Is it possible to solve following integral with partial-fraction decomposition? I have a integral
$$\int_0^1\frac{-x^2+4x+4}{x^2-4}~dx$$
Which I changed to
$$\int_0^1\frac{-x^2+4x+4}{(x-2)(x+2)}~dx$$
But I don't know how to change numerator to have lesser polynom degree than the denominator to use partial-fraction decomposition.

The numerator is
$$8-(x-2)^2$$
so the integrand is
$$\begin{align}\frac{8-(x-2)^2}{(x-2)(x+2)} &= \frac{8}{(x-2)(x+2)} - \frac{x-2}{x+2} \\ &= 2 \left (\frac1{x-2} - \frac1{x+2} \right ) - \frac{4}{x+2} +1 \end{align}$$
You should be able to go from here...
