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Math Help - Solving undefined integral with new variable

  1. #1
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    Solving undefined integral with new variable

    Hy i have a little problem with solving integral. I have to use new variable as t=Sin(x)

    \int \! {Cos(x) \over {Sin(x)^2-3 Sin(x)+2}} \, dx

    But i don't know how to start.
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  2. #2
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    Quote Originally Posted by PJani View Post
    Hy i have a little problem with solving integral. I have to use new variable as t=Sin(x)

    \int \! {Cos(x) \over {Sin(x)^2-3 Sin(x)+2}} \, dx

    But i don't know how to start.
    To start set t= \sin{x} . Then:

    dt = dx \cos{x} and so the integral becomes \int \frac{dt}{t^2-3t+2}

    To proceed try completing the square in the denominator. This should be enough to get you started. Good luck.
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  3. #3
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    There's no need to complete the square, use that t^2-3t+2=(t-1)(t-2).
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