Answer
$$ \displaystyle\int -{\mathrm{e}}^{x}{\cdot}\sqrt{9{\mathrm{e}}^{2x}+4}\, \mathrm d x = -{{4\,{\rm asinh}\; \left({{3\,e^{x}}\over{2}}\right)+3\,e^{x}\, \sqrt{9\,e^{2\,x}+4}}\over{6}} $$
Explanation
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