Why is the integral of (5)/(1+x^2) not tan^-1(5x)?

In calculus, both in the case of finding the derivative
and when we are finding the integral, with differentiation being the inverse of
integration, the constant multiples of the terms with the variables is excluded and only
the final answer is multiplied by the constant. The integral of c*f(x) = c*Int[ f(x)
dx]

Here, we have the integral of f(x) = 5/(1 + x^2). As 5
is a constant it not included while the integral is being
found.

Int[f(x) dx] = Int[5/(1 + x^2
dx]

=> 5*Int[5/(1 + x^2
dx]

=> 5* arc tan x +
C

The correct right integral of 5/(1 + x^2)
is 5*arc tan x + C.