Question

Consider the function f(x) = (4x + 4)/(2x^2+4x) and the function g(x)=(2x+2)/(x^2+2x) Clearly, f(x) = g(x) for any value of x and thus f and g should be thought of as merely different notation for the same function. Now find the integral of f(x)dx and the integral of g(x)dx (without factoring out 2 in the case of f). Explain why it is not a problem that you get different solutions.