You need to consider the following function hence, integrating the function yields:
You may substitute any value for n, this does not affect the way you evaluate the integral.
We'll integrate the negative power as we do when integrate positive powers.
Supposing that we'll have the function f(x) = 1/x^3.
We'll integrate f(x):
Int f(x)dx = Int dx/x^3
We do not know to integrate the expression above, so we'll
apply the following rule:
x^-3 = 1/x^3
As we can remark, the negative power moves the base "x", to the denominator.
Int dx/x^3 = Int x^-3dx
We know now to integrate the power function:
Int x^n dx = x^(n+1)/(n+1) + C
Comparing, we'll get:
Int x^-3dx = x^(-3+1)/(-3+1) + C
Int x^-3dx = x^-2/-2 + C
Int x^-3dx = -1/2x^2 + C