2g convergence of tan function

[Dell]

i need to find the values of p so that the following integral converges

$$\int$$(tan(x))^pdx (from 0-$$\pi$$/2)

the only way i could think of doing this was integration in parts, but i get stuck

$$\int$$(tan(x))^p =$$\int$$(sin^p(x)/cos^p(x))
u=sin^px
du=-p*sin^p-1(x)cos(x)
dv=dx/cos^p(x)

but i don't know how to integrate 1/cos^pdx to find my v

what would be a better way to do this?

 

[lippyka]

The integral does not converge for any value of p. To see this, note that for the given integral the integrand is unbounded near the upper limit of the integral. Therefore, the integral does not converge for any value of p.