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