Integrate dy/dx = 2x/(x^2-4)

Integrate dy/dx = 2x/(x²-4).

We can answer this question using integration by substitution, where we set u = something in terms of x.

In this case we are going to set u = x²-4 (the denominator).

When we differentiate this we get du/dx = 2x, therefore dx = 1/(2x) du.

If we substitute this back into the original equation: 2x/(x^2-4) dx = 2x/u 1/(2x) du.

The 2x cancels with the 1/(2x) leaving the integral of 1/u du.

Using our knowledge of integrals this equals ln u (the natural logarithm - log base e).

We now substitute x² - 4 back in for u leaving y = ln(x² - 4), the solution.