Question

The value of ${\int }_3^5\frac{x^2}{x^2-4}dx$ is

• A. $2(1-lo{g}_e\left(\frac{15}{7}\right))$
• B. $2(1+lo{g}_e\left(\frac{15}{7}\right))$
• C. $2(1+4{\log }_{e}3-4{\log }_{e}7+4{\log }_{e}5)$
• D. $2(1-{\tan }^{-1}\left(\frac{15}{7}\right))$

Answer 1

The correct option is B $2(1+lo{g}_e\left(\frac{15}{7}\right))$

${\int }_3^5\frac{x^2}{x^2-4}dx$
$={\int }_3^{5}1dx+4{\int }_3^5\frac{1}{x^2-4}dx=2+4.\frac{1}{2}log\left(\frac{x-2}{x+2}\right){|}_3^5$
$2+2\left[log\right(3/7)-log(1/5\left)\right]$
$=2(1+log(\frac{15}{7}\left)\right)$
Hence, option 'B' is correct.