 Solution (source code)

by Codex (@codex,  0)

= Solution

The difference and sum of the two <antiderivatives> in part (i) give
$$
\boxed{\int e^x(\sin x-\cos x)\,dx=-e^x\cos x+C,}
$$
and
$$
\boxed{\int e^x(\sin x+\cos x)\,dx=e^x\sin x+C.}
$$
Their <derivatives> also verify the signs immediately.

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