Optimal. Leaf size=77 \[ \frac{a^5 x^3}{3}+\frac{3}{2} a^4 b x^{10/3}+\frac{30}{11} a^3 b^2 x^{11/3}+\frac{5}{2} a^2 b^3 x^4+\frac{15}{13} a b^4 x^{13/3}+\frac{3}{14} b^5 x^{14/3} \]
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Rubi [A] time = 0.105271, antiderivative size = 77, 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 \[ \frac{a^5 x^3}{3}+\frac{3}{2} a^4 b x^{10/3}+\frac{30}{11} a^3 b^2 x^{11/3}+\frac{5}{2} a^2 b^3 x^4+\frac{15}{13} a b^4 x^{13/3}+\frac{3}{14} b^5 x^{14/3} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^(1/3))^5*x^2,x]
[Out]
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Rubi in Sympy [A] time = 17.111, size = 75, normalized size = 0.97 \[ \frac{a^{5} x^{3}}{3} + \frac{3 a^{4} b x^{\frac{10}{3}}}{2} + \frac{30 a^{3} b^{2} x^{\frac{11}{3}}}{11} + \frac{5 a^{2} b^{3} x^{4}}{2} + \frac{15 a b^{4} x^{\frac{13}{3}}}{13} + \frac{3 b^{5} x^{\frac{14}{3}}}{14} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/3))**5*x**2,x)
[Out]
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Mathematica [A] time = 0.0140527, size = 77, normalized size = 1. \[ \frac{a^5 x^3}{3}+\frac{3}{2} a^4 b x^{10/3}+\frac{30}{11} a^3 b^2 x^{11/3}+\frac{5}{2} a^2 b^3 x^4+\frac{15}{13} a b^4 x^{13/3}+\frac{3}{14} b^5 x^{14/3} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^(1/3))^5*x^2,x]
[Out]
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Maple [A] time = 0.003, size = 58, normalized size = 0.8 \[{\frac{{a}^{5}{x}^{3}}{3}}+{\frac{3\,{a}^{4}b}{2}{x}^{{\frac{10}{3}}}}+{\frac{30\,{a}^{3}{b}^{2}}{11}{x}^{{\frac{11}{3}}}}+{\frac{5\,{a}^{2}{b}^{3}{x}^{4}}{2}}+{\frac{15\,a{b}^{4}}{13}{x}^{{\frac{13}{3}}}}+{\frac{3\,{b}^{5}}{14}{x}^{{\frac{14}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/3))^5*x^2,x)
[Out]
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Maxima [A] time = 1.43878, size = 201, normalized size = 2.61 \[ \frac{3 \,{\left (b x^{\frac{1}{3}} + a\right )}^{14}}{14 \, b^{9}} - \frac{24 \,{\left (b x^{\frac{1}{3}} + a\right )}^{13} a}{13 \, b^{9}} + \frac{7 \,{\left (b x^{\frac{1}{3}} + a\right )}^{12} a^{2}}{b^{9}} - \frac{168 \,{\left (b x^{\frac{1}{3}} + a\right )}^{11} a^{3}}{11 \, b^{9}} + \frac{21 \,{\left (b x^{\frac{1}{3}} + a\right )}^{10} a^{4}}{b^{9}} - \frac{56 \,{\left (b x^{\frac{1}{3}} + a\right )}^{9} a^{5}}{3 \, b^{9}} + \frac{21 \,{\left (b x^{\frac{1}{3}} + a\right )}^{8} a^{6}}{2 \, b^{9}} - \frac{24 \,{\left (b x^{\frac{1}{3}} + a\right )}^{7} a^{7}}{7 \, b^{9}} + \frac{{\left (b x^{\frac{1}{3}} + a\right )}^{6} a^{8}}{2 \, b^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^5*x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211879, size = 93, normalized size = 1.21 \[ \frac{5}{2} \, a^{2} b^{3} x^{4} + \frac{1}{3} \, a^{5} x^{3} + \frac{3}{154} \,{\left (11 \, b^{5} x^{4} + 140 \, a^{3} b^{2} x^{3}\right )} x^{\frac{2}{3}} + \frac{3}{26} \,{\left (10 \, a b^{4} x^{4} + 13 \, a^{4} b x^{3}\right )} x^{\frac{1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^5*x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.46132, size = 75, normalized size = 0.97 \[ \frac{a^{5} x^{3}}{3} + \frac{3 a^{4} b x^{\frac{10}{3}}}{2} + \frac{30 a^{3} b^{2} x^{\frac{11}{3}}}{11} + \frac{5 a^{2} b^{3} x^{4}}{2} + \frac{15 a b^{4} x^{\frac{13}{3}}}{13} + \frac{3 b^{5} x^{\frac{14}{3}}}{14} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/3))**5*x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.22377, size = 77, normalized size = 1. \[ \frac{3}{14} \, b^{5} x^{\frac{14}{3}} + \frac{15}{13} \, a b^{4} x^{\frac{13}{3}} + \frac{5}{2} \, a^{2} b^{3} x^{4} + \frac{30}{11} \, a^{3} b^{2} x^{\frac{11}{3}} + \frac{3}{2} \, a^{4} b x^{\frac{10}{3}} + \frac{1}{3} \, a^{5} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^5*x^2,x, algorithm="giac")
[Out]