Optimal. Leaf size=217 \[ \frac{a^{15} x^6}{6}+\frac{45}{19} a^{14} b x^{19/3}+\frac{63}{4} a^{13} b^2 x^{20/3}+65 a^{12} b^3 x^7+\frac{4095}{22} a^{11} b^4 x^{22/3}+\frac{9009}{23} a^{10} b^5 x^{23/3}+\frac{5005}{8} a^9 b^6 x^8+\frac{3861}{5} a^8 b^7 x^{25/3}+\frac{1485}{2} a^7 b^8 x^{26/3}+\frac{5005}{9} a^6 b^9 x^9+\frac{1287}{4} a^5 b^{10} x^{28/3}+\frac{4095}{29} a^4 b^{11} x^{29/3}+\frac{91}{2} a^3 b^{12} x^{10}+\frac{315}{31} a^2 b^{13} x^{31/3}+\frac{45}{32} a b^{14} x^{32/3}+\frac{b^{15} x^{11}}{11} \]
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Rubi [A] time = 0.361593, antiderivative size = 217, 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 \[ \frac{a^{15} x^6}{6}+\frac{45}{19} a^{14} b x^{19/3}+\frac{63}{4} a^{13} b^2 x^{20/3}+65 a^{12} b^3 x^7+\frac{4095}{22} a^{11} b^4 x^{22/3}+\frac{9009}{23} a^{10} b^5 x^{23/3}+\frac{5005}{8} a^9 b^6 x^8+\frac{3861}{5} a^8 b^7 x^{25/3}+\frac{1485}{2} a^7 b^8 x^{26/3}+\frac{5005}{9} a^6 b^9 x^9+\frac{1287}{4} a^5 b^{10} x^{28/3}+\frac{4095}{29} a^4 b^{11} x^{29/3}+\frac{91}{2} a^3 b^{12} x^{10}+\frac{315}{31} a^2 b^{13} x^{31/3}+\frac{45}{32} a b^{14} x^{32/3}+\frac{b^{15} x^{11}}{11} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^(1/3))^15*x^5,x]
[Out]
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Rubi in Sympy [A] time = 68.2499, size = 218, normalized size = 1. \[ \frac{a^{15} x^{6}}{6} + \frac{45 a^{14} b x^{\frac{19}{3}}}{19} + \frac{63 a^{13} b^{2} x^{\frac{20}{3}}}{4} + 65 a^{12} b^{3} x^{7} + \frac{4095 a^{11} b^{4} x^{\frac{22}{3}}}{22} + \frac{9009 a^{10} b^{5} x^{\frac{23}{3}}}{23} + \frac{5005 a^{9} b^{6} x^{8}}{8} + \frac{3861 a^{8} b^{7} x^{\frac{25}{3}}}{5} + \frac{1485 a^{7} b^{8} x^{\frac{26}{3}}}{2} + \frac{5005 a^{6} b^{9} x^{9}}{9} + \frac{1287 a^{5} b^{10} x^{\frac{28}{3}}}{4} + \frac{4095 a^{4} b^{11} x^{\frac{29}{3}}}{29} + \frac{91 a^{3} b^{12} x^{10}}{2} + \frac{315 a^{2} b^{13} x^{\frac{31}{3}}}{31} + \frac{45 a b^{14} x^{\frac{32}{3}}}{32} + \frac{b^{15} x^{11}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/3))**15*x**5,x)
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Mathematica [A] time = 0.0379692, size = 217, normalized size = 1. \[ \frac{a^{15} x^6}{6}+\frac{45}{19} a^{14} b x^{19/3}+\frac{63}{4} a^{13} b^2 x^{20/3}+65 a^{12} b^3 x^7+\frac{4095}{22} a^{11} b^4 x^{22/3}+\frac{9009}{23} a^{10} b^5 x^{23/3}+\frac{5005}{8} a^9 b^6 x^8+\frac{3861}{5} a^8 b^7 x^{25/3}+\frac{1485}{2} a^7 b^8 x^{26/3}+\frac{5005}{9} a^6 b^9 x^9+\frac{1287}{4} a^5 b^{10} x^{28/3}+\frac{4095}{29} a^4 b^{11} x^{29/3}+\frac{91}{2} a^3 b^{12} x^{10}+\frac{315}{31} a^2 b^{13} x^{31/3}+\frac{45}{32} a b^{14} x^{32/3}+\frac{b^{15} x^{11}}{11} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^(1/3))^15*x^5,x]
