Does the integral $\int_{10}^{\infty} \frac{x^{4}}{e^{-x}+x} d x$ converge?

Name: Does the integral $\int_{10}^{\infty} \frac{x^{4}}{e^{-x}+x} d x$ converge?
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Question

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The integral diverges because the denominator $e^{-x} + x$ approaches $x$ as $x$ approaches infinity, making the integrand behave like $\frac{x^4}{x} = x^3$ for large $x$, and the integral of $x^3$ from 10 to infinity diverges.

Does the Integral ∫10∞x4e−x+xdx\int_{10}^{\infty} \frac{x^{4}}{e^{-x}+x} d x∫10∞​e−x+xx4​dx Converge

Does the Integral $\int_{10}^{\infty} \frac{x^{4}}{e^{-x}+x} d x$ Converge