What is f(x) = int 1/(x+3)-1/(x-2) dx if f(-1)=3 ? Calculus Techniques of Integration Evaluating the Constant of Integration 1 Answer Ananda Dasgupta 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 Answer link Related questions How do you find the constant of integration for intf'(x)dx if f(2)=1? What is a line integral? What is f(x) = int x^3-x if f(2)=4 ? What is f(x) = int x^2+x-3 if f(2)=3 ? What is f(x) = int xe^x if f(2)=3 ? What is f(x) = int x - 3 if f(2)=3 ? What is f(x) = int x^2 - 3x if f(2)=1 ? What is f(x) = int 1/x if f(2)=1 ? What is f(x) = int 1/(x+3) if f(2)=1 ? What is f(x) = int 1/(x^2+3) if f(2)=1 ? See all questions in Evaluating the Constant of Integration Impact of this question 1380 views around the world You can reuse this answer Creative Commons License