Optimal. Leaf size=126 \[ -\frac{45 a^8 b^2}{17 x^{17}}-\frac{15 a^7 b^3}{2 x^{16}}-\frac{14 a^6 b^4}{x^{15}}-\frac{18 a^5 b^5}{x^{14}}-\frac{210 a^4 b^6}{13 x^{13}}-\frac{10 a^3 b^7}{x^{12}}-\frac{45 a^2 b^8}{11 x^{11}}-\frac{5 a^9 b}{9 x^{18}}-\frac{a^{10}}{19 x^{19}}-\frac{a b^9}{x^{10}}-\frac{b^{10}}{9 x^9} \]
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Rubi [A] time = 0.0493592, antiderivative size = 126, 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} \[ -\frac{45 a^8 b^2}{17 x^{17}}-\frac{15 a^7 b^3}{2 x^{16}}-\frac{14 a^6 b^4}{x^{15}}-\frac{18 a^5 b^5}{x^{14}}-\frac{210 a^4 b^6}{13 x^{13}}-\frac{10 a^3 b^7}{x^{12}}-\frac{45 a^2 b^8}{11 x^{11}}-\frac{5 a^9 b}{9 x^{18}}-\frac{a^{10}}{19 x^{19}}-\frac{a b^9}{x^{10}}-\frac{b^{10}}{9 x^9} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{(a+b x)^{10}}{x^{20}} \, dx &=\int \left (\frac{a^{10}}{x^{20}}+\frac{10 a^9 b}{x^{19}}+\frac{45 a^8 b^2}{x^{18}}+\frac{120 a^7 b^3}{x^{17}}+\frac{210 a^6 b^4}{x^{16}}+\frac{252 a^5 b^5}{x^{15}}+\frac{210 a^4 b^6}{x^{14}}+\frac{120 a^3 b^7}{x^{13}}+\frac{45 a^2 b^8}{x^{12}}+\frac{10 a b^9}{x^{11}}+\frac{b^{10}}{x^{10}}\right ) \, dx\\ &=-\frac{a^{10}}{19 x^{19}}-\frac{5 a^9 b}{9 x^{18}}-\frac{45 a^8 b^2}{17 x^{17}}-\frac{15 a^7 b^3}{2 x^{16}}-\frac{14 a^6 b^4}{x^{15}}-\frac{18 a^5 b^5}{x^{14}}-\frac{210 a^4 b^6}{13 x^{13}}-\frac{10 a^3 b^7}{x^{12}}-\frac{45 a^2 b^8}{11 x^{11}}-\frac{a b^9}{x^{10}}-\frac{b^{10}}{9 x^9}\\ \end{align*}
Mathematica [A] time = 0.0072441, size = 126, normalized size = 1. \[ -\frac{45 a^8 b^2}{17 x^{17}}-\frac{15 a^7 b^3}{2 x^{16}}-\frac{14 a^6 b^4}{x^{15}}-\frac{18 a^5 b^5}{x^{14}}-\frac{210 a^4 b^6}{13 x^{13}}-\frac{10 a^3 b^7}{x^{12}}-\frac{45 a^2 b^8}{11 x^{11}}-\frac{5 a^9 b}{9 x^{18}}-\frac{a^{10}}{19 x^{19}}-\frac{a b^9}{x^{10}}-\frac{b^{10}}{9 x^9} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 113, normalized size = 0.9 \begin{align*} -{\frac{{a}^{10}}{19\,{x}^{19}}}-{\frac{5\,{a}^{9}b}{9\,{x}^{18}}}-{\frac{45\,{a}^{8}{b}^{2}}{17\,{x}^{17}}}-{\frac{15\,{a}^{7}{b}^{3}}{2\,{x}^{16}}}-14\,{\frac{{a}^{6}{b}^{4}}{{x}^{15}}}-18\,{\frac{{a}^{5}{b}^{5}}{{x}^{14}}}-{\frac{210\,{a}^{4}{b}^{6}}{13\,{x}^{13}}}-10\,{\frac{{a}^{3}{b}^{7}}{{x}^{12}}}-{\frac{45\,{a}^{2}{b}^{8}}{11\,{x}^{11}}}-{\frac{a{b}^{9}}{{x}^{10}}}-{\frac{{b}^{10}}{9\,{x}^{9}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0694, size = 151, normalized size = 1.2 \begin{align*} -\frac{92378 \, b^{10} x^{10} + 831402 \, a b^{9} x^{9} + 3401190 \, a^{2} b^{8} x^{8} + 8314020 \, a^{3} b^{7} x^{7} + 13430340 \, a^{4} b^{6} x^{6} + 14965236 \, a^{5} b^{5} x^{5} + 11639628 \, a^{6} b^{4} x^{4} + 6235515 \, a^{7} b^{3} x^{3} + 2200770 \, a^{8} b^{2} x^{2} + 461890 \, a^{9} b x + 43758 \, a^{10}}{831402 \, x^{19}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.50204, size = 324, normalized size = 2.57 \begin{align*} -\frac{92378 \, b^{10} x^{10} + 831402 \, a b^{9} x^{9} + 3401190 \, a^{2} b^{8} x^{8} + 8314020 \, a^{3} b^{7} x^{7} + 13430340 \, a^{4} b^{6} x^{6} + 14965236 \, a^{5} b^{5} x^{5} + 11639628 \, a^{6} b^{4} x^{4} + 6235515 \, a^{7} b^{3} x^{3} + 2200770 \, a^{8} b^{2} x^{2} + 461890 \, a^{9} b x + 43758 \, a^{10}}{831402 \, x^{19}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.03177, size = 121, normalized size = 0.96 \begin{align*} - \frac{43758 a^{10} + 461890 a^{9} b x + 2200770 a^{8} b^{2} x^{2} + 6235515 a^{7} b^{3} x^{3} + 11639628 a^{6} b^{4} x^{4} + 14965236 a^{5} b^{5} x^{5} + 13430340 a^{4} b^{6} x^{6} + 8314020 a^{3} b^{7} x^{7} + 3401190 a^{2} b^{8} x^{8} + 831402 a b^{9} x^{9} + 92378 b^{10} x^{10}}{831402 x^{19}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19186, size = 151, normalized size = 1.2 \begin{align*} -\frac{92378 \, b^{10} x^{10} + 831402 \, a b^{9} x^{9} + 3401190 \, a^{2} b^{8} x^{8} + 8314020 \, a^{3} b^{7} x^{7} + 13430340 \, a^{4} b^{6} x^{6} + 14965236 \, a^{5} b^{5} x^{5} + 11639628 \, a^{6} b^{4} x^{4} + 6235515 \, a^{7} b^{3} x^{3} + 2200770 \, a^{8} b^{2} x^{2} + 461890 \, a^{9} b x + 43758 \, a^{10}}{831402 \, x^{19}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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