Question

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

Answer 1

`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`.