3.1354 \(\int \frac{-11+6 x}{(-1+2 x) \left (-1+x^2\right )} \, dx\)

Optimal. Leaf size=29 \[ \frac{16}{3} \log (1-2 x)-\frac{5}{2} \log (1-x)-\frac{17}{6} \log (x+1) \]

[Out]

(16*Log[1 - 2*x])/3 - (5*Log[1 - x])/2 - (17*Log[1 + x])/6

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Rubi [A]  time = 0.0538407, antiderivative size = 29, 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 \[ \frac{16}{3} \log (1-2 x)-\frac{5}{2} \log (1-x)-\frac{17}{6} \log (x+1) \]

Antiderivative was successfully verified.

[In]  Int[(-11 + 6*x)/((-1 + 2*x)*(-1 + x^2)),x]

[Out]

(16*Log[1 - 2*x])/3 - (5*Log[1 - x])/2 - (17*Log[1 + x])/6

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Rubi in Sympy [A]  time = 7.15425, size = 26, normalized size = 0.9 \[ \frac{16 \log{\left (- 2 x + 1 \right )}}{3} - \frac{5 \log{\left (- x + 1 \right )}}{2} - \frac{17 \log{\left (x + 1 \right )}}{6} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((-11+6*x)/(-1+2*x)/(x**2-1),x)

[Out]

16*log(-2*x + 1)/3 - 5*log(-x + 1)/2 - 17*log(x + 1)/6

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Mathematica [A]  time = 0.0153157, size = 31, normalized size = 1.07 \[ -\frac{5}{2} \log (2-2 x)+\frac{16}{3} \log (2 x-1)-\frac{17}{6} \log (2 x+2) \]

Antiderivative was successfully verified.

[In]  Integrate[(-11 + 6*x)/((-1 + 2*x)*(-1 + x^2)),x]

[Out]

(-5*Log[2 - 2*x])/2 + (16*Log[-1 + 2*x])/3 - (17*Log[2 + 2*x])/6

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Maple [A]  time = 0.01, size = 22, normalized size = 0.8 \[ -{\frac{5\,\ln \left ( -1+x \right ) }{2}}-{\frac{17\,\ln \left ( 1+x \right ) }{6}}+{\frac{16\,\ln \left ( 2\,x-1 \right ) }{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((-11+6*x)/(2*x-1)/(x^2-1),x)

[Out]

-5/2*ln(-1+x)-17/6*ln(1+x)+16/3*ln(2*x-1)

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Maxima [A]  time = 0.691658, size = 28, normalized size = 0.97 \[ \frac{16}{3} \, \log \left (2 \, x - 1\right ) - \frac{17}{6} \, \log \left (x + 1\right ) - \frac{5}{2} \, \log \left (x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((6*x - 11)/((x^2 - 1)*(2*x - 1)),x, algorithm="maxima")

[Out]

16/3*log(2*x - 1) - 17/6*log(x + 1) - 5/2*log(x - 1)

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Fricas [A]  time = 0.278623, size = 28, normalized size = 0.97 \[ \frac{16}{3} \, \log \left (2 \, x - 1\right ) - \frac{17}{6} \, \log \left (x + 1\right ) - \frac{5}{2} \, \log \left (x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((6*x - 11)/((x^2 - 1)*(2*x - 1)),x, algorithm="fricas")

[Out]

16/3*log(2*x - 1) - 17/6*log(x + 1) - 5/2*log(x - 1)

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Sympy [A]  time = 0.303061, size = 26, normalized size = 0.9 \[ - \frac{5 \log{\left (x - 1 \right )}}{2} + \frac{16 \log{\left (x - \frac{1}{2} \right )}}{3} - \frac{17 \log{\left (x + 1 \right )}}{6} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((-11+6*x)/(-1+2*x)/(x**2-1),x)

[Out]

-5*log(x - 1)/2 + 16*log(x - 1/2)/3 - 17*log(x + 1)/6

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GIAC/XCAS [A]  time = 0.302229, size = 32, normalized size = 1.1 \[ \frac{16}{3} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) - \frac{17}{6} \,{\rm ln}\left ({\left | x + 1 \right |}\right ) - \frac{5}{2} \,{\rm ln}\left ({\left | x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((6*x - 11)/((x^2 - 1)*(2*x - 1)),x, algorithm="giac")

[Out]

16/3*ln(abs(2*x - 1)) - 17/6*ln(abs(x + 1)) - 5/2*ln(abs(x - 1))