- #1

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^{p}dx (from 0 to pi/2)

what i actually need to do is find the values of p so that the integral converges in its given limits

i don't see too many options here, so what i did was

t=tan(x)

dt=t'dx=dx/cos

^{2}(x)=(1+tan

^{2}(x))dx=(1+t

^{2})dx

so now we have

[tex]\int[/tex]t

^{p}(1+t

^{2})dt (from 0 to infinity)

and now i have no idea how to continue.

is there a better way to solve this, if not how do i continue from here?