what is the antiderivative of (1/(x^2)) dx?

Answer 1

Integral (1 / (x^2 ) dx

Note that 1/(x^2) is the same as x^(-2).

We have ways of integrating x^n (for n not equal to -1).

The integral of x^n is x^(n + 1) / (n + 1).

Therefore, the integral of x^(-2) is x^(-1) / (-1), or, with better math etiquette

x^(-1) / (-1) = -1/x

Answer 2

I've never heard the term antiderivative, but if what you want to do is integrate the expression then do the following
rewrite the expression as
X^(-2)dx
integration gives
(-1/2)X^(-1)+C
Where C is an arbitrary constant

Answer 3

-1/x.