3.1439 \(\int \frac{(2+3 x)^3 (3+5 x)^2}{1-2 x} \, dx\)

Optimal. Leaf size=44 \[ -\frac{135 x^5}{2}-\frac{4995 x^4}{16}-\frac{5349 x^3}{8}-\frac{30175 x^2}{32}-\frac{39199 x}{32}-\frac{41503}{64} \log (1-2 x) \]

[Out]

(-39199*x)/32 - (30175*x^2)/32 - (5349*x^3)/8 - (4995*x^4)/16 - (135*x^5)/2 - (4
1503*Log[1 - 2*x])/64

_______________________________________________________________________________________

Rubi [A]  time = 0.0488841, antiderivative size = 44, 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 \[ -\frac{135 x^5}{2}-\frac{4995 x^4}{16}-\frac{5349 x^3}{8}-\frac{30175 x^2}{32}-\frac{39199 x}{32}-\frac{41503}{64} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

(-39199*x)/32 - (30175*x^2)/32 - (5349*x^3)/8 - (4995*x^4)/16 - (135*x^5)/2 - (4
1503*Log[1 - 2*x])/64

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{135 x^{5}}{2} - \frac{4995 x^{4}}{16} - \frac{5349 x^{3}}{8} - \frac{41503 \log{\left (- 2 x + 1 \right )}}{64} + \int \left (- \frac{39199}{32}\right )\, dx - \frac{30175 \int x\, dx}{16} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-135*x**5/2 - 4995*x**4/16 - 5349*x**3/8 - 41503*log(-2*x + 1)/64 + Integral(-39
199/32, x) - 30175*Integral(x, x)/16

_______________________________________________________________________________________

Mathematica [A]  time = 0.0184982, size = 37, normalized size = 0.84 \[ \frac{1}{256} \left (-17280 x^5-79920 x^4-171168 x^3-241400 x^2-313592 x-166012 \log (1-2 x)+244077\right ) \]

Antiderivative was successfully verified.

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

[Out]

(244077 - 313592*x - 241400*x^2 - 171168*x^3 - 79920*x^4 - 17280*x^5 - 166012*Lo
g[1 - 2*x])/256

_______________________________________________________________________________________

Maple [A]  time = 0.004, size = 33, normalized size = 0.8 \[ -{\frac{135\,{x}^{5}}{2}}-{\frac{4995\,{x}^{4}}{16}}-{\frac{5349\,{x}^{3}}{8}}-{\frac{30175\,{x}^{2}}{32}}-{\frac{39199\,x}{32}}-{\frac{41503\,\ln \left ( -1+2\,x \right ) }{64}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-135/2*x^5-4995/16*x^4-5349/8*x^3-30175/32*x^2-39199/32*x-41503/64*ln(-1+2*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.33633, size = 43, normalized size = 0.98 \[ -\frac{135}{2} \, x^{5} - \frac{4995}{16} \, x^{4} - \frac{5349}{8} \, x^{3} - \frac{30175}{32} \, x^{2} - \frac{39199}{32} \, x - \frac{41503}{64} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-135/2*x^5 - 4995/16*x^4 - 5349/8*x^3 - 30175/32*x^2 - 39199/32*x - 41503/64*log
(2*x - 1)

_______________________________________________________________________________________

Fricas [A]  time = 0.226785, size = 43, normalized size = 0.98 \[ -\frac{135}{2} \, x^{5} - \frac{4995}{16} \, x^{4} - \frac{5349}{8} \, x^{3} - \frac{30175}{32} \, x^{2} - \frac{39199}{32} \, x - \frac{41503}{64} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-135/2*x^5 - 4995/16*x^4 - 5349/8*x^3 - 30175/32*x^2 - 39199/32*x - 41503/64*log
(2*x - 1)

_______________________________________________________________________________________

Sympy [A]  time = 0.199851, size = 42, normalized size = 0.95 \[ - \frac{135 x^{5}}{2} - \frac{4995 x^{4}}{16} - \frac{5349 x^{3}}{8} - \frac{30175 x^{2}}{32} - \frac{39199 x}{32} - \frac{41503 \log{\left (2 x - 1 \right )}}{64} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-135*x**5/2 - 4995*x**4/16 - 5349*x**3/8 - 30175*x**2/32 - 39199*x/32 - 41503*lo
g(2*x - 1)/64

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.211472, size = 45, normalized size = 1.02 \[ -\frac{135}{2} \, x^{5} - \frac{4995}{16} \, x^{4} - \frac{5349}{8} \, x^{3} - \frac{30175}{32} \, x^{2} - \frac{39199}{32} \, x - \frac{41503}{64} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-135/2*x^5 - 4995/16*x^4 - 5349/8*x^3 - 30175/32*x^2 - 39199/32*x - 41503/64*ln(
abs(2*x - 1))