Question

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

Answer 1

We have ${\int }_2^4\frac{x}{x^2+1}dx=\frac{1}{2}{\int }_2^4\frac{2x}{x^2+1}dx=\frac{1}{2}[log|x^2+1{]}_2^4$

$\therefore {\int }_2^4\frac{x}{x^2+1}dx=\frac{1}{2}[log17-log5]=\frac{1}{2}log\left(\frac{17}{5}\right)$