Integrate and Differentiate

[handsomeboy]

Hello all ^^
If let P=d/dt 1/P=Integrate(from -∞ to t)
In what condition that the following statement is true::

P*1/P*f(t)=1/P*P*f(t)=f(t)

thanks a lot

 

[kordix]

simply, if f belongs to L²(K)!!