Question

Find the integral $\int \frac{2x}{x^2-4}dx$

• A. $\ln \left(2x\right)+C$
• B. $e^{x^2-4}+C$
• C. $\ln (x^2-4)+C$
• D. $\frac{e^{x^2-4}}{2x}+C$

Answer 1

The correct option is C $\ln (x^2-4)+C$

Given, $f\left(x\right)=\frac{2x}{x^2-4}$
So, to integrate the given function we use substitution method.
Let $t=x^2-4\Rightarrow \frac{dt}{dx}=2x$
Or, $dt=2xdx$
Thus, substituting this value in the given function we have,
$\int \frac{2x}{x^2-4}dx=\int \frac{1}{t}dt=\ln t+C$
$\Rightarrow \ln (x^2-4)+C$