Answer :

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,



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