[Out]
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Maple [A] time = 0.004, size = 168, normalized size = 0.8 \[{\frac{{a}^{15}{x}^{6}}{6}}+{\frac{45\,{a}^{14}b}{19}{x}^{{\frac{19}{3}}}}+{\frac{63\,{a}^{13}{b}^{2}}{4}{x}^{{\frac{20}{3}}}}+65\,{a}^{12}{b}^{3}{x}^{7}+{\frac{4095\,{a}^{11}{b}^{4}}{22}{x}^{{\frac{22}{3}}}}+{\frac{9009\,{a}^{10}{b}^{5}}{23}{x}^{{\frac{23}{3}}}}+{\frac{5005\,{a}^{9}{b}^{6}{x}^{8}}{8}}+{\frac{3861\,{a}^{8}{b}^{7}}{5}{x}^{{\frac{25}{3}}}}+{\frac{1485\,{a}^{7}{b}^{8}}{2}{x}^{{\frac{26}{3}}}}+{\frac{5005\,{a}^{6}{b}^{9}{x}^{9}}{9}}+{\frac{1287\,{a}^{5}{b}^{10}}{4}{x}^{{\frac{28}{3}}}}+{\frac{4095\,{a}^{4}{b}^{11}}{29}{x}^{{\frac{29}{3}}}}+{\frac{91\,{a}^{3}{b}^{12}{x}^{10}}{2}}+{\frac{315\,{a}^{2}{b}^{13}}{31}{x}^{{\frac{31}{3}}}}+{\frac{45\,a{b}^{14}}{32}{x}^{{\frac{32}{3}}}}+{\frac{{b}^{15}{x}^{11}}{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/3))^15*x^5,x)
[Out]
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Maxima [A] time = 1.46231, size = 408, normalized size = 1.88 \[ \frac{{\left (b x^{\frac{1}{3}} + a\right )}^{33}}{11 \, b^{18}} - \frac{51 \,{\left (b x^{\frac{1}{3}} + a\right )}^{32} a}{32 \, b^{18}} + \frac{408 \,{\left (b x^{\frac{1}{3}} + a\right )}^{31} a^{2}}{31 \, b^{18}} - \frac{68 \,{\left (b x^{\frac{1}{3}} + a\right )}^{30} a^{3}}{b^{18}} + \frac{7140 \,{\left (b x^{\frac{1}{3}} + a\right )}^{29} a^{4}}{29 \, b^{18}} - \frac{663 \,{\left (b x^{\frac{1}{3}} + a\right )}^{28} a^{5}}{b^{18}} + \frac{12376 \,{\left (b x^{\frac{1}{3}} + a\right )}^{27} a^{6}}{9 \, b^{18}} - \frac{2244 \,{\left (b x^{\frac{1}{3}} + a\right )}^{26} a^{7}}{b^{18}} + \frac{14586 \,{\left (b x^{\frac{1}{3}} + a\right )}^{25} a^{8}}{5 \, b^{18}} - \frac{12155 \,{\left (b x^{\frac{1}{3}} + a\right )}^{24} a^{9}}{4 \, b^{18}} + \frac{58344 \,{\left (b x^{\frac{1}{3}} + a\right )}^{23} a^{10}}{23 \, b^{18}} - \frac{18564 \,{\left (b x^{\frac{1}{3}} + a\right )}^{22} a^{11}}{11 \, b^{18}} + \frac{884 \,{\left (b x^{\frac{1}{3}} + a\right )}^{21} a^{12}}{b^{18}} - \frac{357 \,{\left (b x^{\frac{1}{3}} + a\right )}^{20} a^{13}}{b^{18}} + \frac{2040 \,{\left (b x^{\frac{1}{3}} + a\right )}^{19} a^{14}}{19 \, b^{18}} - \frac{68 \,{\left (b x^{\frac{1}{3}} + a\right )}^{18} a^{15}}{3 \, b^{18}} + \frac{3 \,{\left (b x^{\frac{1}{3}} + a\right )}^{17} a^{16}}{b^{18}} - \frac{3 \,{\left (b x^{\frac{1}{3}} + a\right )}^{16} a^{17}}{16 \, b^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^15*x^5,x, algorithm="maxima")
