3.1487 \(\int \frac{(2+3 x)^5}{(1-2 x) (3+5 x)^2} \, dx\)

Optimal. Leaf size=51 \[ -\frac{81 x^3}{50}-\frac{6399 x^2}{1000}-\frac{69039 x}{5000}-\frac{1}{34375 (5 x+3)}-\frac{16807 \log (1-2 x)}{1936}+\frac{167 \log (5 x+3)}{378125} \]

[Out]

(-69039*x)/5000 - (6399*x^2)/1000 - (81*x^3)/50 - 1/(34375*(3 + 5*x)) - (16807*L
og[1 - 2*x])/1936 + (167*Log[3 + 5*x])/378125

_______________________________________________________________________________________

Rubi [A]  time = 0.0552156, antiderivative size = 51, 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 \[ -\frac{81 x^3}{50}-\frac{6399 x^2}{1000}-\frac{69039 x}{5000}-\frac{1}{34375 (5 x+3)}-\frac{16807 \log (1-2 x)}{1936}+\frac{167 \log (5 x+3)}{378125} \]

Antiderivative was successfully verified.

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

[Out]

(-69039*x)/5000 - (6399*x^2)/1000 - (81*x^3)/50 - 1/(34375*(3 + 5*x)) - (16807*L
og[1 - 2*x])/1936 + (167*Log[3 + 5*x])/378125

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{81 x^{3}}{50} - \frac{16807 \log{\left (- 2 x + 1 \right )}}{1936} + \frac{167 \log{\left (5 x + 3 \right )}}{378125} + \int \left (- \frac{69039}{5000}\right )\, dx - \frac{6399 \int x\, dx}{500} - \frac{1}{34375 \left (5 x + 3\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-81*x**3/50 - 16807*log(-2*x + 1)/1936 + 167*log(5*x + 3)/378125 + Integral(-690
39/5000, x) - 6399*Integral(x, x)/500 - 1/(34375*(5*x + 3))

_______________________________________________________________________________________

Mathematica [A]  time = 0.038077, size = 50, normalized size = 0.98 \[ \frac{-\frac{11 \left (8910000 x^4+40540500 x^3+97059600 x^2-2318085 x-28730263\right )}{5 x+3}-105043750 \log (1-2 x)+5344 \log (10 x+6)}{12100000} \]

Antiderivative was successfully verified.

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

[Out]

((-11*(-28730263 - 2318085*x + 97059600*x^2 + 40540500*x^3 + 8910000*x^4))/(3 +
5*x) - 105043750*Log[1 - 2*x] + 5344*Log[6 + 10*x])/12100000

_______________________________________________________________________________________

Maple [A]  time = 0.013, size = 40, normalized size = 0.8 \[ -{\frac{81\,{x}^{3}}{50}}-{\frac{6399\,{x}^{2}}{1000}}-{\frac{69039\,x}{5000}}-{\frac{1}{103125+171875\,x}}+{\frac{167\,\ln \left ( 3+5\,x \right ) }{378125}}-{\frac{16807\,\ln \left ( -1+2\,x \right ) }{1936}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-81/50*x^3-6399/1000*x^2-69039/5000*x-1/34375/(3+5*x)+167/378125*ln(3+5*x)-16807
/1936*ln(-1+2*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.32809, size = 53, normalized size = 1.04 \[ -\frac{81}{50} \, x^{3} - \frac{6399}{1000} \, x^{2} - \frac{69039}{5000} \, x - \frac{1}{34375 \,{\left (5 \, x + 3\right )}} + \frac{167}{378125} \, \log \left (5 \, x + 3\right ) - \frac{16807}{1936} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-81/50*x^3 - 6399/1000*x^2 - 69039/5000*x - 1/34375/(5*x + 3) + 167/378125*log(5
*x + 3) - 16807/1936*log(2*x - 1)

_______________________________________________________________________________________

Fricas [A]  time = 0.219699, size = 74, normalized size = 1.45 \[ -\frac{49005000 \, x^{4} + 222972750 \, x^{3} + 533827800 \, x^{2} - 2672 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 52521875 \,{\left (5 \, x + 3\right )} \log \left (2 \, x - 1\right ) + 250611570 \, x + 176}{6050000 \,{\left (5 \, x + 3\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/6050000*(49005000*x^4 + 222972750*x^3 + 533827800*x^2 - 2672*(5*x + 3)*log(5*
x + 3) + 52521875*(5*x + 3)*log(2*x - 1) + 250611570*x + 176)/(5*x + 3)

_______________________________________________________________________________________

Sympy [A]  time = 0.369072, size = 44, normalized size = 0.86 \[ - \frac{81 x^{3}}{50} - \frac{6399 x^{2}}{1000} - \frac{69039 x}{5000} - \frac{16807 \log{\left (x - \frac{1}{2} \right )}}{1936} + \frac{167 \log{\left (x + \frac{3}{5} \right )}}{378125} - \frac{1}{171875 x + 103125} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-81*x**3/50 - 6399*x**2/1000 - 69039*x/5000 - 16807*log(x - 1/2)/1936 + 167*log(
x + 3/5)/378125 - 1/(171875*x + 103125)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.211934, size = 97, normalized size = 1.9 \[ -\frac{27}{25000} \,{\left (5 \, x + 3\right )}^{3}{\left (\frac{129}{5 \, x + 3} + \frac{1459}{{\left (5 \, x + 3\right )}^{2}} + 12\right )} - \frac{1}{34375 \,{\left (5 \, x + 3\right )}} + \frac{434043}{50000} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) - \frac{16807}{1936} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-27/25000*(5*x + 3)^3*(129/(5*x + 3) + 1459/(5*x + 3)^2 + 12) - 1/34375/(5*x + 3
) + 434043/50000*ln(1/5*abs(5*x + 3)/(5*x + 3)^2) - 16807/1936*ln(abs(-11/(5*x +
3) + 2))