Optimal. Leaf size=215 \[ -\frac{63 a^{13} b^2}{5 x^{25/3}}-\frac{455 a^{12} b^3}{8 x^8}-\frac{4095 a^{11} b^4}{23 x^{23/3}}-\frac{819 a^{10} b^5}{2 x^{22/3}}-\frac{715 a^9 b^6}{x^7}-\frac{3861 a^8 b^7}{4 x^{20/3}}-\frac{19305 a^7 b^8}{19 x^{19/3}}-\frac{5005 a^6 b^9}{6 x^6}-\frac{9009 a^5 b^{10}}{17 x^{17/3}}-\frac{4095 a^4 b^{11}}{16 x^{16/3}}-\frac{91 a^3 b^{12}}{x^5}-\frac{45 a^2 b^{13}}{2 x^{14/3}}-\frac{45 a^{14} b}{26 x^{26/3}}-\frac{a^{15}}{9 x^9}-\frac{45 a b^{14}}{13 x^{13/3}}-\frac{b^{15}}{4 x^4} \]
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Rubi [A] time = 0.112684, antiderivative size = 215, 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} \[ -\frac{63 a^{13} b^2}{5 x^{25/3}}-\frac{455 a^{12} b^3}{8 x^8}-\frac{4095 a^{11} b^4}{23 x^{23/3}}-\frac{819 a^{10} b^5}{2 x^{22/3}}-\frac{715 a^9 b^6}{x^7}-\frac{3861 a^8 b^7}{4 x^{20/3}}-\frac{19305 a^7 b^8}{19 x^{19/3}}-\frac{5005 a^6 b^9}{6 x^6}-\frac{9009 a^5 b^{10}}{17 x^{17/3}}-\frac{4095 a^4 b^{11}}{16 x^{16/3}}-\frac{91 a^3 b^{12}}{x^5}-\frac{45 a^2 b^{13}}{2 x^{14/3}}-\frac{45 a^{14} b}{26 x^{26/3}}-\frac{a^{15}}{9 x^9}-\frac{45 a b^{14}}{13 x^{13/3}}-\frac{b^{15}}{4 x^4} \]
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 )^{15}}{x^{10}} \, dx &=3 \operatorname{Subst}\left (\int \frac{(a+b x)^{15}}{x^{28}} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname{Subst}\left (\int \left (\frac{a^{15}}{x^{28}}+\frac{15 a^{14} b}{x^{27}}+\frac{105 a^{13} b^2}{x^{26}}+\frac{455 a^{12} b^3}{x^{25}}+\frac{1365 a^{11} b^4}{x^{24}}+\frac{3003 a^{10} b^5}{x^{23}}+\frac{5005 a^9 b^6}{x^{22}}+\frac{6435 a^8 b^7}{x^{21}}+\frac{6435 a^7 b^8}{x^{20}}+\frac{5005 a^6 b^9}{x^{19}}+\frac{3003 a^5 b^{10}}{x^{18}}+\frac{1365 a^4 b^{11}}{x^{17}}+\frac{455 a^3 b^{12}}{x^{16}}+\frac{105 a^2 b^{13}}{x^{15}}+\frac{15 a b^{14}}{x^{14}}+\frac{b^{15}}{x^{13}}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=-\frac{a^{15}}{9 x^9}-\frac{45 a^{14} b}{26 x^{26/3}}-\frac{63 a^{13} b^2}{5 x^{25/3}}-\frac{455 a^{12} b^3}{8 x^8}-\frac{4095 a^{11} b^4}{23 x^{23/3}}-\frac{819 a^{10} b^5}{2 x^{22/3}}-\frac{715 a^9 b^6}{x^7}-\frac{3861 a^8 b^7}{4 x^{20/3}}-\frac{19305 a^7 b^8}{19 x^{19/3}}-\frac{5005 a^6 b^9}{6 x^6}-\frac{9009 a^5 b^{10}}{17 x^{17/3}}-\frac{4095 a^4 b^{11}}{16 x^{16/3}}-\frac{91 a^3 b^{12}}{x^5}-\frac{45 a^2 b^{13}}{2 x^{14/3}}-\frac{45 a b^{14}}{13 x^{13/3}}-\frac{b^{15}}{4 x^4}\\ \end{align*}
