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    Vi Nguyen's Avatar
    Vi Nguyen Posts: 48, Reputation: 2
    Junior Member
     
    #1

    May 7, 2009, 07:52 AM
    integral of sec to an odd power
    Can someone tell me how to evaluate the integral:

    ∫tan(2x)sec³(2x)dx

    I don't know what to do when sec is cubed and which substitution to make, or if there even is a substitution, if I express sec³(2x) as sec²(2x)sec(2x) and change sec²(2x) to (tan²(2x)+1), then let u=tan(2x) du/dx=sec²(2x) but I only have a sec(2x) left to cancel, :(
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
    Ultra Member
     
    #2

    May 7, 2009, 08:25 AM


    Make the sub:





    Now, make the sub

    See? The dw takes up everything but , which we use w^2 on

    So, we have:



    Integrate:



    Resub:



    resub:



    The C is a hanger on. Add it if the professor is anal.

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