int {{e^x}sin ({e^x})} ,dx = | vedclass

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Question

(A) To evaluate the integral $I = \int {{e^x}\sin ({e^x})} \,dx$,we use the method of substitution.Let $t = {e^x}$.Then,differentiating both sides wit

Vedclass · Accepted Answer

$-\cos({e^x}) + c$

Vedclass · Answer

(A) To evaluate the integral $I = \int {{e^x}\sin ({e^x})} \,dx$,we use the method of substitution.Let $t = {e^x}$.Then,differentiating both sides with respect to $x$,we get $\frac{dt}{dx} = {e^x}$,which implies $dt = {e^x}dx$.Substituting these into the integral,we get:$I = \int \sin(t) \,dt$.The integral of $\sin(t)$ is $-\cos(t) + c$.Substituting back $t = {e^x}$,we get $I = -\cos({e^x}) + c$.

$\int {{e^x}\sin ({e^x})} \,dx = $

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