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" 14."int(0)^((1)/(4))(sqrt(tan x)+sqrt(...

" 14."int_(0)^((1)/(4))(sqrt(tan x)+sqrt(cot x))dx=

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int_(0)^(pi//2)(1)/(sqrt(tan x)-sqrt(cot x))dx=

int_(0)^((pi)/(4))sqrt(tan x)dx

Evaluate int_(0)^((pi)/(4))(sqrt(tan x)+sqrt(cot x))dx

Prove that: int_(0)^((pi)/(4))(sqrt(tan x)+sqrt(cot x)dx=sqrt(2)*(pi)/(2)

int sqrt(cot x)dx

int_(0)^(pi//4) [sqrt(tan x)+sqrt(cot x)]dx

int( sqrt(tan x) + sqrt(cot x) ) dx =

int_(0)^(pi//4)[sqrt(tan x) + sqrt(cot x)] = dx

Show that int_(0)^(pi//4) (sqrt(tan x )+sqrt(cot x))dx= pi/sqrt(2)