3.301 \(\int \frac{-1+7 x+2 x^2}{-1-x+x^2+x^3} \, dx\)

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

[Out]

-3/(1 + x) + 2*Log[1 - x]

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Rubi [A]  time = 0.0495433, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042 \[ 2 \log (1-x)-\frac{3}{x+1} \]

Antiderivative was successfully verified.

[In]  Int[(-1 + 7*x + 2*x^2)/(-1 - x + x^2 + x^3),x]

[Out]

-3/(1 + x) + 2*Log[1 - x]

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Rubi in Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((2*x**2+7*x-1)/(x**3+x**2-x-1),x)

[Out]

Timed out

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Mathematica [A]  time = 0.0121834, size = 14, normalized size = 0.88 \[ 2 \log (x-1)-\frac{3}{x+1} \]

Antiderivative was successfully verified.

[In]  Integrate[(-1 + 7*x + 2*x^2)/(-1 - x + x^2 + x^3),x]

[Out]

-3/(1 + x) + 2*Log[-1 + x]

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Maple [A]  time = 0.008, size = 15, normalized size = 0.9 \[ 2\,\ln \left ( -1+x \right ) -3\, \left ( 1+x \right ) ^{-1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2*x^2+7*x-1)/(x^3+x^2-x-1),x)

[Out]

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

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Maxima [A]  time = 0.786818, size = 19, normalized size = 1.19 \[ -\frac{3}{x + 1} + 2 \, \log \left (x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x^2 + 7*x - 1)/(x^3 + x^2 - x - 1),x, algorithm="maxima")

[Out]

-3/(x + 1) + 2*log(x - 1)

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Fricas [A]  time = 0.251811, size = 23, normalized size = 1.44 \[ \frac{2 \,{\left (x + 1\right )} \log \left (x - 1\right ) - 3}{x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x^2 + 7*x - 1)/(x^3 + x^2 - x - 1),x, algorithm="fricas")

[Out]

(2*(x + 1)*log(x - 1) - 3)/(x + 1)

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Sympy [A]  time = 0.185855, size = 10, normalized size = 0.62 \[ 2 \log{\left (x - 1 \right )} - \frac{3}{x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x**2+7*x-1)/(x**3+x**2-x-1),x)

[Out]

2*log(x - 1) - 3/(x + 1)

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GIAC/XCAS [A]  time = 0.262542, size = 20, normalized size = 1.25 \[ -\frac{3}{x + 1} + 2 \,{\rm ln}\left ({\left | x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x^2 + 7*x - 1)/(x^3 + x^2 - x - 1),x, algorithm="giac")

[Out]

-3/(x + 1) + 2*ln(abs(x - 1))