Question

I have an interesting intergral that seems pretty challenging. After attempting to solve it for some time, I've come up empty handed. Can you solve this integral?
Indefinite Integral of:
${x}^{4} { {e}^{x} }^{3}$
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Answer 1

${x}^{4} { {e}^{x} }^{3} = 0 \\ \Leftrightarrow {x}^{4} = 0 \: \vee \: { {e}^{x} }^{3} = 0 \\ \Leftrightarrow x = 0\: \vee \:x \in \emptyset \\ \Leftrightarrow x = 0$