Question

What is `int 1/(cos(5x-1)) dx`?

Answer 1

`intdx/cos(5x-1)=1/5ln|sec(5x-1)+tan(5x-1)|+C`

Explanation:

Recalling that `1/cosx=secx,`

`1/cos(5x-1)=sec(5x-1)`

So, we have

`intsec(5x-1)dx`

This is almost a simple integral, just use a quick substitution.

`u=5x-1`

`du=5dx`

`1/5du=dx`

`1/5intsecudu=1/5ln|secu+tanu|+C`

Rewriting in terms of `x` yields

1. `intdx/cos(5x-1)=1/5ln|sec(5x-1)+tan(5x-1)|+C`