Hullo, I'm not sure what you mean, the 'extra' s is there because that's the integral, well aside the constant. Do you mean how do you do the integral? Well one way is a trig substitution as is usually the case when we have square roots and square floating about.
Edit: I'm a fool, Ben-Smith is right, that's not the integral, nearly is though.
You need to make the substitution that s = 0.1sec(u). This probably seems pulled out of thin air , but comes from the fact that you have the square root of some number squared minus a constant, all inside a square root. Because would be .
We also have , so our overall integral is
because the tangents cancel.
Is that enough to get you started? If not, let me know and I can keep going.
Edit: Sorry - that came out slightly brusque upon rereading. It should have said something more like: If not, just let me know and I would be happy to keep going.