Optimal. Leaf size=75 \[ \frac{a^5 x^4}{4}+\frac{15}{13} a^4 b x^{13/3}+\frac{15}{7} a^3 b^2 x^{14/3}+2 a^2 b^3 x^5+\frac{15}{16} a b^4 x^{16/3}+\frac{3}{17} b^5 x^{17/3} \]
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Rubi [A] time = 0.111378, antiderivative size = 75, 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 \[ \frac{a^5 x^4}{4}+\frac{15}{13} a^4 b x^{13/3}+\frac{15}{7} a^3 b^2 x^{14/3}+2 a^2 b^3 x^5+\frac{15}{16} a b^4 x^{16/3}+\frac{3}{17} b^5 x^{17/3} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^(1/3))^5*x^3,x]
[Out]
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Rubi in Sympy [A] time = 18.7879, size = 73, normalized size = 0.97 \[ \frac{a^{5} x^{4}}{4} + \frac{15 a^{4} b x^{\frac{13}{3}}}{13} + \frac{15 a^{3} b^{2} x^{\frac{14}{3}}}{7} + 2 a^{2} b^{3} x^{5} + \frac{15 a b^{4} x^{\frac{16}{3}}}{16} + \frac{3 b^{5} x^{\frac{17}{3}}}{17} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/3))**5*x**3,x)
[Out]
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Mathematica [A] time = 0.0141429, size = 75, normalized size = 1. \[ \frac{a^5 x^4}{4}+\frac{15}{13} a^4 b x^{13/3}+\frac{15}{7} a^3 b^2 x^{14/3}+2 a^2 b^3 x^5+\frac{15}{16} a b^4 x^{16/3}+\frac{3}{17} b^5 x^{17/3} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^(1/3))^5*x^3,x]
[Out]
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Maple [A] time = 0.003, size = 58, normalized size = 0.8 \[{\frac{{a}^{5}{x}^{4}}{4}}+{\frac{15\,{a}^{4}b}{13}{x}^{{\frac{13}{3}}}}+{\frac{15\,{a}^{3}{b}^{2}}{7}{x}^{{\frac{14}{3}}}}+2\,{a}^{2}{b}^{3}{x}^{5}+{\frac{15\,a{b}^{4}}{16}{x}^{{\frac{16}{3}}}}+{\frac{3\,{b}^{5}}{17}{x}^{{\frac{17}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/3))^5*x^3,x)
[Out]
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Maxima [A] time = 1.44093, size = 270, normalized size = 3.6 \[ \frac{3 \,{\left (b x^{\frac{1}{3}} + a\right )}^{17}}{17 \, b^{12}} - \frac{33 \,{\left (b x^{\frac{1}{3}} + a\right )}^{16} a}{16 \, b^{12}} + \frac{11 \,{\left (b x^{\frac{1}{3}} + a\right )}^{15} a^{2}}{b^{12}} - \frac{495 \,{\left (b x^{\frac{1}{3}} + a\right )}^{14} a^{3}}{14 \, b^{12}} + \frac{990 \,{\left (b x^{\frac{1}{3}} + a\right )}^{13} a^{4}}{13 \, b^{12}} - \frac{231 \,{\left (b x^{\frac{1}{3}} + a\right )}^{12} a^{5}}{2 \, b^{12}} + \frac{126 \,{\left (b x^{\frac{1}{3}} + a\right )}^{11} a^{6}}{b^{12}} - \frac{99 \,{\left (b x^{\frac{1}{3}} + a\right )}^{10} a^{7}}{b^{12}} + \frac{55 \,{\left (b x^{\frac{1}{3}} + a\right )}^{9} a^{8}}{b^{12}} - \frac{165 \,{\left (b x^{\frac{1}{3}} + a\right )}^{8} a^{9}}{8 \, b^{12}} + \frac{33 \,{\left (b x^{\frac{1}{3}} + a\right )}^{7} a^{10}}{7 \, b^{12}} - \frac{{\left (b x^{\frac{1}{3}} + a\right )}^{6} a^{11}}{2 \, b^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^5*x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212473, size = 93, normalized size = 1.24 \[ 2 \, a^{2} b^{3} x^{5} + \frac{1}{4} \, a^{5} x^{4} + \frac{3}{119} \,{\left (7 \, b^{5} x^{5} + 85 \, a^{3} b^{2} x^{4}\right )} x^{\frac{2}{3}} + \frac{15}{208} \,{\left (13 \, a b^{4} x^{5} + 16 \, a^{4} b x^{4}\right )} x^{\frac{1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^5*x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.79276, size = 73, normalized size = 0.97 \[ \frac{a^{5} x^{4}}{4} + \frac{15 a^{4} b x^{\frac{13}{3}}}{13} + \frac{15 a^{3} b^{2} x^{\frac{14}{3}}}{7} + 2 a^{2} b^{3} x^{5} + \frac{15 a b^{4} x^{\frac{16}{3}}}{16} + \frac{3 b^{5} x^{\frac{17}{3}}}{17} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/3))**5*x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.250162, size = 77, normalized size = 1.03 \[ \frac{3}{17} \, b^{5} x^{\frac{17}{3}} + \frac{15}{16} \, a b^{4} x^{\frac{16}{3}} + 2 \, a^{2} b^{3} x^{5} + \frac{15}{7} \, a^{3} b^{2} x^{\frac{14}{3}} + \frac{15}{13} \, a^{4} b x^{\frac{13}{3}} + \frac{1}{4} \, a^{5} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^5*x^3,x, algorithm="giac")
[Out]