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integration(1/(cosx*(sqrt(cos2x))))dx=?

integration(1/(cosx*(sqrt(cos2x))))dx=?

Grade:12th pass

1 Answers

Rinkoo Gupta
askIITians Faculty 81 Points
9 years ago
integral cosx/sqrt(cos2x) dx
=integral cosx/sqrt(1-2sin^2x0 dx
dividing by cos^2x in num.and denom. both,we get
integral sec^2x dx/sqrt(sec^2x-2tan^2x)
=integralsec^2xdx/sqrt(1+tan^2x-2 tan^2x)
=integral sec^2x dx/sqrt(1-tan^2x)
put tanx=t
on diff. w.r.t. x we get sec^2xdx=dt
=integral dt/sqrt(1-t^2)
=arcsin(t)
=arcsin(tanx)

Thanks & Regards
Rinkoo Gupta
AskIITians Faculty

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