$\int_2^3 \frac{d x}{x^2-x}$ is equal to

$\int_2^3 \frac{d x}{x^2-x}$ is equal to
  1. $\log \frac{2}{3}$
  2. $\log \frac{4}{3}$
  3. $\log \frac{8}{3}$
  4. $\log \frac{1}{4}$

Solution

We have, $ \begin{aligned} \int_2^3 \frac{d x}{x^2-x} & =\int_2^3 \frac{1}{x(x-1)} d x \\ & =\int_2^3\left[-\frac{1}{x}+\frac{1}{x-1}\right] d x \\ & =\left[\log \frac{x-1}{x}\right]_2^3=\log \frac{2}{3}-\log \frac{1}{2}=\log \frac{4}{3} \end{aligned} $

Asked in: AP EAMCET 2002

Practice more Definite Integration questions on Aicharya