Question

Find the integral of the function $\frac{1}{x^2+6x+5}$

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$\int \frac{dx}{x^2+6x+5}$
When we get an integral of this form we try to express it as perfect square and proceed.
$\Rightarrow \int \frac{dx}{x^2+6x+5}=\int \frac{dx}{(x+3{)}^2-4}$
This integral is of the form $\int \frac{dx}{x^2-a^2}$ which will be equal to $\frac{1}{2a}$ ln$|\frac{x-a}{x+a}|+c$
$\Rightarrow \int \frac{dx}{(x+3{)}^2-4}=\frac{1}{4}ln|\frac{(x+3)-2}{(x+3)+2}|+c\frac{1}{4}ln|\frac{(x+1)}{(x+5)}|+c$