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Question

Evaluate: sinxcosxex+sinxdx

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Solution

sinxcosxex+sinxdx
=(sinx+exexcosxex+sinx)dx
=(sinx+exex+sinx(ex+cosx)ex+sinx)dx
=dxex+cosxex+sinxdx
Let ex+sinx=t
(ex+cosx)dx=dt
=xdtt
=xlnt+c
=xln(ex+sinx)+c
(sinxcosxex+sinx)dx=xln(ex+sinx)+c.

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