Comment on Activity 3

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

`1/c ln x-1/c lntext[(]c-x text[)]`

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

`1/c ln x/(c-x)`.