Optimal. Leaf size=140 \[ -\frac{5 a^8 b^2}{x^9}-\frac{240 a^7 b^3}{17 x^{17/2}}-\frac{105 a^6 b^4}{4 x^8}-\frac{168 a^5 b^5}{5 x^{15/2}}-\frac{30 a^4 b^6}{x^7}-\frac{240 a^3 b^7}{13 x^{13/2}}-\frac{15 a^2 b^8}{2 x^6}-\frac{20 a^9 b}{19 x^{19/2}}-\frac{a^{10}}{10 x^{10}}-\frac{20 a b^9}{11 x^{11/2}}-\frac{b^{10}}{5 x^5} \]
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Rubi [A] time = 0.0662356, antiderivative size = 140, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {266, 43} \[ -\frac{5 a^8 b^2}{x^9}-\frac{240 a^7 b^3}{17 x^{17/2}}-\frac{105 a^6 b^4}{4 x^8}-\frac{168 a^5 b^5}{5 x^{15/2}}-\frac{30 a^4 b^6}{x^7}-\frac{240 a^3 b^7}{13 x^{13/2}}-\frac{15 a^2 b^8}{2 x^6}-\frac{20 a^9 b}{19 x^{19/2}}-\frac{a^{10}}{10 x^{10}}-\frac{20 a b^9}{11 x^{11/2}}-\frac{b^{10}}{5 x^5} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{\left (a+b \sqrt{x}\right )^{10}}{x^{11}} \, dx &=2 \operatorname{Subst}\left (\int \frac{(a+b x)^{10}}{x^{21}} \, dx,x,\sqrt{x}\right )\\ &=2 \operatorname{Subst}\left (\int \left (\frac{a^{10}}{x^{21}}+\frac{10 a^9 b}{x^{20}}+\frac{45 a^8 b^2}{x^{19}}+\frac{120 a^7 b^3}{x^{18}}+\frac{210 a^6 b^4}{x^{17}}+\frac{252 a^5 b^5}{x^{16}}+\frac{210 a^4 b^6}{x^{15}}+\frac{120 a^3 b^7}{x^{14}}+\frac{45 a^2 b^8}{x^{13}}+\frac{10 a b^9}{x^{12}}+\frac{b^{10}}{x^{11}}\right ) \, dx,x,\sqrt{x}\right )\\ &=-\frac{a^{10}}{10 x^{10}}-\frac{20 a^9 b}{19 x^{19/2}}-\frac{5 a^8 b^2}{x^9}-\frac{240 a^7 b^3}{17 x^{17/2}}-\frac{105 a^6 b^4}{4 x^8}-\frac{168 a^5 b^5}{5 x^{15/2}}-\frac{30 a^4 b^6}{x^7}-\frac{240 a^3 b^7}{13 x^{13/2}}-\frac{15 a^2 b^8}{2 x^6}-\frac{20 a b^9}{11 x^{11/2}}-\frac{b^{10}}{5 x^5}\\ \end{align*}
Mathematica [A] time = 0.0569377, size = 140, normalized size = 1. \[ -\frac{5 a^8 b^2}{x^9}-\frac{240 a^7 b^3}{17 x^{17/2}}-\frac{105 a^6 b^4}{4 x^8}-\frac{168 a^5 b^5}{5 x^{15/2}}-\frac{30 a^4 b^6}{x^7}-\frac{240 a^3 b^7}{13 x^{13/2}}-\frac{15 a^2 b^8}{2 x^6}-\frac{20 a^9 b}{19 x^{19/2}}-\frac{a^{10}}{10 x^{10}}-\frac{20 a b^9}{11 x^{11/2}}-\frac{b^{10}}{5 x^5} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 113, normalized size = 0.8 \begin{align*} -{\frac{{a}^{10}}{10\,{x}^{10}}}-{\frac{20\,{a}^{9}b}{19}{x}^{-{\frac{19}{2}}}}-5\,{\frac{{a}^{8}{b}^{2}}{{x}^{9}}}-{\frac{240\,{a}^{7}{b}^{3}}{17}{x}^{-{\frac{17}{2}}}}-{\frac{105\,{a}^{6}{b}^{4}}{4\,{x}^{8}}}-{\frac{168\,{a}^{5}{b}^{5}}{5}{x}^{-{\frac{15}{2}}}}-30\,{\frac{{a}^{4}{b}^{6}}{{x}^{7}}}-{\frac{240\,{a}^{3}{b}^{7}}{13}{x}^{-{\frac{13}{2}}}}-{\frac{15\,{a}^{2}{b}^{8}}{2\,{x}^{6}}}-{\frac{20\,a{b}^{9}}{11}{x}^{-{\frac{11}{2}}}}-{\frac{{b}^{10}}{5\,{x}^{5}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.963822, size = 151, normalized size = 1.08 \begin{align*} -\frac{184756 \, b^{10} x^{5} + 1679600 \, a b^{9} x^{\frac{9}{2}} + 6928350 \, a^{2} b^{8} x^{4} + 17054400 \, a^{3} b^{7} x^{\frac{7}{2}} + 27713400 \, a^{4} b^{6} x^{3} + 31039008 \, a^{5} b^{5} x^{\frac{5}{2}} + 24249225 \, a^{6} b^{4} x^{2} + 13041600 \, a^{7} b^{3} x^{\frac{3}{2}} + 4618900 \, a^{8} b^{2} x + 972400 \, a^{9} b \sqrt{x} + 92378 \, a^{10}}{923780 \, x^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.27818, size = 329, normalized size = 2.35 \begin{align*} -\frac{184756 \, b^{10} x^{5} + 6928350 \, a^{2} b^{8} x^{4} + 27713400 \, a^{4} b^{6} x^{3} + 24249225 \, a^{6} b^{4} x^{2} + 4618900 \, a^{8} b^{2} x + 92378 \, a^{10} + 16 \,{\left (104975 \, a b^{9} x^{4} + 1065900 \, a^{3} b^{7} x^{3} + 1939938 \, a^{5} b^{5} x^{2} + 815100 \, a^{7} b^{3} x + 60775 \, a^{9} b\right )} \sqrt{x}}{923780 \, x^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 13.7908, size = 141, normalized size = 1.01 \begin{align*} - \frac{a^{10}}{10 x^{10}} - \frac{20 a^{9} b}{19 x^{\frac{19}{2}}} - \frac{5 a^{8} b^{2}}{x^{9}} - \frac{240 a^{7} b^{3}}{17 x^{\frac{17}{2}}} - \frac{105 a^{6} b^{4}}{4 x^{8}} - \frac{168 a^{5} b^{5}}{5 x^{\frac{15}{2}}} - \frac{30 a^{4} b^{6}}{x^{7}} - \frac{240 a^{3} b^{7}}{13 x^{\frac{13}{2}}} - \frac{15 a^{2} b^{8}}{2 x^{6}} - \frac{20 a b^{9}}{11 x^{\frac{11}{2}}} - \frac{b^{10}}{5 x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16607, size = 151, normalized size = 1.08 \begin{align*} -\frac{184756 \, b^{10} x^{5} + 1679600 \, a b^{9} x^{\frac{9}{2}} + 6928350 \, a^{2} b^{8} x^{4} + 17054400 \, a^{3} b^{7} x^{\frac{7}{2}} + 27713400 \, a^{4} b^{6} x^{3} + 31039008 \, a^{5} b^{5} x^{\frac{5}{2}} + 24249225 \, a^{6} b^{4} x^{2} + 13041600 \, a^{7} b^{3} x^{\frac{3}{2}} + 4618900 \, a^{8} b^{2} x + 972400 \, a^{9} b \sqrt{x} + 92378 \, a^{10}}{923780 \, x^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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