Question

Evaluate the following integral : ∫ 2x/((x²+1)(x²+2)²)dx

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

Answer 1

Let I = ∫ 2x/((x²+1)(x²+2)²)dx

Let x² + 2 = t 

⇒ 2x dx = dt

Now,

Let,

⇒ 1 = At² + B t (t – 1) + C(t – 1) 

For t =1, A = 1 

For t = 0,C = – 1 

For t = –1,B= – 1