What is the anti derivative of 1/x^2 dx?

Question

Calculus Integrals

Answer 1

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

So, ask what function has a derivative that equals x^(-2).
The general form of the antiderivative of x^r is (1/(r + 1))x^(r + 1) + k

dy/dx = x^(-2), so:

y= -1 x ^(-1) + k (where k is a constant, since dk/dx=0)

Answer 2

The antiderivative of x^r is (1/(r + 1))x^(r + 1) + C. You can rewrite 1/x^2 as x^-2, making the antiderivative (1/-1)x^-1 + C = -x^-1 + C= -1/x + C.