How to implement static class member functions in *.cpp file?

It is. The key is to use the static keyword only in the header file, not in the source file!

test.hpp:

class A {
public:
    static int a(int i);  // use `static` here
};

test.cpp:

#include <iostream>
#include "test.hpp"


int A::a(int i) {  // do **not** use `static` here!
    return i + 2;
}

using namespace std;
int main() {
    cout << A::a(4) << endl;
}

They're not always inline, no, but the compiler can make them.

Try this:

header.hxx:

class CFoo
{
public: 
    static bool IsThisThingOn();
};

class.cxx:

#include "header.hxx"
bool CFoo::IsThisThingOn() // note: no static keyword here
{
    return true;
}

helper.hxx

class helper
{
 public: 
   static void fn1 () 
   { /* defined in header itself */ }

   /* fn2 defined in src file helper.cxx */
   static void fn2(); 
};

helper.cxx

#include "helper.hxx"
void helper::fn2()
{
  /* fn2 defined in helper.cxx */
  /* do something */
}

A.cxx

#include "helper.hxx"
A::foo() {
  helper::fn1(); 
  helper::fn2();
}

To know more about how c++ handles static functions visit: Are static member functions in c++ copied in multiple translation units?