Evaluate:

To find:

Formula Used:

1. sec² x = 1 + tan² x

2.

Dividing by cos² x in the numerator and denominator,

Let y = tan x

dy = sec² x dx

Therefore,

… (1)

Let

1 = A (2y + 1) + B(y – 2)

When y = 0,

1 = A – 2B … (2)

When y = 1,

1 = 3A – B ⇒ 2 = 6A – 2B … (3)

Solving (2) and (3),

1 = 5A

A

So, B

(1) becomes,

Since y = tan x,

Therefore,