3.1609 \(\int \frac{1}{(1-2 x)^2 (2+3 x) (3+5 x)^3} \, dx\)

Optimal. Leaf size=64 \[ \frac{8}{9317 (1-2 x)}+\frac{725}{1331 (5 x+3)}-\frac{25}{242 (5 x+3)^2}-\frac{1104 \log (1-2 x)}{717409}-\frac{81}{49} \log (3 x+2)+\frac{24225 \log (5 x+3)}{14641} \]

[Out]

8/(9317*(1 - 2*x)) - 25/(242*(3 + 5*x)^2) + 725/(1331*(3 + 5*x)) - (1104*Log[1 -
2*x])/717409 - (81*Log[2 + 3*x])/49 + (24225*Log[3 + 5*x])/14641

_______________________________________________________________________________________

Rubi [A]  time = 0.0753131, antiderivative size = 64, 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 \[ \frac{8}{9317 (1-2 x)}+\frac{725}{1331 (5 x+3)}-\frac{25}{242 (5 x+3)^2}-\frac{1104 \log (1-2 x)}{717409}-\frac{81}{49} \log (3 x+2)+\frac{24225 \log (5 x+3)}{14641} \]

Antiderivative was successfully verified.

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

[Out]

8/(9317*(1 - 2*x)) - 25/(242*(3 + 5*x)^2) + 725/(1331*(3 + 5*x)) - (1104*Log[1 -
2*x])/717409 - (81*Log[2 + 3*x])/49 + (24225*Log[3 + 5*x])/14641

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 10.0448, size = 53, normalized size = 0.83 \[ - \frac{1104 \log{\left (- 2 x + 1 \right )}}{717409} - \frac{81 \log{\left (3 x + 2 \right )}}{49} + \frac{24225 \log{\left (5 x + 3 \right )}}{14641} + \frac{725}{1331 \left (5 x + 3\right )} - \frac{25}{242 \left (5 x + 3\right )^{2}} + \frac{8}{9317 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1104*log(-2*x + 1)/717409 - 81*log(3*x + 2)/49 + 24225*log(5*x + 3)/14641 + 725
/(1331*(5*x + 3)) - 25/(242*(5*x + 3)**2) + 8/(9317*(-2*x + 1))

_______________________________________________________________________________________

Mathematica [A]  time = 0.052018, size = 60, normalized size = 0.94 \[ \frac{3 \left (\frac{1232}{3-6 x}+\frac{781550}{15 x+9}-\frac{148225}{3 (5 x+3)^2}-736 \log (3-6 x)-790614 \log (3 x+2)+791350 \log (-3 (5 x+3))\right )}{1434818} \]

Antiderivative was successfully verified.

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

[Out]

(3*(1232/(3 - 6*x) - 148225/(3*(3 + 5*x)^2) + 781550/(9 + 15*x) - 736*Log[3 - 6*
x] - 790614*Log[2 + 3*x] + 791350*Log[-3*(3 + 5*x)]))/1434818

_______________________________________________________________________________________

Maple [A]  time = 0.017, size = 53, normalized size = 0.8 \[ -{\frac{25}{242\, \left ( 3+5\,x \right ) ^{2}}}+{\frac{725}{3993+6655\,x}}+{\frac{24225\,\ln \left ( 3+5\,x \right ) }{14641}}-{\frac{81\,\ln \left ( 2+3\,x \right ) }{49}}-{\frac{8}{-9317+18634\,x}}-{\frac{1104\,\ln \left ( -1+2\,x \right ) }{717409}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25/242/(3+5*x)^2+725/1331/(3+5*x)+24225/14641*ln(3+5*x)-81/49*ln(2+3*x)-8/9317/
(-1+2*x)-1104/717409*ln(-1+2*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.34697, size = 73, normalized size = 1.14 \[ \frac{101100 \, x^{2} + 5820 \, x - 28669}{18634 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} + \frac{24225}{14641} \, \log \left (5 \, x + 3\right ) - \frac{81}{49} \, \log \left (3 \, x + 2\right ) - \frac{1104}{717409} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/18634*(101100*x^2 + 5820*x - 28669)/(50*x^3 + 35*x^2 - 12*x - 9) + 24225/14641
*log(5*x + 3) - 81/49*log(3*x + 2) - 1104/717409*log(2*x - 1)

_______________________________________________________________________________________

Fricas [A]  time = 0.216501, size = 132, normalized size = 2.06 \[ \frac{7784700 \, x^{2} + 2374050 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (5 \, x + 3\right ) - 2371842 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (3 \, x + 2\right ) - 2208 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (2 \, x - 1\right ) + 448140 \, x - 2207513}{1434818 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/1434818*(7784700*x^2 + 2374050*(50*x^3 + 35*x^2 - 12*x - 9)*log(5*x + 3) - 237
1842*(50*x^3 + 35*x^2 - 12*x - 9)*log(3*x + 2) - 2208*(50*x^3 + 35*x^2 - 12*x -
9)*log(2*x - 1) + 448140*x - 2207513)/(50*x^3 + 35*x^2 - 12*x - 9)

_______________________________________________________________________________________

Sympy [A]  time = 0.537373, size = 54, normalized size = 0.84 \[ \frac{101100 x^{2} + 5820 x - 28669}{931700 x^{3} + 652190 x^{2} - 223608 x - 167706} - \frac{1104 \log{\left (x - \frac{1}{2} \right )}}{717409} + \frac{24225 \log{\left (x + \frac{3}{5} \right )}}{14641} - \frac{81 \log{\left (x + \frac{2}{3} \right )}}{49} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(101100*x**2 + 5820*x - 28669)/(931700*x**3 + 652190*x**2 - 223608*x - 167706) -
1104*log(x - 1/2)/717409 + 24225*log(x + 3/5)/14641 - 81*log(x + 2/3)/49

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.210901, size = 89, normalized size = 1.39 \[ -\frac{8}{9317 \,{\left (2 \, x - 1\right )}} - \frac{250 \,{\left (\frac{297}{2 \, x - 1} + 140\right )}}{14641 \,{\left (\frac{11}{2 \, x - 1} + 5\right )}^{2}} - \frac{81}{49} \,{\rm ln}\left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) + \frac{24225}{14641} \,{\rm ln}\left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8/9317/(2*x - 1) - 250/14641*(297/(2*x - 1) + 140)/(11/(2*x - 1) + 5)^2 - 81/49
*ln(abs(-7/(2*x - 1) - 3)) + 24225/14641*ln(abs(-11/(2*x - 1) - 5))