What is f(x) = int 1/(x-3)-1/(x-2) dx if f(-1)=6 ?

1 Answer
Aug 10, 2017

f(x) = ln|((x - 3)/(x - 2))| + 6 - ln(4/3)

Explanation:

We use the commonly used result int (1/x) dx = ln|x| to solve.

f(x) = ln|x - 3| - ln|x - 2| + C

f(x) = ln|(x- 3)/(x - 2)| + C

Now we determine the value of the constant of integration.

6 = ln|(-1 - 3)/(-1 - 2)| + C

6 = ln|4/3| + C

C = 6 - ln(4/3)

So the function is

f(x) = ln|((x - 3)/(x - 2))| + 6 - ln(4/3)

Hopefully this helps!