Optimal. Leaf size=200 \[ -\frac{a^{15}}{3 x^3}-\frac{45 a^{14} b}{8 x^{8/3}}-\frac{45 a^{13} b^2}{x^{7/3}}-\frac{455 a^{12} b^3}{2 x^2}-\frac{819 a^{11} b^4}{x^{5/3}}-\frac{9009 a^{10} b^5}{4 x^{4/3}}-\frac{5005 a^9 b^6}{x}-\frac{19305 a^8 b^7}{2 x^{2/3}}-\frac{19305 a^7 b^8}{\sqrt [3]{x}}+5005 a^6 b^9 \log (x)+9009 a^5 b^{10} \sqrt [3]{x}+\frac{4095}{2} a^4 b^{11} x^{2/3}+455 a^3 b^{12} x+\frac{315}{4} a^2 b^{13} x^{4/3}+9 a b^{14} x^{5/3}+\frac{b^{15} x^2}{2} \]
[Out]
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Rubi [A] time = 0.300902, antiderivative size = 200, 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 \[ -\frac{a^{15}}{3 x^3}-\frac{45 a^{14} b}{8 x^{8/3}}-\frac{45 a^{13} b^2}{x^{7/3}}-\frac{455 a^{12} b^3}{2 x^2}-\frac{819 a^{11} b^4}{x^{5/3}}-\frac{9009 a^{10} b^5}{4 x^{4/3}}-\frac{5005 a^9 b^6}{x}-\frac{19305 a^8 b^7}{2 x^{2/3}}-\frac{19305 a^7 b^8}{\sqrt [3]{x}}+5005 a^6 b^9 \log (x)+9009 a^5 b^{10} \sqrt [3]{x}+\frac{4095}{2} a^4 b^{11} x^{2/3}+455 a^3 b^{12} x+\frac{315}{4} a^2 b^{13} x^{4/3}+9 a b^{14} x^{5/3}+\frac{b^{15} x^2}{2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^(1/3))^15/x^4,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{15}}{3 x^{3}} - \frac{45 a^{14} b}{8 x^{\frac{8}{3}}} - \frac{45 a^{13} b^{2}}{x^{\frac{7}{3}}} - \frac{455 a^{12} b^{3}}{2 x^{2}} - \frac{819 a^{11} b^{4}}{x^{\frac{5}{3}}} - \frac{9009 a^{10} b^{5}}{4 x^{\frac{4}{3}}} - \frac{5005 a^{9} b^{6}}{x} - \frac{19305 a^{8} b^{7}}{2 x^{\frac{2}{3}}} - \frac{19305 a^{7} b^{8}}{\sqrt [3]{x}} + 15015 a^{6} b^{9} \log{\left (\sqrt [3]{x} \right )} + 9009 a^{5} b^{10} \sqrt [3]{x} + 4095 a^{4} b^{11} \int ^{\sqrt [3]{x}} x\, dx + 455 a^{3} b^{12} x + \frac{315 a^{2} b^{13} x^{\frac{4}{3}}}{4} + 9 a b^{14} x^{\frac{5}{3}} + \frac{b^{15} x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/3))**15/x**4,x)
[Out]
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Mathematica [A] time = 0.111945, size = 200, normalized size = 1. \[ -\frac{a^{15}}{3 x^3}-\frac{45 a^{14} b}{8 x^{8/3}}-\frac{45 a^{13} b^2}{x^{7/3}}-\frac{455 a^{12} b^3}{2 x^2}-\frac{819 a^{11} b^4}{x^{5/3}}-\frac{9009 a^{10} b^5}{4 x^{4/3}}-\frac{5005 a^9 b^6}{x}-\frac{19305 a^8 b^7}{2 x^{2/3}}-\frac{19305 a^7 b^8}{\sqrt [3]{x}}+5005 a^6 b^9 \log (x)+9009 a^5 b^{10} \sqrt [3]{x}+\frac{4095}{2} a^4 b^{11} x^{2/3}+455 a^3 b^{12} x+\frac{315}{4} a^2 b^{13} x^{4/3}+9 a b^{14} x^{5/3}+\frac{b^{15} x^2}{2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^(1/3))^15/x^4,x]
[Out]
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Maple [A] time = 0.014, size = 165, normalized size = 0.8 \[ -{\frac{{a}^{15}}{3\,{x}^{3}}}-{\frac{45\,{a}^{14}b}{8}{x}^{-{\frac{8}{3}}}}-45\,{\frac{{a}^{13}{b}^{2}}{{x}^{7/3}}}-{\frac{455\,{a}^{12}{b}^{3}}{2\,{x}^{2}}}-819\,{\frac{{a}^{11}{b}^{4}}{{x}^{5/3}}}-{\frac{9009\,{a}^{10}{b}^{5}}{4}{x}^{-{\frac{4}{3}}}}-5005\,{\frac{{a}^{9}{b}^{6}}{x}}-{\frac{19305\,{a}^{8}{b}^{7}}{2}{x}^{-{\frac{2}{3}}}}-19305\,{\frac{{a}^{7}{b}^{8}}{\sqrt [3]{x}}}+9009\,{a}^{5}{b}^{10}\sqrt [3]{x}+{\frac{4095\,{a}^{4}{b}^{11}}{2}{x}^{{\frac{2}{3}}}}+455\,{a}^{3}{b}^{12}x+{\frac{315\,{a}^{2}{b}^{13}}{4}{x}^{{\frac{4}{3}}}}+9\,a{b}^{14}{x}^{5/3}+{\frac{{b}^{15}{x}^{2}}{2}}+5005\,{a}^{6}{b}^{9}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/3))^15/x^4,x)
