For \( a0 \), find the minimum value of the integral \( \int_{0}^{1 / a}\left(a^{3}+4 x-a^{5} x^...

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For \( a0 \), find the minimum value of the integral \( \int_{0}^{1 / a}\left(a^{3}+4 x-a^{5} x^{2}\right) e^{a x} d x \).
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