3.1593 \(\int \frac{2+3 x}{(1-2 x)^2 (3+5 x)^2} \, dx\)

Optimal. Leaf size=43 \[ \frac{7}{121 (1-2 x)}-\frac{1}{121 (5 x+3)}-\frac{37 \log (1-2 x)}{1331}+\frac{37 \log (5 x+3)}{1331} \]

[Out]

7/(121*(1 - 2*x)) - 1/(121*(3 + 5*x)) - (37*Log[1 - 2*x])/1331 + (37*Log[3 + 5*x
])/1331

_______________________________________________________________________________________

Rubi [A]  time = 0.0466695, antiderivative size = 43, 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 \[ \frac{7}{121 (1-2 x)}-\frac{1}{121 (5 x+3)}-\frac{37 \log (1-2 x)}{1331}+\frac{37 \log (5 x+3)}{1331} \]

Antiderivative was successfully verified.

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

[Out]

7/(121*(1 - 2*x)) - 1/(121*(3 + 5*x)) - (37*Log[1 - 2*x])/1331 + (37*Log[3 + 5*x
])/1331

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 7.3502, size = 32, normalized size = 0.74 \[ - \frac{37 \log{\left (- 2 x + 1 \right )}}{1331} + \frac{37 \log{\left (5 x + 3 \right )}}{1331} - \frac{1}{121 \left (5 x + 3\right )} + \frac{7}{121 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-37*log(-2*x + 1)/1331 + 37*log(5*x + 3)/1331 - 1/(121*(5*x + 3)) + 7/(121*(-2*x
+ 1))

_______________________________________________________________________________________

Mathematica [A]  time = 0.0288538, size = 40, normalized size = 0.93 \[ \frac{-37 x-20}{121 \left (10 x^2+x-3\right )}-\frac{37 \log (1-2 x)}{1331}+\frac{37 \log (5 x+3)}{1331} \]

Antiderivative was successfully verified.

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

[Out]

(-20 - 37*x)/(121*(-3 + x + 10*x^2)) - (37*Log[1 - 2*x])/1331 + (37*Log[3 + 5*x]
)/1331

_______________________________________________________________________________________

Maple [A]  time = 0.013, size = 36, normalized size = 0.8 \[ -{\frac{1}{363+605\,x}}+{\frac{37\,\ln \left ( 3+5\,x \right ) }{1331}}-{\frac{7}{-121+242\,x}}-{\frac{37\,\ln \left ( -1+2\,x \right ) }{1331}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/121/(3+5*x)+37/1331*ln(3+5*x)-7/121/(-1+2*x)-37/1331*ln(-1+2*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.3486, size = 46, normalized size = 1.07 \[ -\frac{37 \, x + 20}{121 \,{\left (10 \, x^{2} + x - 3\right )}} + \frac{37}{1331} \, \log \left (5 \, x + 3\right ) - \frac{37}{1331} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/121*(37*x + 20)/(10*x^2 + x - 3) + 37/1331*log(5*x + 3) - 37/1331*log(2*x - 1
)

_______________________________________________________________________________________

Fricas [A]  time = 0.204272, size = 66, normalized size = 1.53 \[ \frac{37 \,{\left (10 \, x^{2} + x - 3\right )} \log \left (5 \, x + 3\right ) - 37 \,{\left (10 \, x^{2} + x - 3\right )} \log \left (2 \, x - 1\right ) - 407 \, x - 220}{1331 \,{\left (10 \, x^{2} + x - 3\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/1331*(37*(10*x^2 + x - 3)*log(5*x + 3) - 37*(10*x^2 + x - 3)*log(2*x - 1) - 40
7*x - 220)/(10*x^2 + x - 3)

_______________________________________________________________________________________

Sympy [A]  time = 0.297972, size = 34, normalized size = 0.79 \[ - \frac{37 x + 20}{1210 x^{2} + 121 x - 363} - \frac{37 \log{\left (x - \frac{1}{2} \right )}}{1331} + \frac{37 \log{\left (x + \frac{3}{5} \right )}}{1331} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(37*x + 20)/(1210*x**2 + 121*x - 363) - 37*log(x - 1/2)/1331 + 37*log(x + 3/5)/
1331

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.209757, size = 54, normalized size = 1.26 \[ -\frac{1}{121 \,{\left (5 \, x + 3\right )}} + \frac{70}{1331 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}} - \frac{37}{1331} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/121/(5*x + 3) + 70/1331/(11/(5*x + 3) - 2) - 37/1331*ln(abs(-11/(5*x + 3) + 2
))