Does $\int_{1}^{\infty} \frac{7+e^{-z}}{z} d z$ converge?

Name: Does $\int_{1}^{\infty} \frac{7+e^{-z}}{z} d z$ converge?
Brand: Quizplus
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Question

Quizplus · Accepted Answer

The integral $\int_{1}^{\infty} \frac{7+e^{-z}}{z} d z$ diverges because the integral $\int_{1}^{\infty} \frac{1}{z} d z$ diverges, and since $7+e^{-z} > 1$ for all $z > 0$, the given integral diverges by comparison.

Does ∫1∞7+e−zzdz\int_{1}^{\infty} \frac{7+e^{-z}}{z} d z∫1∞​z7+e−z​dz Converge

Does $\int_{1}^{\infty} \frac{7+e^{-z}}{z} d z$ Converge