What is f(x) = int 1/(x+3)-1/(x-4) dx if f(-2)=3 ?

1 Answer
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.