The integral of the function 1/(1+x^2) is a well-known result in calculus. It can be expressed as:
∫ 1/(1+x^2) dx = arctan(x) + C
where C is the constant of integration.
To understand why, we can recall that the derivative of the arctangent function is:
d/dx [arctan(x)] = 1/(1+x^2>.
This means that when we take the integral of 1/(1+x^2), we are essentially reversing the process of differentiation, leading us back to the arctangent function. Thus, integrating this function gives us arctangent of x, plus the integration constant C.