3.1508 \(\int \frac{1}{(1-2 x) (2+3 x) (3+5 x)^3} \, dx\)

Optimal. Leaf size=53 \[ \frac{155}{121 (5 x+3)}-\frac{5}{22 (5 x+3)^2}-\frac{8 \log (1-2 x)}{9317}-\frac{27}{7} \log (3 x+2)+\frac{5135 \log (5 x+3)}{1331} \]

[Out]

-5/(22*(3 + 5*x)^2) + 155/(121*(3 + 5*x)) - (8*Log[1 - 2*x])/9317 - (27*Log[2 +
3*x])/7 + (5135*Log[3 + 5*x])/1331

_______________________________________________________________________________________

Rubi [A]  time = 0.0609731, antiderivative size = 53, 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 \[ \frac{155}{121 (5 x+3)}-\frac{5}{22 (5 x+3)^2}-\frac{8 \log (1-2 x)}{9317}-\frac{27}{7} \log (3 x+2)+\frac{5135 \log (5 x+3)}{1331} \]

Antiderivative was successfully verified.

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

[Out]

-5/(22*(3 + 5*x)^2) + 155/(121*(3 + 5*x)) - (8*Log[1 - 2*x])/9317 - (27*Log[2 +
3*x])/7 + (5135*Log[3 + 5*x])/1331

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 8.72743, size = 46, normalized size = 0.87 \[ - \frac{8 \log{\left (- 2 x + 1 \right )}}{9317} - \frac{27 \log{\left (3 x + 2 \right )}}{7} + \frac{5135 \log{\left (5 x + 3 \right )}}{1331} + \frac{155}{121 \left (5 x + 3\right )} - \frac{5}{22 \left (5 x + 3\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8*log(-2*x + 1)/9317 - 27*log(3*x + 2)/7 + 5135*log(5*x + 3)/1331 + 155/(121*(5
*x + 3)) - 5/(22*(5*x + 3)**2)

_______________________________________________________________________________________

Mathematica [A]  time = 0.0614703, size = 43, normalized size = 0.81 \[ \frac{\frac{1925 (62 x+35)}{(5 x+3)^2}-16 \log (1-2 x)-71874 \log (6 x+4)+71890 \log (10 x+6)}{18634} \]

Antiderivative was successfully verified.

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

[Out]

((1925*(35 + 62*x))/(3 + 5*x)^2 - 16*Log[1 - 2*x] - 71874*Log[4 + 6*x] + 71890*L
og[6 + 10*x])/18634

_______________________________________________________________________________________

Maple [A]  time = 0.013, size = 44, normalized size = 0.8 \[ -{\frac{5}{22\, \left ( 3+5\,x \right ) ^{2}}}+{\frac{155}{363+605\,x}}+{\frac{5135\,\ln \left ( 3+5\,x \right ) }{1331}}-{\frac{27\,\ln \left ( 2+3\,x \right ) }{7}}-{\frac{8\,\ln \left ( -1+2\,x \right ) }{9317}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-5/22/(3+5*x)^2+155/121/(3+5*x)+5135/1331*ln(3+5*x)-27/7*ln(2+3*x)-8/9317*ln(-1+
2*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.33652, size = 59, normalized size = 1.11 \[ \frac{25 \,{\left (62 \, x + 35\right )}}{242 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{5135}{1331} \, \log \left (5 \, x + 3\right ) - \frac{27}{7} \, \log \left (3 \, x + 2\right ) - \frac{8}{9317} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

25/242*(62*x + 35)/(25*x^2 + 30*x + 9) + 5135/1331*log(5*x + 3) - 27/7*log(3*x +
2) - 8/9317*log(2*x - 1)

_______________________________________________________________________________________

Fricas [A]  time = 0.211754, size = 99, normalized size = 1.87 \[ \frac{71890 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 71874 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (3 \, x + 2\right ) - 16 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (2 \, x - 1\right ) + 119350 \, x + 67375}{18634 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/18634*(71890*(25*x^2 + 30*x + 9)*log(5*x + 3) - 71874*(25*x^2 + 30*x + 9)*log(
3*x + 2) - 16*(25*x^2 + 30*x + 9)*log(2*x - 1) + 119350*x + 67375)/(25*x^2 + 30*
x + 9)

_______________________________________________________________________________________

Sympy [A]  time = 0.478021, size = 44, normalized size = 0.83 \[ \frac{1550 x + 875}{6050 x^{2} + 7260 x + 2178} - \frac{8 \log{\left (x - \frac{1}{2} \right )}}{9317} + \frac{5135 \log{\left (x + \frac{3}{5} \right )}}{1331} - \frac{27 \log{\left (x + \frac{2}{3} \right )}}{7} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(1550*x + 875)/(6050*x**2 + 7260*x + 2178) - 8*log(x - 1/2)/9317 + 5135*log(x +
3/5)/1331 - 27*log(x + 2/3)/7

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.21213, size = 57, normalized size = 1.08 \[ \frac{25 \,{\left (62 \, x + 35\right )}}{242 \,{\left (5 \, x + 3\right )}^{2}} + \frac{5135}{1331} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{27}{7} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{8}{9317} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

25/242*(62*x + 35)/(5*x + 3)^2 + 5135/1331*ln(abs(5*x + 3)) - 27/7*ln(abs(3*x +
2)) - 8/9317*ln(abs(2*x - 1))