3.1588 \(\int \frac{(2+3 x)^6}{(1-2 x)^2 (3+5 x)^2} \, dx\)

Optimal. Leaf size=62 \[ \frac{243 x^3}{100}+\frac{13851 x^2}{1000}+\frac{473607 x}{10000}+\frac{117649}{3872 (1-2 x)}-\frac{1}{378125 (5 x+3)}+\frac{67228 \log (1-2 x)}{1331}+\frac{202 \log (5 x+3)}{4159375} \]

[Out]

117649/(3872*(1 - 2*x)) + (473607*x)/10000 + (13851*x^2)/1000 + (243*x^3)/100 -
1/(378125*(3 + 5*x)) + (67228*Log[1 - 2*x])/1331 + (202*Log[3 + 5*x])/4159375

_______________________________________________________________________________________

Rubi [A]  time = 0.0719885, antiderivative size = 62, 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 \[ \frac{243 x^3}{100}+\frac{13851 x^2}{1000}+\frac{473607 x}{10000}+\frac{117649}{3872 (1-2 x)}-\frac{1}{378125 (5 x+3)}+\frac{67228 \log (1-2 x)}{1331}+\frac{202 \log (5 x+3)}{4159375} \]

Antiderivative was successfully verified.

[In]  Int[(2 + 3*x)^6/((1 - 2*x)^2*(3 + 5*x)^2),x]

[Out]

117649/(3872*(1 - 2*x)) + (473607*x)/10000 + (13851*x^2)/1000 + (243*x^3)/100 -
1/(378125*(3 + 5*x)) + (67228*Log[1 - 2*x])/1331 + (202*Log[3 + 5*x])/4159375

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{243 x^{3}}{100} + \frac{67228 \log{\left (- 2 x + 1 \right )}}{1331} + \frac{202 \log{\left (5 x + 3 \right )}}{4159375} + \int \frac{473607}{10000}\, dx + \frac{13851 \int x\, dx}{500} - \frac{1}{378125 \left (5 x + 3\right )} + \frac{117649}{3872 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((2+3*x)**6/(1-2*x)**2/(3+5*x)**2,x)

[Out]

243*x**3/100 + 67228*log(-2*x + 1)/1331 + 202*log(5*x + 3)/4159375 + Integral(47
3607/10000, x) + 13851*Integral(x, x)/500 - 1/(378125*(5*x + 3)) + 117649/(3872*
(-2*x + 1))

_______________________________________________________________________________________

Mathematica [A]  time = 0.0601078, size = 65, normalized size = 1.05 \[ \frac{-\frac{11 (1838265689 x+1102959343)}{10 x^2+x-3}[phone] (3 x+2)^3+132966900 (3 x+2)^2+1425620790 (3 x+2)[phone] \log (3-6 x)+6464 \log (-3 (5 x+3))}{133100000} \]

Antiderivative was successfully verified.

[In]  Integrate[(2 + 3*x)^6/((1 - 2*x)^2*(3 + 5*x)^2),x]

[Out]

(1425620790*(2 + 3*x) + 132966900*(2 + 3*x)^2 + 11979000*(2 + 3*x)^3 - (11*(1102
959343 + 1838265689*x))/(-3 + x + 10*x^2) + 6722800000*Log[3 - 6*x] + 6464*Log[-
3*(3 + 5*x)])/133100000

_______________________________________________________________________________________

Maple [A]  time = 0.016, size = 49, normalized size = 0.8 \[{\frac{243\,{x}^{3}}{100}}+{\frac{13851\,{x}^{2}}{1000}}+{\frac{473607\,x}{10000}}-{\frac{1}{1134375+1890625\,x}}+{\frac{202\,\ln \left ( 3+5\,x \right ) }{4159375}}-{\frac{117649}{-3872+7744\,x}}+{\frac{67228\,\ln \left ( -1+2\,x \right ) }{1331}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2+3*x)^6/(1-2*x)^2/(3+5*x)^2,x)

[Out]

