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Calculus: Integral

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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.

  • Calculus: Integral - ,

    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.

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