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Question

If exsinxdx=12ex2+c,then a=

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Solution

I=exsinxdx
Integratation by part
I=sinxexexcosxdx=exsinx[cosxex+exsinx]=exsinxexcosxI+C2I=ex(sinxcosx)+CI=ex2(sinxcosx)+CTherefore,a=sinxcosx

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