Question

Evaluate the integrals
${\int }_1^2\frac{1}{(x^2+2x)}dx$

Answer 1

$\Rightarrow {\int }_1^2\frac{1}{(x+1{)}^2-1}dx$

Formula :$\int \frac{1}{x^2-a^2}dx=\frac{1}{2a}\ln \left(\frac{x-a}{x+a}\right)$

$\Rightarrow \frac{1}{2.1}\ln {\left(\left|\frac{x}{x+2}\right|\right)}_1^2$

$\Rightarrow \frac{1}{2}\ln \left(\frac{6}{4}\right)$