Mathematica [A] time = 0.109709, size = 215, normalized size = 1. \[ -\frac{63 a^{13} b^2}{5 x^{25/3}}-\frac{455 a^{12} b^3}{8 x^8}-\frac{4095 a^{11} b^4}{23 x^{23/3}}-\frac{819 a^{10} b^5}{2 x^{22/3}}-\frac{715 a^9 b^6}{x^7}-\frac{3861 a^8 b^7}{4 x^{20/3}}-\frac{19305 a^7 b^8}{19 x^{19/3}}-\frac{5005 a^6 b^9}{6 x^6}-\frac{9009 a^5 b^{10}}{17 x^{17/3}}-\frac{4095 a^4 b^{11}}{16 x^{16/3}}-\frac{91 a^3 b^{12}}{x^5}-\frac{45 a^2 b^{13}}{2 x^{14/3}}-\frac{45 a^{14} b}{26 x^{26/3}}-\frac{a^{15}}{9 x^9}-\frac{45 a b^{14}}{13 x^{13/3}}-\frac{b^{15}}{4 x^4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.008, size = 168, normalized size = 0.8 \begin{align*} -{\frac{{a}^{15}}{9\,{x}^{9}}}-{\frac{45\,{a}^{14}b}{26}{x}^{-{\frac{26}{3}}}}-{\frac{63\,{a}^{13}{b}^{2}}{5}{x}^{-{\frac{25}{3}}}}-{\frac{455\,{a}^{12}{b}^{3}}{8\,{x}^{8}}}-{\frac{4095\,{a}^{11}{b}^{4}}{23}{x}^{-{\frac{23}{3}}}}-{\frac{819\,{a}^{10}{b}^{5}}{2}{x}^{-{\frac{22}{3}}}}-715\,{\frac{{a}^{9}{b}^{6}}{{x}^{7}}}-{\frac{3861\,{a}^{8}{b}^{7}}{4}{x}^{-{\frac{20}{3}}}}-{\frac{19305\,{a}^{7}{b}^{8}}{19}{x}^{-{\frac{19}{3}}}}-{\frac{5005\,{a}^{6}{b}^{9}}{6\,{x}^{6}}}-{\frac{9009\,{a}^{5}{b}^{10}}{17}{x}^{-{\frac{17}{3}}}}-{\frac{4095\,{a}^{4}{b}^{11}}{16}{x}^{-{\frac{16}{3}}}}-91\,{\frac{{a}^{3}{b}^{12}}{{x}^{5}}}-{\frac{45\,{a}^{2}{b}^{13}}{2}{x}^{-{\frac{14}{3}}}}-{\frac{45\,a{b}^{14}}{13}{x}^{-{\frac{13}{3}}}}-{\frac{{b}^{15}}{4\,{x}^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.991521, size = 225, normalized size = 1.05 \begin{align*} -\frac{17383860 \, b^{15} x^{5} + 240699600 \, a b^{14} x^{\frac{14}{3}} + 1564547400 \, a^{2} b^{13} x^{\frac{13}{3}} + 6327725040 \, a^{3} b^{12} x^{4} + 17796726675 \, a^{4} b^{11} x^{\frac{11}{3}} + 36849692880 \, a^{5} b^{10} x^{\frac{10}{3}} + 58004146200 \, a^{6} b^{9} x^{3} + 70651666800 \, a^{7} b^{8} x^{\frac{8}{3}} + 67119083460 \, a^{8} b^{7} x^{\frac{7}{3}} + 49717839600 \, a^{9} b^{6} x^{2} + 28474762680 \, a^{10} b^{5} x^{\frac{5}{3}} + 12380331600 \, a^{11} b^{4} x^{\frac{4}{3}} + 3954828150 \, a^{12} b^{3} x + 876146544 \, a^{13} b^{2} x^{\frac{2}{3}} + 120349800 \, a^{14} b x^{\frac{1}{3}} + 7726160 \, a^{15}}{69535440 