## Example 7.2.6(c): Applying Integration by Parts

Integration by parts seems not applicable here because there is no product. But we can trivially write the integrand as*1 ln(x)*. Then we define the functions

With

g'(x) = 1so thatg(x) = xf(x) = ln(x)so thatf'(x) = 1/x

*G(x) = x ln(x)*we have

The trick here was to realize that integration by parts could be used at all, not the actual mechanics of the process.ln(x) dx = G(b) - G(a) - x 1/x dx =

= b ln(b) - a ln(a) - (b - a)