3.1530 \(\int \frac{3+5 x}{(1-2 x)^2 (2+3 x)} \, dx\)

Optimal. Leaf size=32 \[ \frac{11}{14 (1-2 x)}+\frac{1}{49} \log (1-2 x)-\frac{1}{49} \log (3 x+2) \]

[Out]

11/(14*(1 - 2*x)) + Log[1 - 2*x]/49 - Log[2 + 3*x]/49

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Rubi [A]  time = 0.0384898, antiderivative size = 32, 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 \[ \frac{11}{14 (1-2 x)}+\frac{1}{49} \log (1-2 x)-\frac{1}{49} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

11/(14*(1 - 2*x)) + Log[1 - 2*x]/49 - Log[2 + 3*x]/49

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Rubi in Sympy [A]  time = 6.25683, size = 22, normalized size = 0.69 \[ \frac{\log{\left (- 2 x + 1 \right )}}{49} - \frac{\log{\left (3 x + 2 \right )}}{49} + \frac{11}{14 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

log(-2*x + 1)/49 - log(3*x + 2)/49 + 11/(14*(-2*x + 1))

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Mathematica [A]  time = 0.0217012, size = 37, normalized size = 1.16 \[ \frac{(4 x-2) \log (1-2 x)+(2-4 x) \log (6 x+4)-77}{98 (2 x-1)} \]

Antiderivative was successfully verified.

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

[Out]

(-77 + (-2 + 4*x)*Log[1 - 2*x] + (2 - 4*x)*Log[4 + 6*x])/(98*(-1 + 2*x))

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Maple [A]  time = 0.011, size = 27, normalized size = 0.8 \[ -{\frac{\ln \left ( 2+3\,x \right ) }{49}}-{\frac{11}{-14+28\,x}}+{\frac{\ln \left ( -1+2\,x \right ) }{49}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/49*ln(2+3*x)-11/14/(-1+2*x)+1/49*ln(-1+2*x)

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Maxima [A]  time = 1.32604, size = 35, normalized size = 1.09 \[ -\frac{11}{14 \,{\left (2 \, x - 1\right )}} - \frac{1}{49} \, \log \left (3 \, x + 2\right ) + \frac{1}{49} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-11/14/(2*x - 1) - 1/49*log(3*x + 2) + 1/49*log(2*x - 1)

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Fricas [A]  time = 0.214673, size = 50, normalized size = 1.56 \[ -\frac{2 \,{\left (2 \, x - 1\right )} \log \left (3 \, x + 2\right ) - 2 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) + 77}{98 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/98*(2*(2*x - 1)*log(3*x + 2) - 2*(2*x - 1)*log(2*x - 1) + 77)/(2*x - 1)

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Sympy [A]  time = 0.231038, size = 22, normalized size = 0.69 \[ \frac{\log{\left (x - \frac{1}{2} \right )}}{49} - \frac{\log{\left (x + \frac{2}{3} \right )}}{49} - \frac{11}{28 x - 14} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

log(x - 1/2)/49 - log(x + 2/3)/49 - 11/(28*x - 14)

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GIAC/XCAS [A]  time = 0.20647, size = 34, normalized size = 1.06 \[ -\frac{11}{14 \,{\left (2 \, x - 1\right )}} - \frac{1}{49} \,{\rm ln}\left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-11/14/(2*x - 1) - 1/49*ln(abs(-7/(2*x - 1) - 3))