Evaluate integrals (1 - (1 /w) cos (w

Evaluate integrals (1 - (1 /w) cos (w - ln w) dw, Mathematics

Assignment Help:

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

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