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Integrate √tan x/sin x cos x |
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Answer» 2√tanx +C Step-by-step explanation: The answer is = 2 √ tan x + C
Explanation: We need tan x = sin x cos x
sin x = cos x tan x = tan x sec x
I = ∫ √ tan x d x sin x cos x = ∫ √ tan x d x tan x sec x ⋅ 1 sec x
= ∫ sec 2 x d x √ tan x
u = tan x , ⇒ , d u = sec 2 x d x
The integral is I = ∫ ( d u ) √ u
= √ u 1 2
= 2 √ u
= 2 √ tan x + C |
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