Optimal. Leaf size=27 \[ a^2 x+\frac{4}{3} a b x^{3/2}+\frac{b^2 x^2}{2} \]
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Rubi [A] time = 0.0438566, antiderivative size = 27, 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 \[ a^2 x+\frac{4}{3} a b x^{3/2}+\frac{b^2 x^2}{2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*Sqrt[x])^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{4 a b x^{\frac{3}{2}}}{3} + b^{2} \int x\, dx + \int a^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/2))**2,x)
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Mathematica [A] time = 0.00780663, size = 27, normalized size = 1. \[ a^2 x+\frac{4}{3} a b x^{3/2}+\frac{b^2 x^2}{2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*Sqrt[x])^2,x]
[Out]
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Maple [A] time = 0.002, size = 22, normalized size = 0.8 \[ x{a}^{2}+{\frac{4\,ab}{3}{x}^{{\frac{3}{2}}}}+{\frac{{b}^{2}{x}^{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/2))^2,x)
[Out]
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Maxima [A] time = 1.43792, size = 28, normalized size = 1.04 \[ \frac{1}{2} \, b^{2} x^{2} + \frac{4}{3} \, a b x^{\frac{3}{2}} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.230621, size = 28, normalized size = 1.04 \[ \frac{1}{2} \, b^{2} x^{2} + \frac{4}{3} \, a b x^{\frac{3}{2}} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.353698, size = 24, normalized size = 0.89 \[ a^{2} x + \frac{4 a b x^{\frac{3}{2}}}{3} + \frac{b^{2} x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/2))**2,x)
[Out]
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GIAC/XCAS [A] time = 0.216161, size = 28, normalized size = 1.04 \[ \frac{1}{2} \, b^{2} x^{2} + \frac{4}{3} \, a b x^{\frac{3}{2}} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^2,x, algorithm="giac")
[Out]