Optimal. Leaf size=17 \[ \frac{2 (x+1)}{\sqrt{x^2+3 x+2}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0197919, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ \frac{2 (x+1)}{\sqrt{x^2+3 x+2}} \]
Antiderivative was successfully verified.
[In] Int[(1 + x)/(2 + 3*x + x^2)^(3/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 3.97071, size = 15, normalized size = 0.88 \[ \frac{2 \left (x + 1\right )}{\sqrt{x^{2} + 3 x + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x)/(x**2+3*x+2)**(3/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0208744, size = 19, normalized size = 1.12 \[ \frac{2 \sqrt{x^2+3 x+2}}{x+2} \]
Antiderivative was successfully verified.
[In] Integrate[(1 + x)/(2 + 3*x + x^2)^(3/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.005, size = 21, normalized size = 1.2 \[ 2\,{\frac{ \left ( 1+x \right ) ^{2} \left ( 2+x \right ) }{ \left ({x}^{2}+3\,x+2 \right ) ^{3/2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x)/(x^2+3*x+2)^(3/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.67451, size = 35, normalized size = 2.06 \[ \frac{2 \, x}{\sqrt{x^{2} + 3 \, x + 2}} + \frac{2}{\sqrt{x^{2} + 3 \, x + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)/(x^2 + 3*x + 2)^(3/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.214325, size = 26, normalized size = 1.53 \[ \frac{2}{x - \sqrt{x^{2} + 3 \, x + 2} + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)/(x^2 + 3*x + 2)^(3/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x + 1}{\left (\left (x + 1\right ) \left (x + 2\right )\right )^{\frac{3}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1+x)/(x**2+3*x+2)**(3/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.208836, size = 26, normalized size = 1.53 \[ \frac{2}{x - \sqrt{x^{2} + 3 \, x + 2} + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)/(x^2 + 3*x + 2)^(3/2),x, algorithm="giac")
[Out]