Question

∫[(tanx)/{√(cosx)}] = _____ + c 

(a) [(+ 2)/√(cos x)] 

(b) – [1/√(cosx)] 

(c) [(– 2)/{3√(cosx)}] 

(d) [(– 3)/{2√(cosx)}]

Answer 1

The correct option (a) [(+ 2)/√(cos x)]    

Explanation:

I = ∫[(tanx)/{√(cosx)}]dx 

= ∫sinx ∙ (cosx)^–(3/2)dx 

Put cosx = t 

∴ – sinxdx = dt 

∴ I = ∫– t^(–3/2)dt 

= (– 1)[{(t)^–(1/2)}/{– (1/2)}] + c 

= (2/√t) + c = [2/√(cosx)] + c