3.1440 \(\int \frac{(2+3 x)^2 (3+5 x)^2}{1-2 x} \, dx\)

Optimal. Leaf size=37 \[ -\frac{225 x^4}{8}-\frac{455 x^3}{4}-\frac{3529 x^2}{16}-\frac{5353 x}{16}-\frac{5929}{32} \log (1-2 x) \]

[Out]

(-5353*x)/16 - (3529*x^2)/16 - (455*x^3)/4 - (225*x^4)/8 - (5929*Log[1 - 2*x])/3
2

_______________________________________________________________________________________

Rubi [A]  time = 0.045332, antiderivative size = 37, 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 \[ -\frac{225 x^4}{8}-\frac{455 x^3}{4}-\frac{3529 x^2}{16}-\frac{5353 x}{16}-\frac{5929}{32} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

(-5353*x)/16 - (3529*x^2)/16 - (455*x^3)/4 - (225*x^4)/8 - (5929*Log[1 - 2*x])/3
2

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{225 x^{4}}{8} - \frac{455 x^{3}}{4} - \frac{5929 \log{\left (- 2 x + 1 \right )}}{32} + \int \left (- \frac{5353}{16}\right )\, dx - \frac{3529 \int x\, dx}{8} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225*x**4/8 - 455*x**3/4 - 5929*log(-2*x + 1)/32 + Integral(-5353/16, x) - 3529*
Integral(x, x)/8

_______________________________________________________________________________________

Mathematica [A]  time = 0.0159502, size = 32, normalized size = 0.86 \[ \frac{1}{128} \left (-3600 x^4-14560 x^3-28232 x^2-42824 x-23716 \log (1-2 x)+30515\right ) \]

Antiderivative was successfully verified.

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

[Out]

(30515 - 42824*x - 28232*x^2 - 14560*x^3 - 3600*x^4 - 23716*Log[1 - 2*x])/128

_______________________________________________________________________________________

Maple [A]  time = 0.003, size = 28, normalized size = 0.8 \[ -{\frac{225\,{x}^{4}}{8}}-{\frac{455\,{x}^{3}}{4}}-{\frac{3529\,{x}^{2}}{16}}-{\frac{5353\,x}{16}}-{\frac{5929\,\ln \left ( -1+2\,x \right ) }{32}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225/8*x^4-455/4*x^3-3529/16*x^2-5353/16*x-5929/32*ln(-1+2*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.32634, size = 36, normalized size = 0.97 \[ -\frac{225}{8} \, x^{4} - \frac{455}{4} \, x^{3} - \frac{3529}{16} \, x^{2} - \frac{5353}{16} \, x - \frac{5929}{32} \, \log \left (2 \, x - 1\right ) \]

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]

-225/8*x^4 - 455/4*x^3 - 3529/16*x^2 - 5353/16*x - 5929/32*log(2*x - 1)

_______________________________________________________________________________________

Fricas [A]  time = 0.227479, size = 36, normalized size = 0.97 \[ -\frac{225}{8} \, x^{4} - \frac{455}{4} \, x^{3} - \frac{3529}{16} \, x^{2} - \frac{5353}{16} \, x - \frac{5929}{32} \, \log \left (2 \, x - 1\right ) \]

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="fricas")

[Out]

-225/8*x^4 - 455/4*x^3 - 3529/16*x^2 - 5353/16*x - 5929/32*log(2*x - 1)

_______________________________________________________________________________________

Sympy [A]  time = 0.183634, size = 36, normalized size = 0.97 \[ - \frac{225 x^{4}}{8} - \frac{455 x^{3}}{4} - \frac{3529 x^{2}}{16} - \frac{5353 x}{16} - \frac{5929 \log{\left (2 x - 1 \right )}}{32} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225*x**4/8 - 455*x**3/4 - 3529*x**2/16 - 5353*x/16 - 5929*log(2*x - 1)/32

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.209397, size = 38, normalized size = 1.03 \[ -\frac{225}{8} \, x^{4} - \frac{455}{4} \, x^{3} - \frac{3529}{16} \, x^{2} - \frac{5353}{16} \, x - \frac{5929}{32} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225/8*x^4 - 455/4*x^3 - 3529/16*x^2 - 5353/16*x - 5929/32*ln(abs(2*x - 1))