3.1685 \(\int \frac{(2+3 x)^4}{(1-2 x)^3 (3+5 x)^3} \, dx\)

Optimal. Leaf size=65 \[ -\frac{9261}{58564 (1-2 x)}-\frac{138}{366025 (5 x+3)}+\frac{2401}{10648 (1-2 x)^2}-\frac{1}{66550 (5 x+3)^2}-\frac{294 \log (1-2 x)}{161051}+\frac{294 \log (5 x+3)}{161051} \]

[Out]

2401/(10648*(1 - 2*x)^2) - 9261/(58564*(1 - 2*x)) - 1/(66550*(3 + 5*x)^2) - 138/
(366025*(3 + 5*x)) - (294*Log[1 - 2*x])/161051 + (294*Log[3 + 5*x])/161051

_______________________________________________________________________________________

Rubi [A]  time = 0.0773588, antiderivative size = 65, 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 \[ -\frac{9261}{58564 (1-2 x)}-\frac{138}{366025 (5 x+3)}+\frac{2401}{10648 (1-2 x)^2}-\frac{1}{66550 (5 x+3)^2}-\frac{294 \log (1-2 x)}{161051}+\frac{294 \log (5 x+3)}{161051} \]

Antiderivative was successfully verified.

[In]  Int[(2 + 3*x)^4/((1 - 2*x)^3*(3 + 5*x)^3),x]

[Out]

2401/(10648*(1 - 2*x)^2) - 9261/(58564*(1 - 2*x)) - 1/(66550*(3 + 5*x)^2) - 138/
(366025*(3 + 5*x)) - (294*Log[1 - 2*x])/161051 + (294*Log[3 + 5*x])/161051

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 10.3259, size = 53, normalized size = 0.82 \[ - \frac{294 \log{\left (- 2 x + 1 \right )}}{161051} + \frac{294 \log{\left (5 x + 3 \right )}}{161051} - \frac{138}{366025 \left (5 x + 3\right )} - \frac{1}{66550 \left (5 x + 3\right )^{2}} - \frac{9261}{58564 \left (- 2 x + 1\right )} + \frac{2401}{10648 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((2+3*x)**4/(1-2*x)**3/(3+5*x)**3,x)

[Out]

-294*log(-2*x + 1)/161051 + 294*log(5*x + 3)/161051 - 138/(366025*(5*x + 3)) - 1
/(66550*(5*x + 3)**2) - 9261/(58564*(-2*x + 1)) + 2401/(10648*(-2*x + 1)**2)

_______________________________________________________________________________________

Mathematica [A]  time = 0.0512741, size = 48, normalized size = 0.74 \[ \frac{\frac{11 \left (23130420 x^3+32722281 x^2+14259554 x+1771669\right )}{\left (10 x^2+x-3\right )^2}+58800 \log (-5 x-3)-58800 \log (1-2 x)}{32210200} \]

Antiderivative was successfully verified.

[In]  Integrate[(2 + 3*x)^4/((1 - 2*x)^3*(3 + 5*x)^3),x]

[Out]

((11*(1771669 + 14259554*x + 32722281*x^2 + 23130420*x^3))/(-3 + x + 10*x^2)^2 +
58800*Log[-3 - 5*x] - 58800*Log[1 - 2*x])/32210200

_______________________________________________________________________________________

Maple [A]  time = 0.014, size = 54, normalized size = 0.8 \[ -{\frac{1}{66550\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{138}{1098075+1830125\,x}}+{\frac{294\,\ln \left ( 3+5\,x \right ) }{161051}}+{\frac{2401}{10648\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{9261}{-58564+117128\,x}}-{\frac{294\,\ln \left ( -1+2\,x \right ) }{161051}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2+3*x)^4/(1-2*x)^3/(3+5*x)^3,x)

[Out]

-1/66550/(3+5*x)^2-138/366025/(3+5*x)+294/161051*ln(3+5*x)+2401/10648/(-1+2*x)^2
+9261/58564/(-1+2*x)-294/161051*ln(-1+2*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.34286, size = 76, normalized size = 1.17 \[ \frac{23130420 \, x^{3} + 32722281 \, x^{2} + 14259554 \, x + 1771669}{2928200 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} + \frac{294}{161051} \, \log \left (5 \, x + 3\right ) - \frac{294}{161051} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(3*x + 2)^4/((5*x + 3)^3*(2*x - 1)^3),x, algorithm="maxima")

[Out]

1/2928200*(23130420*x^3 + 32722281*x^2 + 14259554*x + 1771669)/(100*x^4 + 20*x^3
- 59*x^2 - 6*x + 9) + 294/161051*log(5*x + 3) - 294/161051*log(2*x - 1)

_______________________________________________________________________________________

Fricas [A]  time = 0.209676, size = 128, normalized size = 1.97 \[ \frac{254434620 \, x^{3} + 359945091 \, x^{2} + 58800 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 58800 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (2 \, x - 1\right ) + 156855094 \, x + 19488359}{32210200 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(3*x + 2)^4/((5*x + 3)^3*(2*x - 1)^3),x, algorithm="fricas")

[Out]

1/32210200*(254434620*x^3 + 359945091*x^2 + 58800*(100*x^4 + 20*x^3 - 59*x^2 - 6
*x + 9)*log(5*x + 3) - 58800*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(2*x - 1)
+ 156855094*x + 19488359)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)

_______________________________________________________________________________________

Sympy [A]  time = 0.478089, size = 54, normalized size = 0.83 \[ \frac{23130420 x^{3} + 32722281 x^{2} + 14259554 x + 1771669}{292820000 x^{4} + 58564000 x^{3} - 172763800 x^{2} - 17569200 x + 26353800} - \frac{294 \log{\left (x - \frac{1}{2} \right )}}{161051} + \frac{294 \log{\left (x + \frac{3}{5} \right )}}{161051} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2+3*x)**4/(1-2*x)**3/(3+5*x)**3,x)

[Out]

(23130420*x**3 + 32722281*x**2 + 14259554*x + 1771669)/(292820000*x**4 + 5856400
0*x**3 - 172763800*x**2 - 17569200*x + 26353800) - 294*log(x - 1/2)/161051 + 294
*log(x + 3/5)/161051

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.219378, size = 62, normalized size = 0.95 \[ \frac{23130420 \, x^{3} + 32722281 \, x^{2} + 14259554 \, x + 1771669}{2928200 \,{\left (10 \, x^{2} + x - 3\right )}^{2}} + \frac{294}{161051} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{294}{161051} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(3*x + 2)^4/((5*x + 3)^3*(2*x - 1)^3),x, algorithm="giac")

[Out]

1/2928200*(23130420*x^3 + 32722281*x^2 + 14259554*x + 1771669)/(10*x^2 + x - 3)^
2 + 294/161051*ln(abs(5*x + 3)) - 294/161051*ln(abs(2*x - 1))