3.1444 \(\int \frac{(3+5 x)^2}{(1-2 x) (2+3 x)^2} \, dx\)

Optimal. Leaf size=32 \[ -\frac{1}{63 (3 x+2)}-\frac{121}{98} \log (1-2 x)-\frac{68}{441} \log (3 x+2) \]

[Out]

-1/(63*(2 + 3*x)) - (121*Log[1 - 2*x])/98 - (68*Log[2 + 3*x])/441

_______________________________________________________________________________________

Rubi [A]  time = 0.0431859, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ -\frac{1}{63 (3 x+2)}-\frac{121}{98} \log (1-2 x)-\frac{68}{441} \log (3 x+2) \]

Antiderivative was successfully verified.

[In]  Int[(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^2),x]

[Out]

-1/(63*(2 + 3*x)) - (121*Log[1 - 2*x])/98 - (68*Log[2 + 3*x])/441

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 6.83815, size = 27, normalized size = 0.84 \[ - \frac{121 \log{\left (- 2 x + 1 \right )}}{98} - \frac{68 \log{\left (3 x + 2 \right )}}{441} - \frac{1}{63 \left (3 x + 2\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((3+5*x)**2/(1-2*x)/(2+3*x)**2,x)

[Out]

-121*log(-2*x + 1)/98 - 68*log(3*x + 2)/441 - 1/(63*(3*x + 2))

_______________________________________________________________________________________

Mathematica [A]  time = 0.0329845, size = 30, normalized size = 0.94 \[ \frac{1}{882} \left (-\frac{14}{3 x+2}-1089 \log (1-2 x)-136 \log (6 x+4)\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^2),x]

[Out]

(-14/(2 + 3*x) - 1089*Log[1 - 2*x] - 136*Log[4 + 6*x])/882

_______________________________________________________________________________________

Maple [A]  time = 0.011, size = 27, normalized size = 0.8 \[ -{\frac{1}{126+189\,x}}-{\frac{68\,\ln \left ( 2+3\,x \right ) }{441}}-{\frac{121\,\ln \left ( -1+2\,x \right ) }{98}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((3+5*x)^2/(1-2*x)/(2+3*x)^2,x)

[Out]

-1/63/(2+3*x)-68/441*ln(2+3*x)-121/98*ln(-1+2*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.35008, size = 35, normalized size = 1.09 \[ -\frac{1}{63 \,{\left (3 \, x + 2\right )}} - \frac{68}{441} \, \log \left (3 \, x + 2\right ) - \frac{121}{98} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2/((3*x + 2)^2*(2*x - 1)),x, algorithm="maxima")

[Out]

-1/63/(3*x + 2) - 68/441*log(3*x + 2) - 121/98*log(2*x - 1)

_______________________________________________________________________________________

Fricas [A]  time = 0.207197, size = 50, normalized size = 1.56 \[ -\frac{136 \,{\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) + 1089 \,{\left (3 \, x + 2\right )} \log \left (2 \, x - 1\right ) + 14}{882 \,{\left (3 \, x + 2\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2/((3*x + 2)^2*(2*x - 1)),x, algorithm="fricas")

[Out]

-1/882*(136*(3*x + 2)*log(3*x + 2) + 1089*(3*x + 2)*log(2*x - 1) + 14)/(3*x + 2)

_______________________________________________________________________________________

Sympy [A]  time = 0.341792, size = 27, normalized size = 0.84 \[ - \frac{121 \log{\left (x - \frac{1}{2} \right )}}{98} - \frac{68 \log{\left (x + \frac{2}{3} \right )}}{441} - \frac{1}{189 x + 126} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3+5*x)**2/(1-2*x)/(2+3*x)**2,x)

[Out]

-121*log(x - 1/2)/98 - 68*log(x + 2/3)/441 - 1/(189*x + 126)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.208821, size = 58, normalized size = 1.81 \[ -\frac{1}{63 \,{\left (3 \, x + 2\right )}} + \frac{25}{18} \,{\rm ln}\left (\frac{{\left | 3 \, x + 2 \right |}}{3 \,{\left (3 \, x + 2\right )}^{2}}\right ) - \frac{121}{98} \,{\rm ln}\left ({\left | -\frac{7}{3 \, x + 2} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2/((3*x + 2)^2*(2*x - 1)),x, algorithm="giac")

[Out]

-1/63/(3*x + 2) + 25/18*ln(1/3*abs(3*x + 2)/(3*x + 2)^2) - 121/98*ln(abs(-7/(3*x
+ 2) + 2))