Use the Comparison Theorem to Determine Whether $\int _ { 0 } ^ { \infty } \frac { 1 } { x + e ^ { x } } d x$

question 71

Essay

Use the Comparison Theorem to determine whether $\int _ { 0 } ^ { \infty } \frac { 1 } { x + e ^ { x } } d x$ is convergent or divergent. Justify your answer.

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Definitions:

Transverses Thoracis

A muscle within the thorax that plays a role in the movement of the thoracic cage during respiration.

External Obliques

Muscles located on the sides of the abdomen, involved in the rotation of the spine and the lateral flexion of the torso.

External Intercostals

Muscles located between the ribs that help expand the chest cavity during inhalation.

Vertebral Column

The flexible column of vertebrae that extends from the skull to the tailbone, enclosing the spinal cord and providing support to the body.