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,