Dear studentWe cannot integrate ∫secxxtan xdx The question is printed wrong I am assumingI=∫sec2xtan xdxLet tan x=tdt=sec2x dxI=∫1tdt=∫t-12dt=t-12+1-12+1+c=t1212+c=2t+c=2tan x+c

Integrate

D e a r s t u d e n t W e c a n n o t i n t e g r a t e \int \frac{s e c^{x} x}{\sqrt{\tan x}} d x . T h e q u e s t i o n i s p r i n t e d w r o n g . I a m a s s u m i n g I = \int \frac{s e c^{2} x}{\sqrt{\tan x}} d x L e t \tan x = t d t = s e c^{2} x d x I = \int \frac{1}{\sqrt{t}} d t = \int t^{- \frac{1}{2}} d t = \frac{t^{- \frac{1}{2} + 1}}{- \frac{1}{2} + 1} + c = \frac{t^{\frac{1}{2}}}{\frac{1}{2}} + c = 2 \sqrt{t} + c = 2 \sqrt{\tan x} + c

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