243/100*x^3+13851/1000*x^2+473607/10000*x-1/378125/(3+5*x)+202/4159375*ln(3+5*x)
-117649/3872/(-1+2*x)+67228/1331*ln(-1+2*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.33051, size = 63, normalized size = 1.02 \[ \frac{243}{100} \, x^{3} + \frac{13851}{1000} \, x^{2} + \frac{473607}{10000} \, x - \frac{1838265689 \, x + 1102959343}{12100000 \,{\left (10 \, x^{2} + x - 3\right )}} + \frac{202}{4159375} \, \log \left (5 \, x + 3\right ) + \frac{67228}{1331} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x + 2)^6/((5*x + 3)^2*(2*x - 1)^2),x, algorithm="maxima")

[Out]

243/100*x^3 + 13851/1000*x^2 + 473607/10000*x - 1/12100000*(1838265689*x + 11029
59343)/(10*x^2 + x - 3) + 202/4159375*log(5*x + 3) + 67228/1331*log(2*x - 1)

_______________________________________________________________________________________

Fricas [A]  time = 0.221225, size = 93, normalized size = 1.5 \[ \frac{3234330000 \, x^{5} + 18759114000 \, x^{4} + 63910360800 \, x^{3} + 773004870 \, x^{2} + 6464 \,{\left (10 \, x^{2} + x - 3\right )} \log \left (5 \, x + 3\right ) + 6722800000 \,{\left (10 \, x^{2} + x - 3\right )} \log \left (2 \, x - 1\right ) - 39132050089 \, x - 12132552773}{133100000 \,{\left (10 \, x^{2} + x - 3\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x + 2)^6/((5*x + 3)^2*(2*x - 1)^2),x, algorithm="fricas")

[Out]

1/133100000*(3234330000*x^5 + 18759114000*x^4 + 63910360800*x^3 + 773004870*x^2
+ 6464*(10*x^2 + x - 3)*log(5*x + 3) + 6722800000*(10*x^2 + x - 3)*log(2*x - 1)
- 39132050089*x - 12132552773)/(10*x^2 + x - 3)

_______________________________________________________________________________________

Sympy [A]  time = 0.407629, size = 53, normalized size = 0.85 \[ \frac{243 x^{3}}{100} + \frac{13851 x^{2}}{1000} + \frac{473607 x}{10000} - \frac{1838265689 x + 1102959343}{121000000 x^{2} + 12100000 x - 36300000} + \frac{67228 \log{\left (x - \frac{1}{2} \right )}}{1331} + \frac{202 \log{\left (x + \frac{3}{5} \right )}}{4159375} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2+3*x)**6/(1-2*x)**2/(3+5*x)**2,x)

[Out]

243*x**3/100 + 13851*x**2/1000 + 473607*x/10000 - (1838265689*x + 1102959343)/(1
21000000*x**2 + 12100000*x - 36300000) + 67228*log(x - 1/2)/1331 + 202*log(x + 3
/5)/4159375

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.213211, size = 127, normalized size = 2.05 \[ -\frac{{\left (5 \, x + 3\right )}^{3}{\left (\frac{4528062}{5 \, x + 3} + \frac{76330188}{{\left (5 \, x + 3\right )}^{2}} - \frac{840384278}{{\left (5 \, x + 3\right )}^{3}} + 323433\right )}}{8318750 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}} - \frac{1}{378125 \,{\left (5 \, x + 3\right )}} - \frac{157842}{3125} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) + \frac{67228}{1331} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x + 2)^6/((5*x + 3)^2*(2*x - 1)^2),x, algorithm="giac")

[Out]

-1/8318750*(5*x + 3)^3*(4528062/(5*x + 3) + 76330188/(5*x + 3)^2 - 840384278/(5*
x + 3)^3 + 323433)/(11/(5*x + 3) - 2) - 1/378125/(5*x + 3) - 157842/3125*ln(1/5*
abs(5*x + 3)/(5*x + 3)^2) + 67228/1331*ln(abs(-11/(5*x + 3) + 2))