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Math Help - Integral of sec(6x)tan(6x)

  1. #1
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    Integral of sec(6x)tan(6x)

    I have really been struggling to do this integral. Please help!

    again, it's:

    Integral of: sec(6x)tan(6x)

    Thanks!
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  2. #2
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    Quote Originally Posted by sj9110 View Post
    I have really been struggling to do this integral. Please help!

    again, it's:

    Integral of: sec(6x)tan(6x)

    Thanks!
    Try this substitution u=6x.
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  3. #3
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    actually i just realized the whole thing is in parentheses if that makes a difference

    intsec(6x)tan(6x))dx
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  4. #4
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    Quote Originally Posted by sj9110 View Post
    actually i just realized the whole thing is in parentheses if that makes a difference

    intsec(6x)tan(6x))dx
    Did you try what I said?
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  5. #5
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    yes, but i'm stuck at

    (1/6) integral [sec(u)tan(u)]du
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  6. #6
    Super Member General's Avatar
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    Quote Originally Posted by sj9110 View Post
    yes, but i'm stuck at

    (1/6) integral [sec(u)tan(u)]du
    What is the derivative of sec(u) ?
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  7. #7
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    sec(x)tan(x) ...but i don't see how to incorporate it all.
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  8. #8
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    If the derivative of g(x) is f(x), it means that the integral of f(x) is g(x) plus a constant.
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  9. #9
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    Quote Originally Posted by sj9110 View Post
    sec(x)tan(x) ...but i don't see how to incorporate it all.
    No. Its sec(u)tan(u).

    If the derivative of sec(u) is sec(u)tan(u) .. then what is the integral of sec(u)tan(u) ?

    Excause me, Do you know the Fundamental Theorem of Calculus ?
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  10. #10
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    i got an answer of (1/6)sec(6x) + c ... is this right?
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  11. #11
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    Quote Originally Posted by sj9110 View Post
    i got an answer of (1/6)sec(6x) + c ... is this right?
    Yes. You are correct.
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  12. #12
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    Quote Originally Posted by General View Post
    No. Its sec(u)tan(u).

    If the derivative of sec(u) is sec(u)tan(u) .. then what is the integral of sec(u)tan(u) ?

    Excause me, Do you know the Fundamental Theorem of Calculus ?
    It's been a year since I took calculus 1 and 2, so I am pretty rusty.
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  13. #13
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    Quote Originally Posted by General View Post
    Yes. You are correct.
    great!..i was just getting a bit confused with all the substitution and stuff. Thanks for your help!
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