3.1446 \(\int \frac{(3+5 x)^2}{(1-2 x) (2+3 x)^4} \, dx\)

Optimal. Leaf size=54 \[ -\frac{121}{343 (3 x+2)}+\frac{34}{441 (3 x+2)^2}-\frac{1}{189 (3 x+2)^3}-\frac{242 \log (1-2 x)}{2401}+\frac{242 \log (3 x+2)}{2401} \]

[Out]

-1/(189*(2 + 3*x)^3) + 34/(441*(2 + 3*x)^2) - 121/(343*(2 + 3*x)) - (242*Log[1 -
2*x])/2401 + (242*Log[2 + 3*x])/2401

_______________________________________________________________________________________

Rubi [A]  time = 0.0570184, antiderivative size = 54, 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 \[ -\frac{121}{343 (3 x+2)}+\frac{34}{441 (3 x+2)^2}-\frac{1}{189 (3 x+2)^3}-\frac{242 \log (1-2 x)}{2401}+\frac{242 \log (3 x+2)}{2401} \]

Antiderivative was successfully verified.

[In]  Int[(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^4),x]

[Out]

-1/(189*(2 + 3*x)^3) + 34/(441*(2 + 3*x)^2) - 121/(343*(2 + 3*x)) - (242*Log[1 -
2*x])/2401 + (242*Log[2 + 3*x])/2401

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 8.97691, size = 46, normalized size = 0.85 \[ - \frac{242 \log{\left (- 2 x + 1 \right )}}{2401} + \frac{242 \log{\left (3 x + 2 \right )}}{2401} - \frac{121}{343 \left (3 x + 2\right )} + \frac{34}{441 \left (3 x + 2\right )^{2}} - \frac{1}{189 \left (3 x + 2\right )^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((3+5*x)**2/(1-2*x)/(2+3*x)**4,x)

[Out]

-242*log(-2*x + 1)/2401 + 242*log(3*x + 2)/2401 - 121/(343*(3*x + 2)) + 34/(441*
(3*x + 2)**2) - 1/(189*(3*x + 2)**3)

_______________________________________________________________________________________

Mathematica [A]  time = 0.0398254, size = 40, normalized size = 0.74 \[ \frac{-\frac{7 \left (29403 x^2+37062 x+11689\right )}{(3 x+2)^3}-6534 \log (1-2 x)+6534 \log (6 x+4)}{64827} \]

Antiderivative was successfully verified.

[In]  Integrate[(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^4),x]

[Out]

((-7*(11689 + 37062*x + 29403*x^2))/(2 + 3*x)^3 - 6534*Log[1 - 2*x] + 6534*Log[4
+ 6*x])/64827

_______________________________________________________________________________________

Maple [A]  time = 0.012, size = 45, normalized size = 0.8 \[ -{\frac{1}{189\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{34}{441\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{121}{686+1029\,x}}+{\frac{242\,\ln \left ( 2+3\,x \right ) }{2401}}-{\frac{242\,\ln \left ( -1+2\,x \right ) }{2401}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((3+5*x)^2/(1-2*x)/(2+3*x)^4,x)

[Out]

-1/189/(2+3*x)^3+34/441/(2+3*x)^2-121/343/(2+3*x)+242/2401*ln(2+3*x)-242/2401*ln
(-1+2*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.32609, size = 62, normalized size = 1.15 \[ -\frac{29403 \, x^{2} + 37062 \, x + 11689}{9261 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + \frac{242}{2401} \, \log \left (3 \, x + 2\right ) - \frac{242}{2401} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2/((3*x + 2)^4*(2*x - 1)),x, algorithm="maxima")

[Out]

-1/9261*(29403*x^2 + 37062*x + 11689)/(27*x^3 + 54*x^2 + 36*x + 8) + 242/2401*lo
g(3*x + 2) - 242/2401*log(2*x - 1)

_______________________________________________________________________________________

Fricas [A]  time = 0.211679, size = 101, normalized size = 1.87 \[ -\frac{205821 \, x^{2} - 6534 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) + 6534 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (2 \, x - 1\right ) + 259434 \, x + 81823}{64827 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2/((3*x + 2)^4*(2*x - 1)),x, algorithm="fricas")

[Out]

-1/64827*(205821*x^2 - 6534*(27*x^3 + 54*x^2 + 36*x + 8)*log(3*x + 2) + 6534*(27
*x^3 + 54*x^2 + 36*x + 8)*log(2*x - 1) + 259434*x + 81823)/(27*x^3 + 54*x^2 + 36
*x + 8)

_______________________________________________________________________________________

Sympy [A]  time = 0.426278, size = 44, normalized size = 0.81 \[ - \frac{29403 x^{2} + 37062 x + 11689}{250047 x^{3} + 500094 x^{2} + 333396 x + 74088} - \frac{242 \log{\left (x - \frac{1}{2} \right )}}{2401} + \frac{242 \log{\left (x + \frac{2}{3} \right )}}{2401} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3+5*x)**2/(1-2*x)/(2+3*x)**4,x)

[Out]

-(29403*x**2 + 37062*x + 11689)/(250047*x**3 + 500094*x**2 + 333396*x + 74088) -
242*log(x - 1/2)/2401 + 242*log(x + 2/3)/2401

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.208886, size = 51, normalized size = 0.94 \[ -\frac{29403 \, x^{2} + 37062 \, x + 11689}{9261 \,{\left (3 \, x + 2\right )}^{3}} + \frac{242}{2401} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{242}{2401} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2/((3*x + 2)^4*(2*x - 1)),x, algorithm="giac")

[Out]

-1/9261*(29403*x^2 + 37062*x + 11689)/(3*x + 2)^3 + 242/2401*ln(abs(3*x + 2)) -
242/2401*ln(abs(2*x - 1))