`int sqrt(cot(x)) csc^2(x) dx` Evaluate the indefinite integral.

You need to use the following substitution  `cot x = t` , such that:

`cot x = t=>-csc^2 x dx = dt => csc^2 x dx = -dt`

`int sqrt(cot x)* csc^2 x dx = - int sqrt t dt`

`- int sqrt t dt = -(t^(3/2))/(3/2) + c`

Replacing back cot x for t yields:

`int sqrt(cot x)* csc^2 x dx = -(2/3)((cot x)^(3/2)) + c`

Hence, evaluating the indefinite integral, yields `int sqrt(cot...

You need to use the following substitution  `cot x = t` , such that:

`cot x = t=>-csc^2 x dx = dt => csc^2 x dx = -dt`

`int sqrt(cot x)* csc^2 x dx = - int sqrt t dt`

`- int sqrt t dt = -(t^(3/2))/(3/2) + c`

Replacing back cot x for t yields:

`int sqrt(cot x)* csc^2 x dx = -(2/3)((cot x)^(3/2)) + c`

Hence, evaluating the indefinite integral, yields `int sqrt(cot x)* csc^2 x dx = -(2/3)((cot x)^(3/2)) + c`