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2 integration problems watch

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    I am having problems integrating:

    ∫(2-√x)((1/x)+1)
    and
    ∫ex /(e2x -1)

    Help would be really apprieciated, thanks
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    (Original post by wibble...)
    ∫(2-√x)((1/x)+1)
    ∫(2-√x)((1/x)+1).dx
    => ∫(2-√x)(1/x+1).dx
    = ∫(2/x - √x/x + 2 - √x).dx
    => ∫(2x-1 - x-1/2 + 2 - x1/2).dx
    = 2lnx - 2x1/2 + 2x - 2/3x3/2
    = 2lnx - 2√x + 2x - 2√x³/3
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    (Original post by wibble...)
    ∫ex /(e2x -1)
    Use integration by parts..
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    ∫ex/(e2x -1) dx

    Consider ln|e2x -1| = g(x)
    g'(x) = 2e2x/(e2x-1)
    Therefore,
    ∫ex/(e2x -1) dx
    = ½ln|e2x -1|

    --------------

    (Original post by Dekota)
    Use integration by parts..
    top is differential of bottom much easier.
 
 
 
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