Optimal. Leaf size=211 \[ -\frac{a^{15}}{5 x^5}-\frac{45 a^{14} b}{14 x^{14/3}}-\frac{315 a^{13} b^2}{13 x^{13/3}}-\frac{455 a^{12} b^3}{4 x^4}-\frac{4095 a^{11} b^4}{11 x^{11/3}}-\frac{9009 a^{10} b^5}{10 x^{10/3}}-\frac{5005 a^9 b^6}{3 x^3}-\frac{19305 a^8 b^7}{8 x^{8/3}}-\frac{19305 a^7 b^8}{7 x^{7/3}}-\frac{5005 a^6 b^9}{2 x^2}-\frac{9009 a^5 b^{10}}{5 x^{5/3}}-\frac{4095 a^4 b^{11}}{4 x^{4/3}}-\frac{455 a^3 b^{12}}{x}-\frac{315 a^2 b^{13}}{2 x^{2/3}}-\frac{45 a b^{14}}{\sqrt [3]{x}}+b^{15} \log (x) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.300943, antiderivative size = 211, 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 \[ -\frac{a^{15}}{5 x^5}-\frac{45 a^{14} b}{14 x^{14/3}}-\frac{315 a^{13} b^2}{13 x^{13/3}}-\frac{455 a^{12} b^3}{4 x^4}-\frac{4095 a^{11} b^4}{11 x^{11/3}}-\frac{9009 a^{10} b^5}{10 x^{10/3}}-\frac{5005 a^9 b^6}{3 x^3}-\frac{19305 a^8 b^7}{8 x^{8/3}}-\frac{19305 a^7 b^8}{7 x^{7/3}}-\frac{5005 a^6 b^9}{2 x^2}-\frac{9009 a^5 b^{10}}{5 x^{5/3}}-\frac{4095 a^4 b^{11}}{4 x^{4/3}}-\frac{455 a^3 b^{12}}{x}-\frac{315 a^2 b^{13}}{2 x^{2/3}}-\frac{45 a b^{14}}{\sqrt [3]{x}}+b^{15} \log (x) \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^(1/3))^15/x^6,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 51.6058, size = 218, normalized size = 1.03 \[ - \frac{a^{15}}{5 x^{5}} - \frac{45 a^{14} b}{14 x^{\frac{14}{3}}} - \frac{315 a^{13} b^{2}}{13 x^{\frac{13}{3}}} - \frac{455 a^{12} b^{3}}{4 x^{4}} - \frac{4095 a^{11} b^{4}}{11 x^{\frac{11}{3}}} - \frac{9009 a^{10} b^{5}}{10 x^{\frac{10}{3}}} - \frac{5005 a^{9} b^{6}}{3 x^{3}} - \frac{19305 a^{8} b^{7}}{8 x^{\frac{8}{3}}} - \frac{19305 a^{7} b^{8}}{7 x^{\frac{7}{3}}} - \frac{5005 a^{6} b^{9}}{2 x^{2}} - \frac{9009 a^{5} b^{10}}{5 x^{\frac{5}{3}}} - \frac{4095 a^{4} b^{11}}{4 x^{\frac{4}{3}}} - \frac{455 a^{3} b^{12}}{x} - \frac{315 a^{2} b^{13}}{2 x^{\frac{2}{3}}} - \frac{45 a b^{14}}{\sqrt [3]{x}} + 3 b^{15} \log{\left (\sqrt [3]{x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/3))**15/x**6,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.184138, size = 211, normalized size = 1. \[ -\frac{a^{15}}{5 x^5}-\frac{45 a^{14} b}{14 x^{14/3}}-\frac{315 a^{13} b^2}{13 x^{13/3}}-\frac{455 a^{12} b^3}{4 x^4}-\frac{4095 a^{11} b^4}{11 x^{11/3}}-\frac{9009 a^{10} b^5}{10 x^{10/3}}-\frac{5005 a^9 b^6}{3 x^3}-\frac{19305 a^8 b^7}{8 x^{8/3}}-\frac{19305 a^7 b^8}{7 x^{7/3}}-\frac{5005 a^6 b^9}{2 x^2}-\frac{9009 a^5 b^{10}}{5 x^{5/3}}-\frac{4095 a^4 b^{11}}{4 x^{4/3}}-\frac{455 a^3 b^{12}}{x}-\frac{315 a^2 b^{13}}{2 x^{2/3}}-\frac{45 a b^{14}}{\sqrt [3]{x}}+b^{15} \log (x) \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^(1/3))^15/x^6,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.014, size = 166, normalized size = 0.8 \[ -{\frac{{a}^{15}}{5\,{x}^{5}}}-{\frac{45\,{a}^{14}b}{14}{x}^{-{\frac{14}{3}}}}-{\frac{315\,{a}^{13}{b}^{2}}{13}{x}^{-{\frac{13}{3}}}}-{\frac{455\,{a}^{12}{b}^{3}}{4\,{x}^{4}}}-{\frac{4095\,{a}^{11}{b}^{4}}{11}{x}^{-{\frac{11}{3}}}}-{\frac{9009\,{a}^{10}{b}^{5}}{10}{x}^{-{\frac{10}{3}}}}-{\frac{5005\,{a}^{9}{b}^{6}}{3\,{x}^{3}}}-{\frac{19305\,{a}^{8}{b}^{7}}{8}{x}^{-{\frac{8}{3}}}}-{\frac{19305\,{a}^{7}{b}^{8}}{7}{x}^{-{\frac{7}{3}}}}-{\frac{5005\,{a}^{6}{b}^{9}}{2\,{x}^{2}}}-{\frac{9009\,{a}^{5}{b}^{10}}{5}{x}^{-{\frac{5}{3}}}}-{\frac{4095\,{a}^{4}{b}^{11}}{4}{x}^{-{\frac{4}{3}}}}-455\,{\frac{{a}^{3}{b}^{12}}{x}}-{\frac{315\,{a}^{2}{b}^{13}}{2}{x}^{-{\frac{2}{3}}}}-45\,{\frac{a{b}^{14}}{\sqrt [3]{x}}}+{b}^{15}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/3))^15/x^6,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.44061, size = 224, normalized size = 1.06 \[ b^{15} \log \left (x\right ) - \frac{5405400 \, a b^{14} x^{\frac{14}{3}} + 18918900 \, a^{2} b^{13} x^{\frac{13}{3}} + 54654600 \, a^{3} b^{12} x^{4} + 122972850 \, a^{4} b^{11} x^{\frac{11}{3}} + 216432216 \, a^{5} b^{10} x^{\frac{10}{3}} + 300600300 \, a^{6} b^{9} x^{3} + 331273800 \, a^{7} b^{8} x^{\frac{8}{3}} + 289864575 \, a^{8} b^{7} x^{\frac{7}{3}} + 200400200 \, a^{9} b^{6} x^{2} + 108216108 \, a^{10} b^{5} x^{\frac{5}{3}} + 44717400 \, a^{11} b^{4} x^{\frac{4}{3}} + 13663650 \, a^{12} b^{3} x + 2910600 \, a^{13} b^{2} x^{\frac{2}{3}} + 386100 \, a^{14} b x^{\frac{1}{3}} + 24024 \, a^{15}}{120120 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^15/x^6,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.221001, size = 234, normalized size = 1.11 \[ \frac{360360 \, b^{15} x^{5} \log \left (x^{\frac{1}{3}}\right ) - 54654600 \, a^{3} b^{12} x^{4} - 300600300 \, a^{6} b^{9} x^{3} - 200400200 \, a^{9} b^{6} x^{2} - 13663650 \, a^{12} b^{3} x - 24024 \, a^{15} - 594 \,{\left (9100 \, a b^{14} x^{4} + 207025 \, a^{4} b^{11} x^{3} + 557700 \, a^{7} b^{8} x^{2} + 182182 \, a^{10} b^{5} x + 4900 \, a^{13} b^{2}\right )} x^{\frac{2}{3}} - 351 \,{\left (53900 \, a^{2} b^{13} x^{4} + 616616 \, a^{5} b^{10} x^{3} + 825825 \, a^{8} b^{7} x^{2} + 127400 \, a^{11} b^{4} x + 1100 \, a^{14} b\right )} x^{\frac{1}{3}}}{120120 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^15/x^6,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 28.6659, size = 212, normalized size = 1. \[ - \frac{a^{15}}{5 x^{5}} - \frac{45 a^{14} b}{14 x^{\frac{14}{3}}} - \frac{315 a^{13} b^{2}}{13 x^{\frac{13}{3}}} - \frac{455 a^{12} b^{3}}{4 x^{4}} - \frac{4095 a^{11} b^{4}}{11 x^{\frac{11}{3}}} - \frac{9009 a^{10} b^{5}}{10 x^{\frac{10}{3}}} - \frac{5005 a^{9} b^{6}}{3 x^{3}} - \frac{19305 a^{8} b^{7}}{8 x^{\frac{8}{3}}} - \frac{19305 a^{7} b^{8}}{7 x^{\frac{7}{3}}} - \frac{5005 a^{6} b^{9}}{2 x^{2}} - \frac{9009 a^{5} b^{10}}{5 x^{\frac{5}{3}}} - \frac{4095 a^{4} b^{11}}{4 x^{\frac{4}{3}}} - \frac{455 a^{3} b^{12}}{x} - \frac{315 a^{2} b^{13}}{2 x^{\frac{2}{3}}} - \frac{45 a b^{14}}{\sqrt [3]{x}} + b^{15} \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/3))**15/x**6,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.222597, size = 225, normalized size = 1.07 \[ b^{15}{\rm ln}\left ({\left | x \right |}\right ) - \frac{5405400 \, a b^{14} x^{\frac{14}{3}} + 18918900 \, a^{2} b^{13} x^{\frac{13}{3}} + 54654600 \, a^{3} b^{12} x^{4} + 122972850 \, a^{4} b^{11} x^{\frac{11}{3}} + 216432216 \, a^{5} b^{10} x^{\frac{10}{3}} + 300600300 \, a^{6} b^{9} x^{3} + 331273800 \, a^{7} b^{8} x^{\frac{8}{3}} + 289864575 \, a^{8} b^{7} x^{\frac{7}{3}} + 200400200 \, a^{9} b^{6} x^{2} + 108216108 \, a^{10} b^{5} x^{\frac{5}{3}} + 44717400 \, a^{11} b^{4} x^{\frac{4}{3}} + 13663650 \, a^{12} b^{3} x + 2910600 \, a^{13} b^{2} x^{\frac{2}{3}} + 386100 \, a^{14} b x^{\frac{1}{3}} + 24024 \, a^{15}}{120120 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^15/x^6,x, algorithm="giac")
[Out]