Complete the indefinite integral : ∫x lnx dx
Use the formula: ∫uv' dx = uv - ∫u'v dx (use I = the integral we're looking for)Note we cant integrate ln x easily but we can differentiate into 1/x so we use:u = ln x and v' = x we have u' = 1/x and v = x2/2 subbing these values into the above formula we get:I = x2/2 lnx - ∫1/x x2/2 dx = x2/2 lnx - ∫x/2 dx= x2/2 lnx - x2/4 + C
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