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Question

Evaluate exsinx dx
  1. ex(cosxsinx)
  2. ex2(cosxsinx)
  3. ex2(cosx+sinx)
  4. ex(cosx+sinx)


Solution

The correct option is B ex2(cosxsinx)
Let I=exsinx dx
Using Integration by parts method we have,
exsinx dx=exsinxdx(dexdxsinxdx) dx
 excosx+excosxdx
 excosx+excosxdx(dexdxcosxdx)dx
 excosx+exsinxexsinxdx
 I=excosx+exsinxexsinxdx
 I=excosx+exsinxI
 2I=ex(cosxsinx)
 I=ex2(cosxsinx)

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