# Thread: Integrating 1/x^4

1. ## Integrating 1/x^4

I have just been introduced to Integration and was hoping someone might be able to start me off on this one. It has stumped me for some reason. It is part of some tutorial questions I was given but I cannot find the example answer. Can you show how you worked it out so as to help me understand.

Integrate the following with respect to x:

1/x^4

Thanks

M

2. Originally Posted by mm874
Integrate the following with respect to x: 1/x^4

$\displaystyle \int \dfrac{1}{x^4}\;dx=\int x^{-4}\;dx=\ldots$

3. You should have already learned two things: (1) the derivative of $\displaystyle x^n$ is $\displaystyle nx^{n-1}$ and (2) integration is the reverse of differentiation.

Since differentiating a power of x lowers the power by 1, integration must increase it so the integral of $\displaystyle x^n$ must involve $\displaystyle x^{n+1}$. But it can't be just $\displaystyle x^{n+1}$ because its derivative is $\displaystyle (n+1)x^n$. What constant, C, must $\displaystyle x^{n+1}$ be multiplied by so that the derivative of $\displaystyle Cx^{n+1}$ is just $\displaystyle x^{n+1}$?

Here, as FernandoRevilla said, n= -4. What is n+1?