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Math Help - Trig integral:

  1. #1
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    Trig integral:

    \int \frac{1}{5+4\sec{x}} dx

    please give only hints in solving this integral
    ireally dont know what to do first


    thanks
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  2. #2
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    Try this substitution: u=tan(x/2)
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  3. #3
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    whats the u here?
    x = 2arctan(u)
    dx = 2 ( 1/ (1 + u^2))

    i dint understand still
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  4. #4
    Senior Member tukeywilliams's Avatar
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     \sec x = \frac{(1+u^2)^2}{(1-u^2)^2}
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  5. #5
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    whats the u here?
    x = 2arctan(u)
    dx = 2 ( 1/ (1 + u^2))du
    Yes. And cosx=(1-u^2)/(1+u^2). So this makes the integrand a rational fraction.
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  6. #6
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    thanks!
    oh yeahhh i forgot this was all easy using trig sub...
    thanks a lot for the help
    Last edited by ^_^Engineer_Adam^_^; August 3rd 2007 at 04:23 AM.
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