Optimal. Leaf size=69 \[ -\frac{5 a^3 b^2}{4 x^8}-\frac{10 a^2 b^3}{7 x^7}-\frac{5 a^4 b}{9 x^9}-\frac{a^5}{10 x^{10}}-\frac{5 a b^4}{6 x^6}-\frac{b^5}{5 x^5} \]
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Rubi [A] time = 0.0205153, antiderivative size = 69, 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} \[ -\frac{5 a^3 b^2}{4 x^8}-\frac{10 a^2 b^3}{7 x^7}-\frac{5 a^4 b}{9 x^9}-\frac{a^5}{10 x^{10}}-\frac{5 a b^4}{6 x^6}-\frac{b^5}{5 x^5} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{(a+b x)^5}{x^{11}} \, dx &=\int \left (\frac{a^5}{x^{11}}+\frac{5 a^4 b}{x^{10}}+\frac{10 a^3 b^2}{x^9}+\frac{10 a^2 b^3}{x^8}+\frac{5 a b^4}{x^7}+\frac{b^5}{x^6}\right ) \, dx\\ &=-\frac{a^5}{10 x^{10}}-\frac{5 a^4 b}{9 x^9}-\frac{5 a^3 b^2}{4 x^8}-\frac{10 a^2 b^3}{7 x^7}-\frac{5 a b^4}{6 x^6}-\frac{b^5}{5 x^5}\\ \end{align*}
Mathematica [A] time = 0.0061435, size = 69, normalized size = 1. \[ -\frac{5 a^3 b^2}{4 x^8}-\frac{10 a^2 b^3}{7 x^7}-\frac{5 a^4 b}{9 x^9}-\frac{a^5}{10 x^{10}}-\frac{5 a b^4}{6 x^6}-\frac{b^5}{5 x^5} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 58, normalized size = 0.8 \begin{align*} -{\frac{{a}^{5}}{10\,{x}^{10}}}-{\frac{5\,{a}^{4}b}{9\,{x}^{9}}}-{\frac{5\,{a}^{3}{b}^{2}}{4\,{x}^{8}}}-{\frac{10\,{a}^{2}{b}^{3}}{7\,{x}^{7}}}-{\frac{5\,a{b}^{4}}{6\,{x}^{6}}}-{\frac{{b}^{5}}{5\,{x}^{5}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.05087, size = 77, normalized size = 1.12 \begin{align*} -\frac{252 \, b^{5} x^{5} + 1050 \, a b^{4} x^{4} + 1800 \, a^{2} b^{3} x^{3} + 1575 \, a^{3} b^{2} x^{2} + 700 \, a^{4} b x + 126 \, a^{5}}{1260 \, x^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.31939, size = 144, normalized size = 2.09 \begin{align*} -\frac{252 \, b^{5} x^{5} + 1050 \, a b^{4} x^{4} + 1800 \, a^{2} b^{3} x^{3} + 1575 \, a^{3} b^{2} x^{2} + 700 \, a^{4} b x + 126 \, a^{5}}{1260 \, x^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.738283, size = 61, normalized size = 0.88 \begin{align*} - \frac{126 a^{5} + 700 a^{4} b x + 1575 a^{3} b^{2} x^{2} + 1800 a^{2} b^{3} x^{3} + 1050 a b^{4} x^{4} + 252 b^{5} x^{5}}{1260 x^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17538, size = 77, normalized size = 1.12 \begin{align*} -\frac{252 \, b^{5} x^{5} + 1050 \, a b^{4} x^{4} + 1800 \, a^{2} b^{3} x^{3} + 1575 \, a^{3} b^{2} x^{2} + 700 \, a^{4} b x + 126 \, a^{5}}{1260 \, x^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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