You had to subtract the k=0 term, which ended up being just "x".
I don't see it back in your integrated result.
Let me explain with an example.
Suppose you have the function f(x)=x2 + 3
Now you know that f(0)=3 don't you?
Taking the derivative we get f'(x)=2x.
Taking the integral again we get [itex]\int f'(x)dx = x2 + C[/itex]
(This is called an indefinite integral, since the boundaries were not given.)
As you can see the result is not equal to the original function - we lost the '3' in the process.
But since we know that f(0)=3, we can deduce that the integration constant C must be 3.
In which step should i substitute zero to get the constant?