Find the integral of ln(x)
The best way to approach this question is to solve it using integration by parts.First, recognise that ln(x) = 1 x ln(x), and set du/dx = 1 and v = ln(x). We then find that u = x, and dv/dx = 1/x.With this we can easily see, using our rules of integration by parts, that the Integral(lnx) = xln(x) - Integral(x/x) = xln(x) - Integral(1) = xlnx - x (+ some constant).I really like this question because while it seems hard to get started, once you notice that ln(x) = 1 x ln(x), it becomes a simple Integration by Parts problem!
FG
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