Question

Evaluate :

${\int }_0^1\frac{2x}{5x^2+1}dx$

• A. $\frac{1}{2}\log 3$
• B. $\frac{1}{5}\log 6$
• C. $\frac{1}{3}\log 5$
• D. None of these

Answer 1

The correct option is B $\frac{1}{5}\log 6$

$I={\int }_0^1\frac{2x}{5x^2+1}dx$

$I=\frac{1}{5}{\int }_0^1\frac{10x}{5x^2+1}dx$

$I=\frac{1}{5}\left[\log \right(5x^2+1){]}_0^1$

$I=\frac{1}{5}(\log 6-\log 1)$

$I=\frac{1}{5}\log 6$