Posted by **mathstudent** on Wednesday, November 7, 2007 at 8:57pm.

How do I derive the secant reduction rule?

Integral (sec x)^n dx

= Integral (sec x)^(n-2) * (sec x)^2 dx

= Integral ((tan x)^2 + 1)^(n/2-1) * (sec x)^2 dx

Doing a substitution with:

u = tax x

du = (sec x)^2 dx

= Integral (u^2 + 1)^(n/2-1) * du

At this point I'm stuck. Any ideas? Thanks!