Evaluate the integral to three decimal places.
$$\int _ { e } ^ { 8 } \frac { d x } { x \ln x }$$
A) $0.732$
B) $0.194$
C) $0.094$
D) $0.533$
E) $0.183$

Question

Quizplus · Accepted Answer

The integral $\int \frac{dx}{x \ln x}$ can be solved using the substitution $u = \ln x$, $du = \frac{1}{x} dx$. The limits change from $x = e$ to $x = 8$ to $u = 1$ to $u = \ln 8$. The integral becomes $\int \frac{du}{u}$, which evaluates to $\ln |u|$. Evaluating from 1 to $\ln 8$ gives $\ln(\ln 8) - \ln(1) = \ln(\ln 8)$. Calculating this gives approximately 0.732.

Evaluate the Integral to Three Decimal Places ∫e8dxxln⁡x\int _ { e } ^ { 8 } \frac { d x } { x \ln x }∫e8​xlnxdx​

Evaluate the Integral to Three Decimal Places $\int _ { e } ^ { 8 } \frac { d x } { x \ln x }$