[Out]
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Maxima [A] time = 1.44277, size = 223, normalized size = 1.12 \[ \frac{1}{2} \, b^{15} x^{2} + 9 \, a b^{14} x^{\frac{5}{3}} + \frac{315}{4} \, a^{2} b^{13} x^{\frac{4}{3}} + 455 \, a^{3} b^{12} x + 5005 \, a^{6} b^{9} \log \left (x\right ) + \frac{4095}{2} \, a^{4} b^{11} x^{\frac{2}{3}} + 9009 \, a^{5} b^{10} x^{\frac{1}{3}} - \frac{463320 \, a^{7} b^{8} x^{\frac{8}{3}} + 231660 \, a^{8} b^{7} x^{\frac{7}{3}} + 120120 \, a^{9} b^{6} x^{2} + 54054 \, a^{10} b^{5} x^{\frac{5}{3}} + 19656 \, a^{11} b^{4} x^{\frac{4}{3}} + 5460 \, a^{12} b^{3} x + 1080 \, a^{13} b^{2} x^{\frac{2}{3}} + 135 \, a^{14} b x^{\frac{1}{3}} + 8 \, a^{15}}{24 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^15/x^4,x, algorithm="maxima")
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Fricas [A] time = 0.222316, size = 234, normalized size = 1.17 \[ \frac{12 \, b^{15} x^{5} + 10920 \, a^{3} b^{12} x^{4} + 360360 \, a^{6} b^{9} x^{3} \log \left (x^{\frac{1}{3}}\right ) - 120120 \, a^{9} b^{6} x^{2} - 5460 \, a^{12} b^{3} x - 8 \, a^{15} + 54 \,{\left (4 \, a b^{14} x^{4} + 910 \, a^{4} b^{11} x^{3} - 8580 \, a^{7} b^{8} x^{2} - 1001 \, a^{10} b^{5} x - 20 \, a^{13} b^{2}\right )} x^{\frac{2}{3}} + 27 \,{\left (70 \, a^{2} b^{13} x^{4} + 8008 \, a^{5} b^{10} x^{3} - 8580 \, a^{8} b^{7} x^{2} - 728 \, a^{11} b^{4} x - 5 \, a^{14} b\right )} x^{\frac{1}{3}}}{24 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^15/x^4,x, algorithm="fricas")
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Sympy [A] time = 16.9995, size = 202, normalized size = 1.01 \[ - \frac{a^{15}}{3 x^{3}} - \frac{45 a^{14} b}{8 x^{\frac{8}{3}}} - \frac{45 a^{13} b^{2}}{x^{\frac{7}{3}}} - \frac{455 a^{12} b^{3}}{2 x^{2}} - \frac{819 a^{11} b^{4}}{x^{\frac{5}{3}}} - \frac{9009 a^{10} b^{5}}{4 x^{\frac{4}{3}}} - \frac{5005 a^{9} b^{6}}{x} - \frac{19305 a^{8} b^{7}}{2 x^{\frac{2}{3}}} - \frac{19305 a^{7} b^{8}}{\sqrt [3]{x}} + 5005 a^{6} b^{9} \log{\left (x \right )} + 9009 a^{5} b^{10} \sqrt [3]{x} + \frac{4095 a^{4} b^{11} x^{\frac{2}{3}}}{2} + 455 a^{3} b^{12} x + \frac{315 a^{2} b^{13} x^{\frac{4}{3}}}{4} + 9 a b^{14} x^{\frac{5}{3}} + \frac{b^{15} x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/3))**15/x**4,x)
[Out]
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GIAC/XCAS [A] time = 0.221574, size = 224, normalized size = 1.12 \[ \frac{1}{2} \, b^{15} x^{2} + 9 \, a b^{14} x^{\frac{5}{3}} + \frac{315}{4} \, a^{2} b^{13} x^{\frac{4}{3}} + 455 \, a^{3} b^{12} x + 5005 \, a^{6} b^{9}{\rm ln}\left ({\left | x \right |}\right ) + \frac{4095}{2} \, a^{4} b^{11} x^{\frac{2}{3}} + 9009 \, a^{5} b^{10} x^{\frac{1}{3}} - \frac{463320 \, a^{7} b^{8} x^{\frac{8}{3}} + 231660 \, a^{8} b^{7} x^{\frac{7}{3}} + 120120 \, a^{9} b^{6} x^{2} + 54054 \, a^{10} b^{5} x^{\frac{5}{3}} + 19656 \, a^{11} b^{4} x^{\frac{4}{3}} + 5460 \, a^{12} b^{3} x + 1080 \, a^{13} b^{2} x^{\frac{2}{3}} + 135 \, a^{14} b x^{\frac{1}{3}} + 8 \, a^{15}}{24 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^15/x^4,x, algorithm="giac")
[Out]