4} \]
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Rubi [A] time = 0.022074, antiderivative size = 67, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0116235, size = 67, normalized size = 1. \[ -\frac{10 a^3 b^2}{7 x^7}-\frac{5 a^2 b^3}{3 x^6}-\frac{5 a^4 b}{8 x^8}-\frac{a^5}{9 x^9}-\frac{a b^4}{x^5}-\frac{b^5}{4 x^4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 58, normalized size = 0.9 \begin{align*} -{\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*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.05083, size = 77, normalized size = 1.15 \begin{align*} -\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}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.57443, size = 136, normalized size = 2.03 \begin{align*} -\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}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.757735, size = 61, normalized size = 0.91 \begin{align*} - \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}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18753, size = 77, normalized size = 1.15 \begin{align*} -\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}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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