Optimal. Leaf size=144 \[ -\frac{135 a^8 b^2}{22 x^{22/3}}-\frac{120 a^7 b^3}{7 x^7}-\frac{63 a^6 b^4}{2 x^{20/3}}-\frac{756 a^5 b^5}{19 x^{19/3}}-\frac{35 a^4 b^6}{x^6}-\frac{360 a^3 b^7}{17 x^{17/3}}-\frac{135 a^2 b^8}{16 x^{16/3}}-\frac{30 a^9 b}{23 x^{23/3}}-\frac{a^{10}}{8 x^8}-\frac{2 a b^9}{x^5}-\frac{3 b^{10}}{14 x^{14/3}} \]
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Rubi [A] time = 0.0706039, antiderivative size = 144, 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} \[ -\frac{135 a^8 b^2}{22 x^{22/3}}-\frac{120 a^7 b^3}{7 x^7}-\frac{63 a^6 b^4}{2 x^{20/3}}-\frac{756 a^5 b^5}{19 x^{19/3}}-\frac{35 a^4 b^6}{x^6}-\frac{360 a^3 b^7}{17 x^{17/3}}-\frac{135 a^2 b^8}{16 x^{16/3}}-\frac{30 a^9 b}{23 x^{23/3}}-\frac{a^{10}}{8 x^8}-\frac{2 a b^9}{x^5}-\frac{3 b^{10}}{14 x^{14/3}} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{\left (a+b \sqrt [3]{x}\right )^{10}}{x^9} \, dx &=3 \operatorname{Subst}\left (\int \frac{(a+b x)^{10}}{x^{25}} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname{Subst}\left (\int \left (\frac{a^{10}}{x^{25}}+\frac{10 a^9 b}{x^{24}}+\frac{45 a^8 b^2}{x^{23}}+\frac{120 a^7 b^3}{x^{22}}+\frac{210 a^6 b^4}{x^{21}}+\frac{252 a^5 b^5}{x^{20}}+\frac{210 a^4 b^6}{x^{19}}+\frac{120 a^3 b^7}{x^{18}}+\frac{45 a^2 b^8}{x^{17}}+\frac{10 a b^9}{x^{16}}+\frac{b^{10}}{x^{15}}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=-\frac{a^{10}}{8 x^8}-\frac{30 a^9 b}{23 x^{23/3}}-\frac{135 a^8 b^2}{22 x^{22/3}}-\frac{120 a^7 b^3}{7 x^7}-\frac{63 a^6 b^4}{2 x^{20/3}}-\frac{756 a^5 b^5}{19 x^{19/3}}-\frac{35 a^4 b^6}{x^6}-\frac{360 a^3 b^7}{17 x^{17/3}}-\frac{135 a^2 b^8}{16 x^{16/3}}-\frac{2 a b^9}{x^5}-\frac{3 b^{10}}{14 x^{14/3}}\\ \end{align*}
Mathematica [A] time = 0.0575085, size = 144, normalized size = 1. \[ -\frac{135 a^8 b^2}{22 x^{22/3}}-\frac{120 a^7 b^3}{7 x^7}-\frac{63 a^6 b^4}{2 x^{20/3}}-\frac{756 a^5 b^5}{19 x^{19/3}}-\frac{35 a^4 b^6}{x^6}-\frac{360 a^3 b^7}{17 x^{17/3}}-\frac{135 a^2 b^8}{16 x^{16/3}}-\frac{30 a^9 b}{23 x^{23/3}}-\frac{a^{10}}{8 x^8}-\frac{2 a b^9}{x^5}-\frac{3 b^{10}}{14 x^{14/3}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.008, size = 113, normalized size = 0.8 \begin{align*} -{\frac{{a}^{10}}{8\,{x}^{8}}}-{\frac{30\,{a}^{9}b}{23}{x}^{-{\frac{23}{3}}}}-{\frac{135\,{a}^{8}{b}^{2}}{22}{x}^{-{\frac{22}{3}}}}-{\frac{120\,{a}^{7}{b}^{3}}{7\,{x}^{7}}}-{\frac{63\,{a}^{6}{b}^{4}}{2}{x}^{-{\frac{20}{3}}}}-{\frac{756\,{a}^{5}{b}^{5}}{19}{x}^{-{\frac{19}{3}}}}-35\,{\frac{{a}^{4}{b}^{6}}{{x}^{6}}}-{\frac{360\,{a}^{3}{b}^{7}}{17}{x}^{-{\frac{17}{3}}}}-{\frac{135\,{a}^{2}{b}^{8}}{16}{x}^{-{\frac{16}{3}}}}-2\,{\frac{a{b}^{9}}{{x}^{5}}}-{\frac{3\,{b}^{10}}{14}{x}^{-{\frac{14}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.977002, size = 151, normalized size = 1.05 \begin{align*} -\frac{1961256 \, b^{10} x^{\frac{10}{3}} + 18305056 \, a b^{9} x^{3} + 77224455 \, a^{2} b^{8} x^{\frac{8}{3}} + 193818240 \, a^{3} b^{7} x^{\frac{7}{3}} + 320338480 \, a^{4} b^{6} x^{2} + 364174272 \, a^{5} b^{5} x^{\frac{5}{3}} + 288304632 \, a^{6} b^{4} x^{\frac{4}{3}} + 156900480 \, a^{7} b^{3} x + 56163240 \, a^{8} b^{2} x^{\frac{2}{3}} + 11938080 \, a^{9} b x^{\frac{1}{3}} + 1144066 \, a^{10}}{9152528 \, x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.42656, size = 331, normalized size = 2.3 \begin{align*} -\frac{18305056 \, a b^{9} x^{3} + 320338480 \, a^{4} b^{6} x^{2} + 156900480 \, a^{7} b^{3} x + 1144066 \, a^{10} + 73899 \,{\left (1045 \, a^{2} b^{8} x^{2} + 4928 \, a^{5} b^{5} x + 760 \, a^{8} b^{2}\right )} x^{\frac{2}{3}} + 5016 \,{\left (391 \, b^{10} x^{3} + 38640 \, a^{3} b^{7} x^{2} + 57477 \, a^{6} b^{4} x + 2380 \, a^{9} b\right )} x^{\frac{1}{3}}}{9152528 \, x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 29.53, size = 146, normalized size = 1.01 \begin{align*} - \frac{a^{10}}{8 x^{8}} - \frac{30 a^{9} b}{23 x^{\frac{23}{3}}} - \frac{135 a^{8} b^{2}}{22 x^{\frac{22}{3}}} - \frac{120 a^{7} b^{3}}{7 x^{7}} - \frac{63 a^{6} b^{4}}{2 x^{\frac{20}{3}}} - \frac{756 a^{5} b^{5}}{19 x^{\frac{19}{3}}} - \frac{35 a^{4} b^{6}}{x^{6}} - \frac{360 a^{3} b^{7}}{17 x^{\frac{17}{3}}} - \frac{135 a^{2} b^{8}}{16 x^{\frac{16}{3}}} - \frac{2 a b^{9}}{x^{5}} - \frac{3 b^{10}}{14 x^{\frac{14}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18835, size = 151, normalized size = 1.05 \begin{align*} -\frac{1961256 \, b^{10} x^{\frac{10}{3}} + 18305056 \, a b^{9} x^{3} + 77224455 \, a^{2} b^{8} x^{\frac{8}{3}} + 193818240 \, a^{3} b^{7} x^{\frac{7}{3}} + 320338480 \, a^{4} b^{6} x^{2} + 364174272 \, a^{5} b^{5} x^{\frac{5}{3}} + 288304632 \, a^{6} b^{4} x^{\frac{4}{3}} + 156900480 \, a^{7} b^{3} x + 56163240 \, a^{8} b^{2} x^{\frac{2}{3}} + 11938080 \, a^{9} b x^{\frac{1}{3}} + 1144066 \, a^{10}}{9152528 \, x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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