Question

How do you integrate `int tcsctcott` by parts?

Answer 1

`inttcsctcottdt = -tcsct - ln|csct + cott| + C`

Explanation:

Let `dv = csctcottdt` and `u = t`. This means that `v= -csct` and `du = dt`.

Through integration by parts, we have:

`intudv = uv - intvdu`

`inttcsctcottdt = t(-csct) - int(-csctdt)`

`inttcsctcottdt = -tcsct + intcsctdt`

The integral of `csct` can be found here

`inttcsctcottdt = -tcsct - ln|csct + cott| + C`

Hopefully this helps!