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by completing the square we write the equation as (x+b/2)^2-b/2^2+c, in this case b=8 (the coefficient of x) and c=5 so we have (x+4)^2-16-5=0, which equals (x+4)^2-21=0. Now by rearranging we get (x+4)^2...

Here we can use integration by parts. Notice that ln(x) can be written as ln(x)1, so we can integrate 1 and differentiate ln(x).
Then using the formula int(uv') dx = uv - int(u'v) dx, we...