Optimal. Leaf size=34 \[ -\frac{35 x+29}{3 x^2+5 x+2}+35 \log (x+1)-35 \log (3 x+2) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0263384, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167 \[ -\frac{35 x+29}{3 x^2+5 x+2}+35 \log (x+1)-35 \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[(5 - x)/(2 + 5*x + 3*x^2)^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.72814, size = 29, normalized size = 0.85 \[ - \frac{35 x + 29}{3 x^{2} + 5 x + 2} + 35 \log{\left (x + 1 \right )} - 35 \log{\left (3 x + 2 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((5-x)/(3*x**2+5*x+2)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0214203, size = 33, normalized size = 0.97 \[ \frac{-35 x-29}{3 x^2+5 x+2}+35 \log (x+1)-35 \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Integrate[(5 - x)/(2 + 5*x + 3*x^2)^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.013, size = 32, normalized size = 0.9 \[ -17\, \left ( 2+3\,x \right ) ^{-1}-35\,\ln \left ( 2+3\,x \right ) -6\, \left ( 1+x \right ) ^{-1}+35\,\ln \left ( 1+x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((5-x)/(3*x^2+5*x+2)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.688421, size = 46, normalized size = 1.35 \[ -\frac{35 \, x + 29}{3 \, x^{2} + 5 \, x + 2} - 35 \, \log \left (3 \, x + 2\right ) + 35 \, \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x - 5)/(3*x^2 + 5*x + 2)^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.263066, size = 72, normalized size = 2.12 \[ -\frac{35 \,{\left (3 \, x^{2} + 5 \, x + 2\right )} \log \left (3 \, x + 2\right ) - 35 \,{\left (3 \, x^{2} + 5 \, x + 2\right )} \log \left (x + 1\right ) + 35 \, x + 29}{3 \, x^{2} + 5 \, x + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x - 5)/(3*x^2 + 5*x + 2)^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.302194, size = 29, normalized size = 0.85 \[ - \frac{35 x + 29}{3 x^{2} + 5 x + 2} - 35 \log{\left (x + \frac{2}{3} \right )} + 35 \log{\left (x + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5-x)/(3*x**2+5*x+2)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.301508, size = 49, normalized size = 1.44 \[ -\frac{35 \, x + 29}{3 \, x^{2} + 5 \, x + 2} - 35 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) + 35 \,{\rm ln}\left ({\left | x + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x - 5)/(3*x^2 + 5*x + 2)^2,x, algorithm="giac")
[Out]