Question

Solve ${\int }_2^3\frac{x}{x^2-1}dx$

• A. $\frac{1}{2}ln\left(\frac{5}{3}\right)$
• B. $\frac{1}{2}ln\left(\frac{8}{3}\right)$
• C. $\frac{1}{2}ln\left(\frac{4}{3}\right)$
• D. None of these

Answer 1

The correct option is B $\frac{1}{2}ln\left(\frac{8}{3}\right)$

Let, $x^2-1=t$

$⟹2x.dx=dt$

Substituting values , we get

$⟹\int \frac{dt}{2t}$

$⟹\frac{1}{2}lnt$

$⟹\frac{1}{2}\left[ln\right(x^2-1){]}_2^3$

$⟹\frac{1}{2}ln\left(\frac{8}{3}\right)$