Evaluate the following integral:

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,

Thus,