Integrate e^1+cosx .sinx dx =?

Question

$inte^(1+cosx)sinx dx =?$

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Answer 1 · 2018-07-27T04:27:44

$-e^(1+cosx)+C.$

Hoping that, the Question is to find $I=inte^(1+cosx)sinxdx$ ,

let, $(1+cosx)=u," so that, "-sinxdx=du$ .

$:. I=-inte^(1+cosx)*(-sinxdx)$ ,

$=-inte^udu$ ,

$=-e^u$ .

$rArr I=-e^(1+cosx)+C.$