Evaluate $\int _ { 2 } ^ { \infty } \frac { 1 } { x \ln \sqrt { x } } d x$ .
A) 0
B) $\frac { 1 } { 2 \ln 2 }$
C) $- \frac { 1 } { 2 \ln 2 }$
D) Diverges

Name: Evaluate $\int _ { 2 } ^ { \infty } \frac { 1 } { x \ln \sqrt { x } } d x$ . A) 0 B) $\frac { 1 } { 2 \ln 2 }$ C) $- \frac { 1 } { 2 \ln 2 }$ D) Diverges
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Question

Quizplus · Accepted Answer

The integral diverges because the integrand behaves like $\frac{1}{x \ln x}$ as $x \to \infty$, which is known to diverge.

Evaluate ∫2∞1xln⁡xdx\int _ { 2 } ^ { \infty } \frac { 1 } { x \ln \sqrt { x } } d x∫2∞​xlnx​1​dx

Evaluate $\int _ { 2 } ^ { \infty } \frac { 1 } { x \ln \sqrt { x } } d x$