Can someone please explain this integral to me?

1. Mar 1, 2006

nick727kcin

why does this integral

equal this:

thanks,
nick

2. Mar 1, 2006

finchie_88

Well, x^(s+1) = x.x^s where the . means times. This then cancels down with the 1/x to leave the integral of $$\frac{x^s}{s+1}$$, then all you do is increase the power by 1 (to s+1), and then divide by the new power, so leave $$\frac{x^{s+1}}{(s+1)^2}$$ as required.

edit: Does anyone know why the latex maths bits aren't working?

3. Mar 1, 2006

nick727kcin

thank you. i understand even though some of the codes didnt show up. i just didnt get that x^(1+s)= x.x^s

thanks again :!!)

4. Mar 3, 2006

dextercioby

Well, actually

$$\int \frac{x^{s+1}}{s+1} \frac{dx}{x} \neq \frac{x^{s+1}}{(s+1)^{2}}$$

Can you see why...?

Daniel.