Optimal. Leaf size=30 \[ -\frac{a^2}{2 x^2}-\frac{4 a b}{3 x^{3/2}}-\frac{b^2}{x} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0433599, antiderivative size = 30, 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 \[ -\frac{a^2}{2 x^2}-\frac{4 a b}{3 x^{3/2}}-\frac{b^2}{x} \]
Antiderivative was successfully verified.
[In] Int[(a + b*Sqrt[x])^2/x^3,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 6.33381, size = 26, normalized size = 0.87 \[ - \frac{a^{2}}{2 x^{2}} - \frac{4 a b}{3 x^{\frac{3}{2}}} - \frac{b^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/2))**2/x**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0108397, size = 30, normalized size = 1. \[ -\frac{a^2}{2 x^2}-\frac{4 a b}{3 x^{3/2}}-\frac{b^2}{x} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*Sqrt[x])^2/x^3,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.003, size = 25, normalized size = 0.8 \[ -{\frac{{a}^{2}}{2\,{x}^{2}}}-{\frac{4\,ab}{3}{x}^{-{\frac{3}{2}}}}-{\frac{{b}^{2}}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/2))^2/x^3,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.41526, size = 32, normalized size = 1.07 \[ -\frac{6 \, b^{2} x + 8 \, a b \sqrt{x} + 3 \, a^{2}}{6 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^2/x^3,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.232276, size = 32, normalized size = 1.07 \[ -\frac{6 \, b^{2} x + 8 \, a b \sqrt{x} + 3 \, a^{2}}{6 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^2/x^3,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 2.16354, size = 26, normalized size = 0.87 \[ - \frac{a^{2}}{2 x^{2}} - \frac{4 a b}{3 x^{\frac{3}{2}}} - \frac{b^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/2))**2/x**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.220636, size = 32, normalized size = 1.07 \[ -\frac{6 \, b^{2} x + 8 \, a b \sqrt{x} + 3 \, a^{2}}{6 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^2/x^3,x, algorithm="giac")
[Out]