Use substitution to evaluate the indefinite integral:

The integral of [ (sq. root (1 + ln x)) ((ln x)/x) dx]

Im confused on what i should substitute u and du for.

Thank you so much!!

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  1. Let u = 1+ln x
    du = 1/x dx
    ln x = u-1

    So, we have

    u^1/2 * (u-1) du
    = u^3/2 - u^1/2 du

    Integrate that to get

    2/5 u^5/2 - 2/3 u^3/2
    2/5 (1 + ln x)^5/2 - 2/3 (1+ln x)^3/2

    Check your work by taking the derivative. Trust me -- it comes out right.

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