Partial fractions by computer

You will write the cover-up rule as code for a fraction $\dfrac{p(x)}{(x - r)(x - s)}$ with two different roots. Then you will rebuild the fraction from its parts and write the antiderivative.

The idea. For $\dfrac{p(x)}{(x - r)(x - s)} = \dfrac{A}{x - r} + \dfrac{B}{x - s}$, hide the factor $x - r$ and put $x = r$ in the rest to find $A$. In the same way, hide $x - s$ and put $x = s$ to find $B$. The antiderivative is $A\ln|x - r| + B\ln|x - s|$.

Your tasks.

1. Finish cover_up(p, r, s). Return the pair (A, B), where p is a function of x.
2. Finish split_value(A, B, r, s, x). Return the value of $\dfrac{A}{x - r} + \dfrac{B}{x - s}$.
3. Finish antiderivative(A, B, r, s, x). Return $A\ln|x - r| + B\ln|x - s|$.