Question

Evaluate: ${\int }_2^4\frac{x}{x^2+1}dx$

Answer 1

${\int }_2^4\frac{x}{x^2+1}dx$

let $x^2+1$ = $t$ , we get $2xdx=dt$ ( the limits of $t$ are $5$ to $17$)

Therefore the given expression reduces to ${\int }_5^{17}\frac{1}{2t}dt=\frac{1}{2}(\ln 17-\ln 5).$