3.1457 \(\int \frac{(2+3 x) (3+5 x)^3}{1-2 x} \, dx\)

Optimal. Leaf size=37 \[ -\frac{375 x^4}{8}-\frac{2225 x^3}{12}-\frac{5645 x^2}{16}-\frac{8453 x}{16}-\frac{9317}{32} \log (1-2 x) \]

[Out]

(-8453*x)/16 - (5645*x^2)/16 - (2225*x^3)/12 - (375*x^4)/8 - (9317*Log[1 - 2*x])
/32

_______________________________________________________________________________________

Rubi [A]  time = 0.0381535, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{375 x^4}{8}-\frac{2225 x^3}{12}-\frac{5645 x^2}{16}-\frac{8453 x}{16}-\frac{9317}{32} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

(-8453*x)/16 - (5645*x^2)/16 - (2225*x^3)/12 - (375*x^4)/8 - (9317*Log[1 - 2*x])
/32

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{375 x^{4}}{8} - \frac{2225 x^{3}}{12} - \frac{9317 \log{\left (- 2 x + 1 \right )}}{32} + \int \left (- \frac{8453}{16}\right )\, dx - \frac{5645 \int x\, dx}{8} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-375*x**4/8 - 2225*x**3/12 - 9317*log(-2*x + 1)/32 + Integral(-8453/16, x) - 564
5*Integral(x, x)/8

_______________________________________________________________________________________

Mathematica [A]  time = 0.0178272, size = 32, normalized size = 0.86 \[ \frac{1}{384} \left (-18000 x^4-71200 x^3-135480 x^2-202872 x-111804 \log (1-2 x)+145331\right ) \]

Antiderivative was successfully verified.

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

[Out]

(145331 - 202872*x - 135480*x^2 - 71200*x^3 - 18000*x^4 - 111804*Log[1 - 2*x])/3
84

_______________________________________________________________________________________

Maple [A]  time = 0.003, size = 28, normalized size = 0.8 \[ -{\frac{375\,{x}^{4}}{8}}-{\frac{2225\,{x}^{3}}{12}}-{\frac{5645\,{x}^{2}}{16}}-{\frac{8453\,x}{16}}-{\frac{9317\,\ln \left ( -1+2\,x \right ) }{32}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-375/8*x^4-2225/12*x^3-5645/16*x^2-8453/16*x-9317/32*ln(-1+2*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.33568, size = 36, normalized size = 0.97 \[ -\frac{375}{8} \, x^{4} - \frac{2225}{12} \, x^{3} - \frac{5645}{16} \, x^{2} - \frac{8453}{16} \, x - \frac{9317}{32} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-375/8*x^4 - 2225/12*x^3 - 5645/16*x^2 - 8453/16*x - 9317/32*log(2*x - 1)

_______________________________________________________________________________________

Fricas [A]  time = 0.219966, size = 36, normalized size = 0.97 \[ -\frac{375}{8} \, x^{4} - \frac{2225}{12} \, x^{3} - \frac{5645}{16} \, x^{2} - \frac{8453}{16} \, x - \frac{9317}{32} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-375/8*x^4 - 2225/12*x^3 - 5645/16*x^2 - 8453/16*x - 9317/32*log(2*x - 1)

_______________________________________________________________________________________

Sympy [A]  time = 0.17394, size = 36, normalized size = 0.97 \[ - \frac{375 x^{4}}{8} - \frac{2225 x^{3}}{12} - \frac{5645 x^{2}}{16} - \frac{8453 x}{16} - \frac{9317 \log{\left (2 x - 1 \right )}}{32} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-375*x**4/8 - 2225*x**3/12 - 5645*x**2/16 - 8453*x/16 - 9317*log(2*x - 1)/32

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.207994, size = 38, normalized size = 1.03 \[ -\frac{375}{8} \, x^{4} - \frac{2225}{12} \, x^{3} - \frac{5645}{16} \, x^{2} - \frac{8453}{16} \, x - \frac{9317}{32} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-375/8*x^4 - 2225/12*x^3 - 5645/16*x^2 - 8453/16*x - 9317/32*ln(abs(2*x - 1))