What is f(x) = int 1/(x+3)-1/(x-4) dx if f(-2)=3 ? Calculus Techniques of Integration Evaluating the Constant of Integration 1 Answer Trevor Ryan. Jan 9, 2016 therefore f(x)=ln|x+3|-ln|x-4|+3-ln6. Explanation: f(x)=int(1/(x+3)-1/(x-4))dx=int1/(x+3)dx-int1/(x-4)dx =ln|x+3|-ln|x-4|+C. But since f(-2)=3 is given as an initial/boundary condition, we can substitute it into the integral to find the constant of integration : therefore ln|-2+3|+ln|-2-4|+C=3 therefore0+ln6+C=3,=>C=3-ln6. therefore f(x)=ln|x+3|-ln|x-4|+3-ln6. 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 1290 views around the world You can reuse this answer Creative Commons License