Optimal. Leaf size=32 \[ -\frac{a^2}{4 x^4}-\frac{4 a b}{7 x^{7/2}}-\frac{b^2}{3 x^3} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0432035, antiderivative size = 32, 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 \[ -\frac{a^2}{4 x^4}-\frac{4 a b}{7 x^{7/2}}-\frac{b^2}{3 x^3} \]
Antiderivative was successfully verified.
[In] Int[(a + b*Sqrt[x])^2/x^5,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 6.49635, size = 29, normalized size = 0.91 \[ - \frac{a^{2}}{4 x^{4}} - \frac{4 a b}{7 x^{\frac{7}{2}}} - \frac{b^{2}}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/2))**2/x**5,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0110346, size = 28, normalized size = 0.88 \[ -\frac{21 a^2+48 a b \sqrt{x}+28 b^2 x}{84 x^4} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*Sqrt[x])^2/x^5,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 25, normalized size = 0.8 \[ -{\frac{{a}^{2}}{4\,{x}^{4}}}-{\frac{4\,ab}{7}{x}^{-{\frac{7}{2}}}}-{\frac{{b}^{2}}{3\,{x}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/2))^2/x^5,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.41836, size = 32, normalized size = 1. \[ -\frac{28 \, b^{2} x + 48 \, a b \sqrt{x} + 21 \, a^{2}}{84 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^2/x^5,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.237111, size = 32, normalized size = 1. \[ -\frac{28 \, b^{2} x + 48 \, a b \sqrt{x} + 21 \, a^{2}}{84 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^2/x^5,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 4.88277, size = 29, normalized size = 0.91 \[ - \frac{a^{2}}{4 x^{4}} - \frac{4 a b}{7 x^{\frac{7}{2}}} - \frac{b^{2}}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/2))**2/x**5,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.214902, size = 32, normalized size = 1. \[ -\frac{28 \, b^{2} x + 48 \, a b \sqrt{x} + 21 \, a^{2}}{84 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^2/x^5,x, algorithm="giac")
[Out]