Question

Evaluate the integral of dx/(x ln x)

Answer 1

$$\int \dfrac{dx}{x \ln x}$$

Use $u$-substitution

$$u=\ln x, du=\dfrac{1}{x}dx$$

$$\int \dfrac{dx}{x \ln x}=\int \dfrac{du}{u}=\ln|u|+C=\ln{(|\ln x|)}+C$$

$$\int \dfrac{dx}{x \ln x}=\ln{(|\ln x|)}+C$$