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# 2 integration problems watch

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1. I am having problems integrating:

∫(2-√x)((1/x)+1)
and
∫ex /(e2x -1)

Help would be really apprieciated, thanks
2. (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
3. (Original post by wibble...)
∫ex /(e2x -1)
Use integration by parts..
4. ∫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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