I don't understand how to do this one integral problem that involves secant. I'm asked to find the integral of sec^4 (4x). I'm not really sure how to go about solving this problem.

Answer 1

recall that sec^2 = 1+tan^2, so you have

∫sec^4(4x) dx
= ∫sec^2(4x)(1 + tan^2(4x)) dx
= ∫sec^2(4x) dx + ∫tan^2(4x) sec^2(4x) dx
= 1/4 tan(4x) + (1/4)(1/3) tan^3(4x)

and you can massage that in several ways.