Optimal. Leaf size=36 \[ -\frac{139 x+121}{3 \left (3 x^2+5 x+2\right )}+47 \log (x+1)-47 \log (3 x+2) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0448165, antiderivative size = 36, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.13 \[ -\frac{139 x+121}{3 \left (3 x^2+5 x+2\right )}+47 \log (x+1)-47 \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[((5 - x)*(3 + 2*x))/(2 + 5*x + 3*x^2)^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 8.56751, size = 32, normalized size = 0.89 \[ - \frac{\left (- x + 5\right ) \left (8 x + 7\right )}{3 x^{2} + 5 x + 2} + 47 \log{\left (x + 1 \right )} - 47 \log{\left (3 x + 2 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((5-x)*(3+2*x)/(3*x**2+5*x+2)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0254025, size = 34, normalized size = 0.94 \[ -\frac{139 x+121}{9 x^2+15 x+6}+47 \log (x+1)-47 \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Integrate[((5 - x)*(3 + 2*x))/(2 + 5*x + 3*x^2)^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.015, size = 32, normalized size = 0.9 \[ -{\frac{85}{6+9\,x}}-47\,\ln \left ( 2+3\,x \right ) -6\, \left ( 1+x \right ) ^{-1}+47\,\ln \left ( 1+x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((5-x)*(3+2*x)/(3*x^2+5*x+2)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.693901, size = 46, normalized size = 1.28 \[ -\frac{139 \, x + 121}{3 \,{\left (3 \, x^{2} + 5 \, x + 2\right )}} - 47 \, \log \left (3 \, x + 2\right ) + 47 \, \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x + 3)*(x - 5)/(3*x^2 + 5*x + 2)^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.26325, size = 72, normalized size = 2. \[ -\frac{141 \,{\left (3 \, x^{2} + 5 \, x + 2\right )} \log \left (3 \, x + 2\right ) - 141 \,{\left (3 \, x^{2} + 5 \, x + 2\right )} \log \left (x + 1\right ) + 139 \, x + 121}{3 \,{\left (3 \, x^{2} + 5 \, x + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x + 3)*(x - 5)/(3*x^2 + 5*x + 2)^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.333921, size = 29, normalized size = 0.81 \[ - \frac{139 x + 121}{9 x^{2} + 15 x + 6} - 47 \log{\left (x + \frac{2}{3} \right )} + 47 \log{\left (x + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5-x)*(3+2*x)/(3*x**2+5*x+2)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.312157, size = 49, normalized size = 1.36 \[ -\frac{139 \, x + 121}{3 \,{\left (3 \, x^{2} + 5 \, x + 2\right )}} - 47 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) + 47 \,{\rm ln}\left ({\left | x + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x + 3)*(x - 5)/(3*x^2 + 5*x + 2)^2,x, algorithm="giac")
[Out]