Evaluate $\int _ { 2 } ^ { \infty } \frac { 1 } { x ( \ln x ) ^ { 3 } } d x$
A) $- \frac { 1 } { 2 \ln 2 }$
B) $- \frac { 1 } { 2 ( \ln 2 ) ^ { 2 } }$
C) $\frac { 1 } { 2 ( \ln 2 ) ^ { 2 } }$
D) $\frac { 1 } { 2 \ln 2 }$

Question

Quizplus · Accepted Answer

The integral converges and evaluates to $\frac { 1 } { 2 ( \ln 2 ) ^ { 2 } }$ using substitution $u = \ln x$, which simplifies the integral to a form that can be evaluated.

Evaluate ∫2∞1x(ln⁡x)3dx\int _ { 2 } ^ { \infty } \frac { 1 } { x ( \ln x ) ^ { 3 } } d x∫2∞​x(lnx)31​dx

Evaluate $\int _ { 2 } ^ { \infty } \frac { 1 } { x ( \ln x ) ^ { 3 } } d x$