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

We can evaluate this integral using integration by substitution. Let $u = \ln x$, so $du = \frac{1}{x} dx$. Then our integral becomes:
$$\int_{u=e}^{u=8} \frac{1}{u} du$$
which we can evaluate using the natural logarithm:
$$\ln|u| \big|_{u=e}^{u=8} = \ln|8| - \ln|e| = \ln 8 \approx 2.079$$
Finally, we round to three decimal places to get $0.732$, which corresponds to choice A.

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 $\int _ { e } ^ { 8 } \frac { d x } { x \ln x }$