Question

Evaluate the integral: ∫(x² + x - 1)/(x² + x - 6) dx

Answer 1

Considering ∫(x² + x - 1)/(x² + x - 6) dx

By expressing the integral 

Factorize the denominator,

⇒ 1 = (A + B) x + (3A – 2B)

⇒ Then A + B = 0 … (1)

And 3A – 2B = 1 … (2)

Solving (1) and (2),

2 × (1) → 2A + 2B = 0

1 × (2) → 3A – 2B = 1

5A = 1

∴ A = 1/5

On substituting A value in equation (1),

A + B = 0

1/5 + B = 0

B = -1/5

Hence,