Unformatted text preview: Solution 7 The above integral has the form f udo where do = cos (:6) d1:
-— Using the integration by parts formula, we obtain /;ECOS(:E)d1E fade
uv—fvalu “mm—/smmm resin (at) + cos (:0) + C. We conclude that
[$003 (w) dw : wsin(1;) —l— cos ((1)) + 0. Sometimes, it is necessary to use integration by parts more than once, as
in the next example. Example 8 Evaluate the indeﬁnite integral /e‘” cos(x) dx.
Solution 9 Make the following substitutions at» = (9;) dm
—— femcosw) d1: : fad?)
uv/vdu :e%ﬂﬂ—/gm®wt Then 7 ...
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- Fall '08