What is the integral of $int sqrt(Tan x) / (sin x cos x)dx$ ?

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Answer 1 · 2018-05-28T14:22:01

The answer is $=2sqrt(tanx)+C$

We need

$tanx=sinx/cosx$

$sinx=cosxtanx=tanx/secx$

Therefore, the integral is

$I=int(sqrt(tanx)dx)/(sinxcosx)=int(sqrt(tanx)dx)/(tanx/secx*1/secx)$

$=int(sec^2xdx)/sqrt(tanx)$

Let $u=tanx$ , $=>$ , $du=sec^2xdx$

The integral is

$I=int(du)sqrt(u)$

$=sqrt(u)/(1/2)$

$=2sqrt(u)$

$=2sqrt(tanx)+C$

What is the integral of int sqrt(Tan x) / (sin x cos x)dxint sqrt(Tan x) / (sin x cos x)dx?