The wording of the problem is ambiguous because we don't know if the integrals are definite or undefinite integrals.

If the integrals were definite, the bounds should be specified and the problem may have a solution, or no solution, depending on the given bounds.

If the integral were undefinite, there is no solution. For example f(x)=exp(x) doesn't works :

Integral of exp(x)*dx = exp(x)+C1

Integral of (1/exp(x))dx = -exp(-x)+C2

the product = (exp(x)+C1)*(-exp(-x)+C2) is not equal to -1.

Can you clarify the wording of the problem about the bounds of the integrals ?