Optimal. Leaf size=67 \[ -\frac{a^3 b^2}{x^{10}}-\frac{10 a^2 b^3}{9 x^9}-\frac{5 a^4 b}{11 x^{11}}-\frac{a^5}{12 x^{12}}-\frac{5 a b^4}{8 x^8}-\frac{b^5}{7 x^7} \]
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Rubi [A] time = 0.0207173, 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} \[ -\frac{a^3 b^2}{x^{10}}-\frac{10 a^2 b^3}{9 x^9}-\frac{5 a^4 b}{11 x^{11}}-\frac{a^5}{12 x^{12}}-\frac{5 a b^4}{8 x^8}-\frac{b^5}{7 x^7} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{(a+b x)^5}{x^{13}} \, dx &=\int \left (\frac{a^5}{x^{13}}+\frac{5 a^4 b}{x^{12}}+\frac{10 a^3 b^2}{x^{11}}+\frac{10 a^2 b^3}{x^{10}}+\frac{5 a b^4}{x^9}+\frac{b^5}{x^8}\right ) \, dx\\ &=-\frac{a^5}{12 x^{12}}-\frac{5 a^4 b}{11 x^{11}}-\frac{a^3 b^2}{x^{10}}-\frac{10 a^2 b^3}{9 x^9}-\frac{5 a b^4}{8 x^8}-\frac{b^5}{7 x^7}\\ \end{align*}
Mathematica [A] time = 0.0073379, size = 67, normalized size = 1. \[ -\frac{a^3 b^2}{x^{10}}-\frac{10 a^2 b^3}{9 x^9}-\frac{5 a^4 b}{11 x^{11}}-\frac{a^5}{12 x^{12}}-\frac{5 a b^4}{8 x^8}-\frac{b^5}{7 x^7} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 58, normalized size = 0.9 \begin{align*} -{\frac{{a}^{5}}{12\,{x}^{12}}}-{\frac{5\,{a}^{4}b}{11\,{x}^{11}}}-{\frac{{a}^{3}{b}^{2}}{{x}^{10}}}-{\frac{10\,{a}^{2}{b}^{3}}{9\,{x}^{9}}}-{\frac{5\,a{b}^{4}}{8\,{x}^{8}}}-{\frac{{b}^{5}}{7\,{x}^{7}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.999046, size = 77, normalized size = 1.15 \begin{align*} -\frac{792 \, b^{5} x^{5} + 3465 \, a b^{4} x^{4} + 6160 \, a^{2} b^{3} x^{3} + 5544 \, a^{3} b^{2} x^{2} + 2520 \, a^{4} b x + 462 \, a^{5}}{5544 \, x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.36745, size = 146, normalized size = 2.18 \begin{align*} -\frac{792 \, b^{5} x^{5} + 3465 \, a b^{4} x^{4} + 6160 \, a^{2} b^{3} x^{3} + 5544 \, a^{3} b^{2} x^{2} + 2520 \, a^{4} b x + 462 \, a^{5}}{5544 \, x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.08598, size = 61, normalized size = 0.91 \begin{align*} - \frac{462 a^{5} + 2520 a^{4} b x + 5544 a^{3} b^{2} x^{2} + 6160 a^{2} b^{3} x^{3} + 3465 a b^{4} x^{4} + 792 b^{5} x^{5}}{5544 x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19159, size = 77, normalized size = 1.15 \begin{align*} -\frac{792 \, b^{5} x^{5} + 3465 \, a b^{4} x^{4} + 6160 \, a^{2} b^{3} x^{3} + 5544 \, a^{3} b^{2} x^{2} + 2520 \, a^{4} b x + 462 \, a^{5}}{5544 \, x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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