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Math Help - Integrate this

  1. #1
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    Integrate this

    Can someone help me out? I have been gone, and am trying to figure this out myself.
    Just start me?... what u, du, v, and dv equal?

    integrate 3(sin x)^-2 dx


    and


    integrate (x^4)(e^-x) dx


    Please, Id really appreciate it!
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  2. #2
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    Hello, Morgan82!

    Use a trig identity on the first one . . .


    \int 3(\sin x)^{-2} \,dx

    We have: . \int\frac{3\,dx}{\sin^2\!x} \;=\;3\int\csc^2\!x\,dx \;=\;-3\cot x + C

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  3. #3
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    For the second part you will use integration by parts 4 times. Use u = x^4 dv=e^{-x}dx for the first iteration.
    Last edited by lvleph; November 19th 2009 at 05:53 PM.
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  4. #4
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    What is the integral of e^-x?
    Quote Originally Posted by lvleph View Post
    For the second part you will use integration by parts 4 times. Use u = x^4 dv=e^{-x} for the first iteration.
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  5. #5
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    Quote Originally Posted by Morgan82 View Post
    What is the integral of e^-x?
    You can use u-substitution for that; \int \! e^{-x} \,dx = \int \! e^u \cdot \frac{du}{dx} dx
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