What is the step of integrating this?

  • Thread starter Thread starter yungman
  • Start date Start date
  • Tags Tags
    Integrating
yungman
Messages
5,741
Reaction score
294

Homework Statement


I need help in finding the answer of this integration:

\int \frac{d^n [(x^2-1)^n]}{dx^n}dx


I have no idea how to even start, please at least give me hints how to substitude.

Thanks

Alan
 
Physics news on Phys.org
Doesn't the fundamental theorem of calculus say that<br /> \int \frac{df(x)}{dx} dx = f(x) + <br />

? And

<br /> \frac{d^n [(x^2-1)^n]}{dx^n} = \frac{d}{dx} \frac{d^{n-1} [(x^2-1)^n]}{dx^{n-1}}<br />
 
I see, thanks for your time.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top