`int cot\ 4x\ csc^4 4x\ dx`

We write the expression under the integral sign as follows:

`cot\ 4x\ csc^4 4x\ dx=(csc^3 4x)\ cot\ 4x\ csc\ 4x`

Then, let `u = csc\ 4x` and so we have `du = -4\ csc\ 4x\ cot\ 4x\ dx`

That is, `-(du)/4 = csc\ 4x\ cot\ 4x\ dx`

Now we can perform the integral:

`{: (int cot\ 4x\ csc^4 4x\ dx,=int(csc^3 4x)\ cot\ 4x\ csc\ 4x\ dx),(,=-1/4intu^3du),(,=-u^4/16+K),(,=-(csc^4 4x)/16+K) :}`