On Tuesday, October 10, 2017 at 5:00:11 PM UTC-5, Mr : K.H wrote: > the primitive F(x)=ln(x) of function f(x)=1/x can be otherway maybe ? The by-product of an even function is odd. But the primitive of an odd function is not an even function. then F(x) can be odd.
Actually, ln(x) is A primitive of the function f(x) = 1/x, x>0, defined only on the positive integers. This function is neither odd nor even.
A primitive of the function f(x)=1/x is F(x) = ln|x| (natural log of the absolute value of x). This function is even.
However, it is not THE primitive. There are infinitely many primitives; the functions F(x)= ln|x| + C, for any constant C, are all primitives of the function f(x) = 1/x. -- Arturo Magidin