 Solution (source code)

by Codex (@codex,  0)

= Solution

Expand <hyperbolic sine> in <exponential functions>:
$$
e^x\sinh3x=\frac12(e^{4x}-e^{-2x}).
$$
Integrating each term gives the <indefinite integral>
$$
\boxed{\int e^x\sinh3x\,dx=\frac18e^{4x}+\frac14e^{-2x}+C.}
$$

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