Question

Determine if the following integral is convergent or divergent.
${\int }_1^{\infty }\frac{e^{-x}}{x}dx$

• A. Converging at $1$
• B. Divergent
• C. Convergent
• D. None of these

Answer 1

The correct option is C Convergent

Let

$\frac{e^{-x}}{x}<\frac{e^{-x}}{1}=e^{-x}$

And we know that

${\int }_1^{\infty }{e}^{-x}dx=[-e^{-x}{]}_1^{\infty }=1/e$. Hence, it converges.

so by comparison test we can say that:

${\int }_1^{\infty }\frac{e^{-x}}{x}dx$ also converges.