Integration Question, how do you integrate 1/x^2. And how would you do partial integration?

Question

how do you integrage 1/x^2 or 1/x^3 .

Also How would you solve for partial integrals? because there are partial integrals as well as there are partial derivatives right?

would anybody refer me to a basic webpage for integrals? I'm not talking about any of the other methods like substitution or integration by parts, just regular basic integration like for the equation above, I know basic integration but forgot what to do in some cases.

Nice MsMath, when is it that the integral of something = ln x?

I keep on getting confused with it

thought the integral of 1/ x = ln x as you can see I'm a bit confused

Answer 1

1/x^2 = x^(-2)
The antiderivative is x^(-2+1)/(-2+1) + C
= x^(-1)/-1 + C
= -1/x + C
It is similar for 1/x^3
You do partial integrals the same way you do regular integrals. You need to know which one you are integrating with respect to and then pretend the other variable(s) are constants.

Answer 2

Here is a nice overview of integration and reverse derivatives.

To integrate polynomials, visualize the process for differentiation and turn it around, adding a constant that would vanish when the derivative is taken.

Answer 3

∫dx/x^2=-1/3x^3
∫dx/x^3=-1/4x^4

Answer 4

∫dx/x² = -1/x + C
∫dx/x³ = -1/(2x²) + C