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.66385, size = 520, normalized size = 2.42 \begin{align*} -\frac{17383860 \, b^{15} x^{5} + 6327725040 \, a^{3} b^{12} x^{4} + 58004146200 \, a^{6} b^{9} x^{3} + 49717839600 \, a^{9} b^{6} x^{2} + 3954828150 \, a^{12} b^{3} x + 7726160 \, a^{15} + 31671 \,{\left (7600 \, a b^{14} x^{4} + 561925 \, a^{4} b^{11} x^{3} + 2230800 \, a^{7} b^{8} x^{2} + 899080 \, a^{10} b^{5} x + 27664 \, a^{13} b^{2}\right )} x^{\frac{2}{3}} + 30780 \,{\left (50830 \, a^{2} b^{13} x^{4} + 1197196 \, a^{5} b^{10} x^{3} + 2180607 \, a^{8} b^{7} x^{2} + 402220 \, a^{11} b^{4} x + 3910 \, a^{14} b\right )} x^{\frac{1}{3}}}{69535440 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 44.7693, size = 218, normalized size = 1.01 \begin{align*} - \frac{a^{15}}{9 x^{9}} - \frac{45 a^{14} b}{26 x^{\frac{26}{3}}} - \frac{63 a^{13} b^{2}}{5 x^{\frac{25}{3}}} - \frac{455 a^{12} b^{3}}{8 x^{8}} - \frac{4095 a^{11} b^{4}}{23 x^{\frac{23}{3}}} - \frac{819 a^{10} b^{5}}{2 x^{\frac{22}{3}}} - \frac{715 a^{9} b^{6}}{x^{7}} - \frac{3861 a^{8} b^{7}}{4 x^{\frac{20}{3}}} - \frac{19305 a^{7} b^{8}}{19 x^{\frac{19}{3}}} - \frac{5005 a^{6} b^{9}}{6 x^{6}} - \frac{9009 a^{5} b^{10}}{17 x^{\frac{17}{3}}} - \frac{4095 a^{4} b^{11}}{16 x^{\frac{16}{3}}} - \frac{91 a^{3} b^{12}}{x^{5}} - \frac{45 a^{2} b^{13}}{2 x^{\frac{14}{3}}} - \frac{45 a b^{14}}{13 x^{\frac{13}{3}}} - \frac{b^{15}}{4 x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.21269, size = 225, normalized size = 1.05 \begin{align*} -\frac{17383860 \, b^{15} x^{5} + 240699600 \, a b^{14} x^{\frac{14}{3}} + 1564547400 \, a^{2} b^{13} x^{\frac{13}{3}} + 6327725040 \, a^{3} b^{12} x^{4} + 17796726675 \, a^{4} b^{11} x^{\frac{11}{3}} + 36849692880 \, a^{5} b^{10} x^{\frac{10}{3}} + 58004146200 \, a^{6} b^{9} x^{3} + 70651666800 \, a^{7} b^{8} x^{\frac{8}{3}} + 67119083460 \, a^{8} b^{7} x^{\frac{7}{3}} + 49717839600 \, a^{9} b^{6} x^{2} + 28474762680 \, a^{10} b^{5} x^{\frac{5}{3}} + 12380331600 \, a^{11} b^{4} x^{\frac{4}{3}} + 3954828150 \, a^{12} b^{3} x + 876146544 \, a^{13} b^{2} x^{\frac{2}{3}} + 120349800 \, a^{14} b x^{\frac{1}{3}} + 7726160 \, a^{15}}{69535440 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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