Question:
Write a value of $\int \mathrm{e}^{\mathrm{x}}(\sin \mathrm{x}+\cos \mathrm{x}) \mathrm{dx}$.
Solution:
we know $\int e^{x}\left(f(x)+f^{\prime}(x)\right) d x \square=e^{x} f(x)+c$
Given, $\int e^{x}(\sin x+\cos x) d x$
Here $f(x)=\sin x$ and $f^{\prime}(x)=\cos x$
Therefore $\int e^{x}(\sin x+\cos x) d x=e^{x} \sin x+c$
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