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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!

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