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!

Similar Questions
  1. Consider the integral:21 ∫ x^3 dx 3 -Use Left Sum, Right Sum, Midvalue Sum, and Trapezoid Rule methods to approximate this
    1. answers icon 2 answers
  2. How would I solve the following integral with the substitution rule?Integral of: [(x^3)*(1-x^4)^5]dx Put 1-x^4 = y Then -4x^3 dx
    1. answers icon 1 answer
    1. answers icon 1 answer
  3. find integral using table of integrals )integral sin^4xdx this the formula i used integral sin^n xdx =-1/n sin^n-1xcosx +n-1/n
    1. answers icon 3 answers
more similar questions