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Math Help - Integration by Parts Problem

  1. #1
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    Integration by Parts Problem

    According to the directions, I should be using u-substitution and integration by parts to find the indefinite integral of:

    x ln(1 + x) dx

    This is the only problem that I am having an immense amount of trouble with. It seems useless to use any u-substitution (at least at this point). I tried to use integration by parts with u = ln(1 + x) and dv = x dx, but that gave me an integral of (x^2)/(1 + x) which I cannot seem to make go anywhere from that. Am I approaching this problem the wrong way?
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  2. #2
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    If u = 1 + x, then you have x = u - 1, ln(1 + x) = ln(u), and du = dx....
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  3. #3
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    Quote Originally Posted by uberbandgeek6 View Post
    According to the directions, I should be using u-substitution and integration by parts to find the indefinite integral of:

    x ln(1 + x) dx

    This is the only problem that I am having an immense amount of trouble with. It seems useless to use any u-substitution (at least at this point). I tried to use integration by parts with u = ln(1 + x) and dv = x dx, but that gave me an integral of (x^2)/(1 + x) which I cannot seem to make go anywhere from that. Am I approaching this problem the wrong way?
    \frac{x^2}{1+x} = \frac{x^2-1+1}{1+x} = x - 1 + \frac{1}{1+x}
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