3.1608 \(\int \frac{1}{(1-2 x)^2 (3+5 x)^3} \, dx\)

Optimal. Leaf size=54 \[ \frac{4}{1331 (1-2 x)}-\frac{20}{1331 (5 x+3)}-\frac{5}{242 (5 x+3)^2}-\frac{60 \log (1-2 x)}{14641}+\frac{60 \log (5 x+3)}{14641} \]

[Out]

4/(1331*(1 - 2*x)) - 5/(242*(3 + 5*x)^2) - 20/(1331*(3 + 5*x)) - (60*Log[1 - 2*x
])/14641 + (60*Log[3 + 5*x])/14641

_______________________________________________________________________________________

Rubi [A]  time = 0.0504274, antiderivative size = 54, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{4}{1331 (1-2 x)}-\frac{20}{1331 (5 x+3)}-\frac{5}{242 (5 x+3)^2}-\frac{60 \log (1-2 x)}{14641}+\frac{60 \log (5 x+3)}{14641} \]

Antiderivative was successfully verified.

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

[Out]

4/(1331*(1 - 2*x)) - 5/(242*(3 + 5*x)^2) - 20/(1331*(3 + 5*x)) - (60*Log[1 - 2*x
])/14641 + (60*Log[3 + 5*x])/14641

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 7.41507, size = 42, normalized size = 0.78 \[ - \frac{60 \log{\left (- 2 x + 1 \right )}}{14641} + \frac{60 \log{\left (5 x + 3 \right )}}{14641} - \frac{20}{1331 \left (5 x + 3\right )} - \frac{5}{242 \left (5 x + 3\right )^{2}} + \frac{4}{1331 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-60*log(-2*x + 1)/14641 + 60*log(5*x + 3)/14641 - 20/(1331*(5*x + 3)) - 5/(242*(
5*x + 3)**2) + 4/(1331*(-2*x + 1))

_______________________________________________________________________________________

Mathematica [A]  time = 0.036768, size = 47, normalized size = 0.87 \[ \frac{-\frac{11 \left (600 x^2+390 x-103\right )}{(2 x-1) (5 x+3)^2}-120 \log (1-2 x)+120 \log (10 x+6)}{29282} \]

Antiderivative was successfully verified.

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

[Out]

((-11*(-103 + 390*x + 600*x^2))/((-1 + 2*x)*(3 + 5*x)^2) - 120*Log[1 - 2*x] + 12
0*Log[6 + 10*x])/29282

_______________________________________________________________________________________

Maple [A]  time = 0.015, size = 45, normalized size = 0.8 \[ -{\frac{5}{242\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{20}{3993+6655\,x}}+{\frac{60\,\ln \left ( 3+5\,x \right ) }{14641}}-{\frac{4}{-1331+2662\,x}}-{\frac{60\,\ln \left ( -1+2\,x \right ) }{14641}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(1-2*x)^2/(3+5*x)^3,x)

[Out]

-5/242/(3+5*x)^2-20/1331/(3+5*x)+60/14641*ln(3+5*x)-4/1331/(-1+2*x)-60/14641*ln(
-1+2*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.34884, size = 62, normalized size = 1.15 \[ -\frac{600 \, x^{2} + 390 \, x - 103}{2662 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} + \frac{60}{14641} \, \log \left (5 \, x + 3\right ) - \frac{60}{14641} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/2662*(600*x^2 + 390*x - 103)/(50*x^3 + 35*x^2 - 12*x - 9) + 60/14641*log(5*x
+ 3) - 60/14641*log(2*x - 1)

_______________________________________________________________________________________

Fricas [A]  time = 0.212463, size = 101, normalized size = 1.87 \[ -\frac{6600 \, x^{2} - 120 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (5 \, x + 3\right ) + 120 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (2 \, x - 1\right ) + 4290 \, x - 1133}{29282 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/29282*(6600*x^2 - 120*(50*x^3 + 35*x^2 - 12*x - 9)*log(5*x + 3) + 120*(50*x^3
+ 35*x^2 - 12*x - 9)*log(2*x - 1) + 4290*x - 1133)/(50*x^3 + 35*x^2 - 12*x - 9)

_______________________________________________________________________________________

Sympy [A]  time = 0.39466, size = 44, normalized size = 0.81 \[ - \frac{600 x^{2} + 390 x - 103}{133100 x^{3} + 93170 x^{2} - 31944 x - 23958} - \frac{60 \log{\left (x - \frac{1}{2} \right )}}{14641} + \frac{60 \log{\left (x + \frac{3}{5} \right )}}{14641} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(600*x**2 + 390*x - 103)/(133100*x**3 + 93170*x**2 - 31944*x - 23958) - 60*log(
x - 1/2)/14641 + 60*log(x + 3/5)/14641

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.206835, size = 69, normalized size = 1.28 \[ -\frac{4}{1331 \,{\left (2 \, x - 1\right )}} + \frac{50 \,{\left (\frac{66}{2 \, x - 1} + 25\right )}}{14641 \,{\left (\frac{11}{2 \, x - 1} + 5\right )}^{2}} + \frac{60}{14641} \,{\rm ln}\left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-4/1331/(2*x - 1) + 50/14641*(66/(2*x - 1) + 25)/(11/(2*x - 1) + 5)^2 + 60/14641
*ln(abs(-11/(2*x - 1) - 5))