Evaluate the following integral: `int_0^(pi//4)(sqrt(t a n x)+sqrt(cotx))dx`

Explanation

Given,`I=int_0^(pi//4)(sqrt(t a n x)+sqrt(cotx))dx`

I=`int_0^(pi//4)(sqrt(sinx )/(cosx)+sqrt(tanx)/(cosx))dx`

I=`int_0^(pi//4)(sinx+cosx​)/sqrt(sinx cosx)dx`

Let sinx−cosx=t

(cosx+sinx)dx=dt

Now,

`(sinx−cosx)^2=t^2`


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