Indefinite IntegrationHard
Question
The value of 
is equal to
is equal toOptions
A.2 sin-1 √x + C
B.sin-1 (2x - 1) + C
C.C - 2 cos-1 (2x - 1)
D.cos-1 2 
+ C
+ CSolution
= sin-1
= sin-1 (2x - 1) + C ..... (1)Also I =
put √x = t ⇒ 
dx = dt⇒ I =
= 2 sin-1 √x + C .......(2)Now Let θ = sin-1 (2x - 1)
⇒ sin θ = 2x - 1 ⇒ cos θ =
θ = cos-1 2
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