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

1 Answer
Apr 3, 2018

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

Explanation:

f(x) = int [1/(x+3)-1/(x-2)] dx = ln|x+3|-ln|x-2|+C
qquad = ln|(x+3)/(x-2)|+C

Since f(-1) = 3, we have

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

Thus

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