Question

$\underset{1}{\overset{3}{\int }}{\left(\frac{x^2+1}{4x}\right)}^{-1}dx=$______

• A. $\log 5$
• B. $\frac{1}{2}\log 5$
• C. $\log 25$
• D. $\log 100$

Answer 1

The correct option is C $\log 25$

$\underset{1}{\overset{3}{\int }}{\left(\frac{x^2+1}{4x}\right)}^{-1}dx$
$=\underset{1}{\overset{3}{\int }}\frac{4x}{x^2+1}dx$
$=\underset{1}{\overset{3}{\int }}2\left(\frac{2x}{x^2+1}\right)dx$
$=2{\left[\log \right(x^2+1\left)\right]}_1^3$
$=2(\log 10-\log 2)$
$=2\log 5=\log 25$