text: Q:
  
  Looking for a primitive ...
  
  The problem is to find $f$ such that
  $$f^{\prime}(x)+\int_0^x f(t)\times u(t)dt=0$$ where $u$ is given.
  I tried to find a primitive of the function $\frac{f^{\prime\prime}}{f}$ but I think it is not an easy way. 
  Is there any suggestion how to solve this ?.
  Thanks in advance.
  
  A:
  
  You are (essentially) trying to solve the differential equation $y''+uy=0$. 
  While this is a homogeneous linear second order differential equation, it cannot be solved in terms of elementary functions even for some very nice, very reasonable choices of $u$. 
  For example: If you choose $u=-x$, then the solutions of $y''-xy=0$ are called Airy functions. These functions aren't elementary. 
  So in the end, trying to solve this equation for a "general" $u$ is more or less hopeless!
  
  