Determine whether the improper integral converges or diverges.
-$$\int _ { 1 } ^ { \infty } \frac { 8 \mathrm { e } ^ { x } } { \ln x } d x$$
A) Diverges
B) Converges

Question

Quizplus · Accepted Answer

We can use the limit comparison test with $f(x) = \frac{1}{\ln x}$ to see that the given integral is larger than
$$ \int_1^\infty \frac{8e^x}{x}dx $$
which diverges by the integral test. Therefore, by the comparison test, the given integral also diverges.

Determine Whether the Improper Integral Converges or Diverges ∫1∞8exln⁡xdx\int _ { 1 } ^ { \infty } \frac { 8 \mathrm { e } ^ { x } } { \ln x } d x∫1∞​lnx8ex​dx

Determine Whether the Improper Integral Converges or Diverges $\int _ { 1 } ^ { \infty } \frac { 8 \mathrm { e } ^ { x } } { \ln x } d x$