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Question

Solve eaxsinbxdx.

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Solution

Integrating using by part, we get,
v=eax,u=sinbx
v=1aeax,u=bcosbx
eaxsinbxabeaxcosbx dxa
Again using by parts we get,
eaxsinbxabeaxcosbx a2b2eaxsinbx dxa2
(a2+b2)Ia2=eaxsinbxabeaxcosbx a2
I=1a2+b2(aeaxsinbxbeaxcosbx )

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