3.1566 \(\int \frac{(3+5 x)^3}{(1-2 x)^2 (2+3 x)^4} \, dx\)

Optimal. Leaf size=65 \[ \frac{1331}{2401 (1-2 x)}+\frac{363}{2401 (3 x+2)}-\frac{101}{6174 (3 x+2)^2}+\frac{1}{1323 (3 x+2)^3}-\frac{3267 \log (1-2 x)}{16807}+\frac{3267 \log (3 x+2)}{16807} \]

[Out]

1331/(2401*(1 - 2*x)) + 1/(1323*(2 + 3*x)^3) - 101/(6174*(2 + 3*x)^2) + 363/(240
1*(2 + 3*x)) - (3267*Log[1 - 2*x])/16807 + (3267*Log[2 + 3*x])/16807

_______________________________________________________________________________________

Rubi [A]  time = 0.0734643, 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 \[ \frac{1331}{2401 (1-2 x)}+\frac{363}{2401 (3 x+2)}-\frac{101}{6174 (3 x+2)^2}+\frac{1}{1323 (3 x+2)^3}-\frac{3267 \log (1-2 x)}{16807}+\frac{3267 \log (3 x+2)}{16807} \]

Antiderivative was successfully verified.

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

[Out]

1331/(2401*(1 - 2*x)) + 1/(1323*(2 + 3*x)^3) - 101/(6174*(2 + 3*x)^2) + 363/(240
1*(2 + 3*x)) - (3267*Log[1 - 2*x])/16807 + (3267*Log[2 + 3*x])/16807

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 10.2391, size = 53, normalized size = 0.82 \[ - \frac{3267 \log{\left (- 2 x + 1 \right )}}{16807} + \frac{3267 \log{\left (3 x + 2 \right )}}{16807} + \frac{363}{2401 \left (3 x + 2\right )} - \frac{101}{6174 \left (3 x + 2\right )^{2}} + \frac{1}{1323 \left (3 x + 2\right )^{3}} + \frac{1331}{2401 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3267*log(-2*x + 1)/16807 + 3267*log(3*x + 2)/16807 + 363/(2401*(3*x + 2)) - 101
/(6174*(3*x + 2)**2) + 1/(1323*(3*x + 2)**3) + 1331/(2401*(-2*x + 1))

_______________________________________________________________________________________

Mathematica [A]  time = 0.0682914, size = 62, normalized size = 0.95 \[ \frac{\frac{7}{2} \left (\frac{19602}{3 x+2}-\frac{2121}{(3 x+2)^2}+\frac{98}{(3 x+2)^3}+\frac{71874}{1-2 x}\right )-88209 \log (1-2 x)+88209 \log (6 x+4)}{453789} \]

Antiderivative was successfully verified.

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

[Out]

((7*(71874/(1 - 2*x) + 98/(2 + 3*x)^3 - 2121/(2 + 3*x)^2 + 19602/(2 + 3*x)))/2 -
88209*Log[1 - 2*x] + 88209*Log[4 + 6*x])/453789

_______________________________________________________________________________________

Maple [A]  time = 0.015, size = 54, normalized size = 0.8 \[{\frac{1}{1323\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{101}{6174\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{363}{4802+7203\,x}}+{\frac{3267\,\ln \left ( 2+3\,x \right ) }{16807}}-{\frac{1331}{-2401+4802\,x}}-{\frac{3267\,\ln \left ( -1+2\,x \right ) }{16807}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/1323/(2+3*x)^3-101/6174/(2+3*x)^2+363/2401/(2+3*x)+3267/16807*ln(2+3*x)-1331/2
401/(-1+2*x)-3267/16807*ln(-1+2*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.34891, size = 76, normalized size = 1.17 \[ -\frac{1587762 \, x^{3} + 3599892 \, x^{2} + 2667797 \, x + 649256}{129654 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )}} + \frac{3267}{16807} \, \log \left (3 \, x + 2\right ) - \frac{3267}{16807} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/129654*(1587762*x^3 + 3599892*x^2 + 2667797*x + 649256)/(54*x^4 + 81*x^3 + 18
*x^2 - 20*x - 8) + 3267/16807*log(3*x + 2) - 3267/16807*log(2*x - 1)

_______________________________________________________________________________________

Fricas [A]  time = 0.214723, size = 128, normalized size = 1.97 \[ -\frac{11114334 \, x^{3} + 25199244 \, x^{2} - 176418 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (3 \, x + 2\right ) + 176418 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (2 \, x - 1\right ) + 18674579 \, x + 4544792}{907578 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/907578*(11114334*x^3 + 25199244*x^2 - 176418*(54*x^4 + 81*x^3 + 18*x^2 - 20*x
- 8)*log(3*x + 2) + 176418*(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*log(2*x - 1) +
18674579*x + 4544792)/(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)

_______________________________________________________________________________________

Sympy [A]  time = 0.448139, size = 54, normalized size = 0.83 \[ - \frac{1587762 x^{3} + 3599892 x^{2} + 2667797 x + 649256}{7001316 x^{4} + 10501974 x^{3} + 2333772 x^{2} - 2593080 x - 1037232} - \frac{3267 \log{\left (x - \frac{1}{2} \right )}}{16807} + \frac{3267 \log{\left (x + \frac{2}{3} \right )}}{16807} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(1587762*x**3 + 3599892*x**2 + 2667797*x + 649256)/(7001316*x**4 + 10501974*x**
3 + 2333772*x**2 - 2593080*x - 1037232) - 3267*log(x - 1/2)/16807 + 3267*log(x +
2/3)/16807

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.20895, size = 81, normalized size = 1.25 \[ -\frac{1331}{2401 \,{\left (2 \, x - 1\right )}} - \frac{2 \,{\left (\frac{43645}{2 \, x - 1} + \frac{50127}{{\left (2 \, x - 1\right )}^{2}} + 9502\right )}}{16807 \,{\left (\frac{7}{2 \, x - 1} + 3\right )}^{3}} + \frac{3267}{16807} \,{\rm ln}\left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1331/2401/(2*x - 1) - 2/16807*(43645/(2*x - 1) + 50127/(2*x - 1)^2 + 9502)/(7/(
2*x - 1) + 3)^3 + 3267/16807*ln(abs(-7/(2*x - 1) - 3))