For positive values of `x`, we know that `ln x` is an antidifferential for `(dx)/x`. Similarly, for `x` less than `c`, we know `-ln text[(]c-x text[)]` is an antidifferential for `(dx)/(c-x)`. (Here the negative sign in front of the logarithm is necessary to balance the negative sign generated by the Chain Rule in differentiation.) Putting these two antidifferentials together, we obtain
as an antidifferential for `(dx)/[xtext[(]c-x text[)]]`. Now we may factor out the `1/c` and use the fact that a difference of logarithms is the log of the quotient to rewrite the antidifferential as