Integral of (2(1-x-x²))/(1-x²)

What is the integral of (2(1-x-x²))/(1-x²) ?

Note that:
2(1 - x - x^2)/(1 - x^2)
= 2[(1 - x^2) - x]/(1 - x^2)
= 2[1 - x/(1 - x^2)]
= 2 - 2x/(1 - x^2).

Therefore:
∫ 2(1 - x - x^2)/(1 - x^2) dx
= ∫ [2 - 2x/(1 - x^2)] dx
= 2 ∫ dx - ∫ 2x/(1 - x^2) dx
= 2 ∫ dx + ∫ 1/(1 - x^2) d(1 - x^2)
= 2x + ln|1 - x^2| + C.

I hope this helps!

http://integrals.wolfram.com/index.jsp?expr=%282%281-x-x%5E2%29%29%2F%281-x%5E2%29&random=false= (2 -2x -2x^2)/ 1-x^2

=

2*∫(1 - x - x²)/(1 - x²) dx

2*∫(1 - x/(1 - x²)) dx

2x + ln(1 - x²) + C

2*x + log(x^2 - 1)

ln(-x^2+1)+2x+c