Question

Evaluate the following integral: ∫ 1/((x²+1)(x²+4))dx

\(\int\frac{1}{(x^2+1)(x^2+4)}\) dx

Answer 1

I = ∫ 1/((x²+1)(x²+4))dx

1 = (Ax + B)(x² + 4) + (Cx + D)(x² + 1) 

= (A + C)x³ + (B + D)x² + (4A + C)x + 4B + D 

Equating similar terms,

A + C = 0 

B + D = 0 

4A + C = 0 

4B + D = 1 

We get,