Integrate e^x sinx

Since we have two functions of x being multipied togrther, we have to integrate this by parts. Therefore if we say, u=sinx and v'=ex, then u'=cosx and v=ex.Applying the integration by parts rule of: uv' dx = vu - ∫vu' dxso: ∫exsinx dx = exsinx - ∫ excosx dxAs before, since we have two functions of x being multipied togrther, we have to integrate this by parts. Therefore if we say, u=cosx and v'=ex, then u'=-sinx and v=ex.∫exsinx dx = exsinx - (excosx - ∫ -exsinx dx)∫exsinx dx = exsinx - excosx - ∫ exsinx dx2∫exsinx dx = exsinx - excosx ∫exsinx dx = 1/2ex(sinx-cosx)+c

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Answered by Kishan P. Maths tutor

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