Evaluate : ∫2/(1-x)(1+x^2) dx

Question

Evaluate : \(\int\frac{2}{(1-x)(1+x^2)}dx\)

Answer 1

Here,

I = \(\int\frac{2}{(1-x)(1+x^2)}dx\)

Now,

Equating co - efficient both sides, we get

A + C = 2 ...(i)

A - B = 0 ... (ii)

B -  C = 0 ...(iii)

From (ii) and (iii) 

A = B = C

Putting C = A in (i), we get

A + A = 2

⇒ 2A = 2

⇒ A = 1

i.e., A = B = C = 1