Calculate the integral below by partial fractions and by using the indicated substitution. Be sure that you can show how the results you obtain are the same. $$\int \frac{2x}{x^{2}-4}\,dx$$

First, rewrite this with partial fractions:
$\int \frac{2x}{x^{2}-4}\,dx = \int$ $dx + \int$ $dx =$ + $+ C$.
(Note that you should not include the $+C$ in your entered answer, as it has been provided at the end of the expression.)

Next, use the substitution $w = x^2 - 4$ to find the integral:
$\int \frac{2x}{x^{2}-4}\,dx = \int$ $dw =$ $+ C =$ $+ C$.
(For the second answer blank, give your antiderivative in terms of the variable $w$. Again, note that you should not include the $+C$ in your answer.)