Optimal. Leaf size=16 \[ -\frac{1}{4 \left (4 x^2+12 x+13\right )} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.00844147, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ -\frac{1}{4 \left (4 x^2+12 x+13\right )} \]
Antiderivative was successfully verified.
[In] Int[(3 + 2*x)/(13 + 12*x + 4*x^2)^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 3.05497, size = 12, normalized size = 0.75 \[ - \frac{1}{4 \left (4 x^{2} + 12 x + 13\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+2*x)/(4*x**2+12*x+13)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0104798, size = 16, normalized size = 1. \[ -\frac{1}{4 \left (4 x^2+12 x+13\right )} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 2*x)/(13 + 12*x + 4*x^2)^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 15, normalized size = 0.9 \[ -{\frac{1}{16\,{x}^{2}+48\,x+52}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2*x+3)/(4*x^2+12*x+13)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.682622, size = 19, normalized size = 1.19 \[ -\frac{1}{4 \,{\left (4 \, x^{2} + 12 \, x + 13\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x + 3)/(4*x^2 + 12*x + 13)^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.276629, size = 19, normalized size = 1.19 \[ -\frac{1}{4 \,{\left (4 \, x^{2} + 12 \, x + 13\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x + 3)/(4*x^2 + 12*x + 13)^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.225544, size = 12, normalized size = 0.75 \[ - \frac{1}{16 x^{2} + 48 x + 52} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3+2*x)/(4*x**2+12*x+13)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.269334, size = 19, normalized size = 1.19 \[ -\frac{1}{4 \,{\left (4 \, x^{2} + 12 \, x + 13\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x + 3)/(4*x^2 + 12*x + 13)^2,x, algorithm="giac")
[Out]