3.1531 \(\int \frac{3+5 x}{(1-2 x)^2 (2+3 x)^2} \, dx\)

Optimal. Leaf size=43 \[ \frac{11}{49 (1-2 x)}+\frac{1}{49 (3 x+2)}-\frac{31}{343} \log (1-2 x)+\frac{31}{343} \log (3 x+2) \]

[Out]

11/(49*(1 - 2*x)) + 1/(49*(2 + 3*x)) - (31*Log[1 - 2*x])/343 + (31*Log[2 + 3*x])
/343

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Rubi [A]  time = 0.0490224, 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 \[ \frac{11}{49 (1-2 x)}+\frac{1}{49 (3 x+2)}-\frac{31}{343} \log (1-2 x)+\frac{31}{343} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

11/(49*(1 - 2*x)) + 1/(49*(2 + 3*x)) - (31*Log[1 - 2*x])/343 + (31*Log[2 + 3*x])
/343

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Rubi in Sympy [A]  time = 7.3241, size = 32, normalized size = 0.74 \[ - \frac{31 \log{\left (- 2 x + 1 \right )}}{343} + \frac{31 \log{\left (3 x + 2 \right )}}{343} + \frac{1}{49 \left (3 x + 2\right )} + \frac{11}{49 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-31*log(-2*x + 1)/343 + 31*log(3*x + 2)/343 + 1/(49*(3*x + 2)) + 11/(49*(-2*x +
1))

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Mathematica [A]  time = 0.0299533, size = 40, normalized size = 0.93 \[ \frac{-31 x-23}{49 \left (6 x^2+x-2\right )}-\frac{31}{343} \log (1-2 x)+\frac{31}{343} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

(-23 - 31*x)/(49*(-2 + x + 6*x^2)) - (31*Log[1 - 2*x])/343 + (31*Log[2 + 3*x])/3
43

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Maple [A]  time = 0.013, size = 36, normalized size = 0.8 \[{\frac{1}{98+147\,x}}+{\frac{31\,\ln \left ( 2+3\,x \right ) }{343}}-{\frac{11}{-49+98\,x}}-{\frac{31\,\ln \left ( -1+2\,x \right ) }{343}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/49/(2+3*x)+31/343*ln(2+3*x)-11/49/(-1+2*x)-31/343*ln(-1+2*x)

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Maxima [A]  time = 1.33243, size = 46, normalized size = 1.07 \[ -\frac{31 \, x + 23}{49 \,{\left (6 \, x^{2} + x - 2\right )}} + \frac{31}{343} \, \log \left (3 \, x + 2\right ) - \frac{31}{343} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/49*(31*x + 23)/(6*x^2 + x - 2) + 31/343*log(3*x + 2) - 31/343*log(2*x - 1)

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Fricas [A]  time = 0.222081, size = 66, normalized size = 1.53 \[ \frac{31 \,{\left (6 \, x^{2} + x - 2\right )} \log \left (3 \, x + 2\right ) - 31 \,{\left (6 \, x^{2} + x - 2\right )} \log \left (2 \, x - 1\right ) - 217 \, x - 161}{343 \,{\left (6 \, x^{2} + x - 2\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/343*(31*(6*x^2 + x - 2)*log(3*x + 2) - 31*(6*x^2 + x - 2)*log(2*x - 1) - 217*x
- 161)/(6*x^2 + x - 2)

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Sympy [A]  time = 0.297574, size = 34, normalized size = 0.79 \[ - \frac{31 x + 23}{294 x^{2} + 49 x - 98} - \frac{31 \log{\left (x - \frac{1}{2} \right )}}{343} + \frac{31 \log{\left (x + \frac{2}{3} \right )}}{343} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(31*x + 23)/(294*x**2 + 49*x - 98) - 31*log(x - 1/2)/343 + 31*log(x + 2/3)/343

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GIAC/XCAS [A]  time = 0.206455, size = 54, normalized size = 1.26 \[ \frac{1}{49 \,{\left (3 \, x + 2\right )}} + \frac{66}{343 \,{\left (\frac{7}{3 \, x + 2} - 2\right )}} - \frac{31}{343} \,{\rm ln}\left ({\left | -\frac{7}{3 \, x + 2} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/49/(3*x + 2) + 66/343/(7/(3*x + 2) - 2) - 31/343*ln(abs(-7/(3*x + 2) + 2))