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Fricas [A] time = 0.215121, size = 242, normalized size = 1.12 \[ \frac{1}{11} \, b^{15} x^{11} + \frac{91}{2} \, a^{3} b^{12} x^{10} + \frac{5005}{9} \, a^{6} b^{9} x^{9} + \frac{5005}{8} \, a^{9} b^{6} x^{8} + 65 \, a^{12} b^{3} x^{7} + \frac{1}{6} \, a^{15} x^{6} + \frac{9}{21344} \,{\left (3335 \, a b^{14} x^{10} + 334880 \, a^{4} b^{11} x^{9} + 1760880 \, a^{7} b^{8} x^{8} + 928928 \, a^{10} b^{5} x^{7} + 37352 \, a^{13} b^{2} x^{6}\right )} x^{\frac{2}{3}} + \frac{9}{129580} \,{\left (146300 \, a^{2} b^{13} x^{10} + 4632485 \, a^{5} b^{10} x^{9} + 11117964 \, a^{8} b^{7} x^{8} + 2679950 \, a^{11} b^{4} x^{7} + 34100 \, a^{14} b x^{6}\right )} x^{\frac{1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^15*x^5,x, algorithm="fricas")
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Sympy [A] time = 68.3461, size = 218, normalized size = 1. \[ \frac{a^{15} x^{6}}{6} + \frac{45 a^{14} b x^{\frac{19}{3}}}{19} + \frac{63 a^{13} b^{2} x^{\frac{20}{3}}}{4} + 65 a^{12} b^{3} x^{7} + \frac{4095 a^{11} b^{4} x^{\frac{22}{3}}}{22} + \frac{9009 a^{10} b^{5} x^{\frac{23}{3}}}{23} + \frac{5005 a^{9} b^{6} x^{8}}{8} + \frac{3861 a^{8} b^{7} x^{\frac{25}{3}}}{5} + \frac{1485 a^{7} b^{8} x^{\frac{26}{3}}}{2} + \frac{5005 a^{6} b^{9} x^{9}}{9} + \frac{1287 a^{5} b^{10} x^{\frac{28}{3}}}{4} + \frac{4095 a^{4} b^{11} x^{\frac{29}{3}}}{29} + \frac{91 a^{3} b^{12} x^{10}}{2} + \frac{315 a^{2} b^{13} x^{\frac{31}{3}}}{31} + \frac{45 a b^{14} x^{\frac{32}{3}}}{32} + \frac{b^{15} x^{11}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/3))**15*x**5,x)
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GIAC/XCAS [A] time = 0.224153, size = 225, normalized size = 1.04 \[ \frac{1}{11} \, b^{15} x^{11} + \frac{45}{32} \, a b^{14} x^{\frac{32}{3}} + \frac{315}{31} \, a^{2} b^{13} x^{\frac{31}{3}} + \frac{91}{2} \, a^{3} b^{12} x^{10} + \frac{4095}{29} \, a^{4} b^{11} x^{\frac{29}{3}} + \frac{1287}{4} \, a^{5} b^{10} x^{\frac{28}{3}} + \frac{5005}{9} \, a^{6} b^{9} x^{9} + \frac{1485}{2} \, a^{7} b^{8} x^{\frac{26}{3}} + \frac{3861}{5} \, a^{8} b^{7} x^{\frac{25}{3}} + \frac{5005}{8} \, a^{9} b^{6} x^{8} + \frac{9009}{23} \, a^{10} b^{5} x^{\frac{23}{3}} + \frac{4095}{22} \, a^{11} b^{4} x^{\frac{22}{3}} + 65 \, a^{12} b^{3} x^{7} + \frac{63}{4} \, a^{13} b^{2} x^{\frac{20}{3}} + \frac{45}{19} \, a^{14} b x^{\frac{19}{3}} + \frac{1}{6} \, a^{15} x^{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^15*x^5,x, algorithm="giac")
[Out]