integrate (x^2 - x) / (x^2+x+1)

Question

integrate on the range of 0-1 using partial fraction method

Answer 1

We can divide the denominator into the numerator to get:

1-(2x+1)/(x²+x+1). When this is integrated wrt x we get:

x-ln|x²+x+1|+C where C is constant of integration, because the numerator is the derivative of the denominator.

Apply the range:

(1-ln(3))-0=1-ln(3)=-0.09861 approx.