Integrate the rational functions.

On dividing 1 – x2 by x(1 - 2x), we get,

…(1)

Now, let

(2 – x) = A(1 – 2x) + Bx …(2)

Now, substituting x = 0 and in equation (2), we get,

A = 2 and B = 3

Thus,

Now, putting this value in equation (2), we get,