3.281 \(\int \frac{-3+2 x}{-x^2+x^3} \, dx\)

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

[Out]

-3/x - Log[1 - x] + Log[x]

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Rubi [A]  time = 0.0284046, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ -\frac{3}{x}-\log (1-x)+\log (x) \]

Antiderivative was successfully verified.

[In]  Int[(-3 + 2*x)/(-x^2 + x^3),x]

[Out]

-3/x - Log[1 - x] + Log[x]

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Rubi in Sympy [A]  time = 4.26013, size = 10, normalized size = 0.62 \[ \log{\left (x \right )} - \log{\left (- x + 1 \right )} - \frac{3}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

log(x) - log(-x + 1) - 3/x

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Mathematica [A]  time = 0.00581729, size = 16, normalized size = 1. \[ -\frac{3}{x}-\log (1-x)+\log (x) \]

Antiderivative was successfully verified.

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

[Out]

-3/x - Log[1 - x] + Log[x]

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Maple [A]  time = 0.009, size = 15, normalized size = 0.9 \[ \ln \left ( x \right ) -3\,{x}^{-1}-\ln \left ( -1+x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((-3+2*x)/(x^3-x^2),x)

[Out]

ln(x)-3/x-ln(-1+x)

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Maxima [A]  time = 1.35513, size = 19, normalized size = 1.19 \[ -\frac{3}{x} - \log \left (x - 1\right ) + \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3/x - log(x - 1) + log(x)

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Fricas [A]  time = 0.220798, size = 24, normalized size = 1.5 \[ -\frac{x \log \left (x - 1\right ) - x \log \left (x\right ) + 3}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(x*log(x - 1) - x*log(x) + 3)/x

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Sympy [A]  time = 0.096303, size = 10, normalized size = 0.62 \[ \log{\left (x \right )} - \log{\left (x - 1 \right )} - \frac{3}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

log(x) - log(x - 1) - 3/x

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GIAC/XCAS [A]  time = 0.210567, size = 22, normalized size = 1.38 \[ -\frac{3}{x} -{\rm ln}\left ({\left | x - 1 \right |}\right ) +{\rm ln}\left ({\left | x \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3/x - ln(abs(x - 1)) + ln(abs(x))