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Question

Evaluate exsinx dx

A
ex(cosxsinx)
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B
ex2(cosxsinx)
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C
ex2(cosx+sinx)
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D
ex(cosx+sinx)
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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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