Optimal. Leaf size=11 \[ 2 \sqrt{x^2+x} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.00654045, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ 2 \sqrt{x^2+x} \]
Antiderivative was successfully verified.
[In] Int[(1 + 2*x)/Sqrt[x + x^2],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 1.05087, size = 8, normalized size = 0.73 \[ 2 \sqrt{x^{2} + x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+2*x)/(x**2+x)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0138085, size = 11, normalized size = 1. \[ 2 \sqrt{x (x+1)} \]
Antiderivative was successfully verified.
[In] Integrate[(1 + 2*x)/Sqrt[x + x^2],x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.005, size = 14, normalized size = 1.3 \[ 2\,{\frac{x \left ( 1+x \right ) }{\sqrt{{x}^{2}+x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+2*x)/(x^2+x)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.705094, size = 12, normalized size = 1.09 \[ 2 \, \sqrt{x^{2} + x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x + 1)/sqrt(x^2 + x),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.263172, size = 57, normalized size = 5.18 \[ -\frac{8 \, x^{2} - 2 \, \sqrt{x^{2} + x}{\left (4 \, x + 1\right )} + 6 \, x - 1}{2 \,{\left (2 \, x - 2 \, \sqrt{x^{2} + x} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x + 1)/sqrt(x^2 + x),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.293673, size = 8, normalized size = 0.73 \[ 2 \sqrt{x^{2} + x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1+2*x)/(x**2+x)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.261638, size = 12, normalized size = 1.09 \[ 2 \, \sqrt{x^{2} + x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x + 1)/sqrt(x^2 + x),x, algorithm="giac")
[Out]