Indefinite IntegrationHard
Question
The value of 
dx is equal to
dx is equal toOptions
A.sin-1
+ C
+ CB.
+ cos-1 
+ C
+ cos-1 + CC.sec-1 x -
+ C
+ CD.tan-1 
+ C
+ CSolution
I = 
dx Put 
= cos 2θ ⇒ - 
= - 2 sin 2θ dθ
I =
2 sin 2θ dθ
= ∫4sin2θ dθ = 2∫(1 - cos2θ)dθ = 2θ - sin2θ + C = cos-1
dx Put = cos 2θ ⇒ - = - 2 sin 2θ dθ I =
2 sin 2θ dθ= ∫4sin2θ dθ = 2∫(1 - cos2θ)dθ = 2θ - sin2θ + C = cos-1
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