Integrate the function : $e^{x}(\sin x + \cos x)$
(N/A) Let $I = \int e^{x}(\sin x + \cos x) \, dx$.
We know the standard integral formula: $\int e^{x} \{f(x) + f'(x)\} \, dx = e^{x} f(x) + C$.
Let $f(x) = \sin x$.
Then,the derivative is $f'(x) = \cos x$.
Substituting these into the formula,we get:
$I = e^{x} \sin x + C$,where $C$ is an arbitrary constant.
We know the standard integral formula: $\int e^{x} \{f(x) + f'(x)\} \, dx = e^{x} f(x) + C$.
Let $f(x) = \sin x$.
Then,the derivative is $f'(x) = \cos x$.
Substituting these into the formula,we get:
$I = e^{x} \sin x + C$,where $C$ is an arbitrary constant.
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