Optimal. Leaf size=29 \[ a^2 x+\frac{3}{2} a b x^{4/3}+\frac{3}{5} b^2 x^{5/3} \]
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Rubi [A] time = 0.0435078, antiderivative size = 29, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ a^2 x+\frac{3}{2} a b x^{4/3}+\frac{3}{5} b^2 x^{5/3} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^(1/3))^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{3 a b x^{\frac{4}{3}}}{2} + \frac{3 b^{2} x^{\frac{5}{3}}}{5} + \int a^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/3))**2,x)
[Out]
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Mathematica [A] time = 0.00837939, size = 29, normalized size = 1. \[ a^2 x+\frac{3}{2} a b x^{4/3}+\frac{3}{5} b^2 x^{5/3} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^(1/3))^2,x]
[Out]
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Maple [A] time = 0.002, size = 22, normalized size = 0.8 \[ x{a}^{2}+{\frac{3\,ab}{2}{x}^{{\frac{4}{3}}}}+{\frac{3\,{b}^{2}}{5}{x}^{{\frac{5}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/3))^2,x)
[Out]
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Maxima [A] time = 1.43597, size = 28, normalized size = 0.97 \[ \frac{3}{5} \, b^{2} x^{\frac{5}{3}} + \frac{3}{2} \, a b x^{\frac{4}{3}} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.21119, size = 28, normalized size = 0.97 \[ \frac{3}{5} \, b^{2} x^{\frac{5}{3}} + \frac{3}{2} \, a b x^{\frac{4}{3}} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.11379, size = 27, normalized size = 0.93 \[ a^{2} x + \frac{3 a b x^{\frac{4}{3}}}{2} + \frac{3 b^{2} x^{\frac{5}{3}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/3))**2,x)
[Out]
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GIAC/XCAS [A] time = 0.285884, size = 28, normalized size = 0.97 \[ \frac{3}{5} \, b^{2} x^{\frac{5}{3}} + \frac{3}{2} \, a b x^{\frac{4}{3}} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^2,x, algorithm="giac")
[Out]