Optimal. Leaf size=44 \[ \frac{3}{16 (2 x+3) \left (4 x^2+12 x+9\right )^{3/2}}-\frac{1}{12 \left (4 x^2+12 x+9\right )^{3/2}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0313068, antiderivative size = 44, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ \frac{3}{16 (2 x+3) \left (4 x^2+12 x+9\right )^{3/2}}-\frac{1}{12 \left (4 x^2+12 x+9\right )^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[x/(9 + 12*x + 4*x^2)^(5/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 3.73285, size = 36, normalized size = 0.82 \[ \frac{3 \left (8 x + 12\right )}{64 \left (4 x^{2} + 12 x + 9\right )^{\frac{5}{2}}} - \frac{1}{12 \left (4 x^{2} + 12 x + 9\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(4*x**2+12*x+9)**(5/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0140831, size = 27, normalized size = 0.61 \[ \frac{-8 x-3}{48 (2 x+3)^3 \sqrt{(2 x+3)^2}} \]
Antiderivative was successfully verified.
[In] Integrate[x/(9 + 12*x + 4*x^2)^(5/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.005, size = 22, normalized size = 0.5 \[ -{\frac{ \left ( 2\,x+3 \right ) \left ( 8\,x+3 \right ) }{48} \left ( \left ( 2\,x+3 \right ) ^{2} \right ) ^{-{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(4*x^2+12*x+9)^(5/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.771228, size = 32, normalized size = 0.73 \[ -\frac{1}{12 \,{\left (4 \, x^{2} + 12 \, x + 9\right )}^{\frac{3}{2}}} + \frac{3}{16 \,{\left (2 \, x + 3\right )}^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(4*x^2 + 12*x + 9)^(5/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.21804, size = 39, normalized size = 0.89 \[ -\frac{8 \, x + 3}{48 \,{\left (16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(4*x^2 + 12*x + 9)^(5/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x}{\left (\left (2 x + 3\right )^{2}\right )^{\frac{5}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(4*x**2+12*x+9)**(5/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.572296, size = 4, normalized size = 0.09 \[ \mathit{sage}_{0} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(4*x^2 + 12*x + 9)^(5/2),x, algorithm="giac")
[Out]