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Math Help - Indefinite Integrals

  1. #1
    Junior Member
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    Indefinite Integrals

    I can't figure out these indefinite integrals using trigonometry


    Integral(sec^4 x dx)

    Integral(sec^3 x tanx dx)

    Integral(sec^2 x tan^2 x dx)

    Integral(sec x tan^3 x dx)


    It seems everytime I attempt these particular problems I get stuck somewhere in the middle when it comes time to substitute!!!! It's so frustrating!!!
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  2. #2
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    Hello, TreeMoney!


    1) . sec^4x dx

    We have: .
    sec²x sec²x dx .= . (tan²x + 1)(sec²x dx)

    Let: u = tan x . . du = sec²x dx



    2) . sec³x tan x dx

    We have: .
    (sec²x)(sec x tan x dx)

    Let: u = sec x . . du = sec x tan x dx



    3) . sec²x tan²x dx

    We have: .
    tan²x (sec²x dx)

    Let: u = tan x . . du = sec²x dx



    4) . sec x tan³x dx

    We have: .
    tan²x (sec x tan x dx) .= . (sec²x - 1)(sec x tan x dx)

    Let: u = sec x . . du = sec x tan x dx

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