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Answer
$$ \displaystyle\int \mathrm{e}^{{x}^{4}+1}\, \mathrm d x = -{{e\,\Gamma\left({{1}\over{4}} , -x^4\right)\,x}\over{4\,\left(-1 \right)^{{{1}\over{4}}}\,\left| x\right| }} $$
Explanation
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