Integrate the rational functions.

Let

x = (Ax + B)(x -1) + C (x2 + 1)

⇒ x = Ax² – Ax + Bx – B + Cx² + C

Equating the coefficients of x2, x and constant term, we get,

A + C = 0

-A + B = 0

-B + c = 0

On solving these equation, we get,

A = , B = and C =

Thus,

Now, let us consider, ,

Let (x² + 1) = t

2xdx = dt

Thus,

Therefore,