Evaluate following integrals.

                      ( (1 - (1 /w) cos (w - ln w) dw

Solution

In this case we know how to integrate only a cosine therefore let's makes the substitution the stuff i.e. inside the cosine.

u = w - ln w    du = (1 - (1 /w) dw

Thus, we worked the stuff in front of the cosine appears accurately in the differential. Then the integral is,

( (1 - (1 /w) cos (w - ln w) dw

            = ∫ cos (u ) du

= sin (u ) + c

= sin ( w - ln w) + c