How do you integrate this?

[glenjoy]

\[


I = ∫ x(d^w/dx^w(x^2-1)^w)dx ; limits (1 and 0)

\]

 

[DugalMc]

Do you mean

\[\int_{0}^{1}x\frac{d^{n}}{dx^{n}}(x^{2} -1)^{n}dx\] ?

if so first expand \[(x^{2} -1)^{n}\] as a sum (remember binomial expan? then apply differentiation then int. Or just learn about lengendre polynomials ...

 

[steve10]

here it is.

 

[eda_freak]

Actually the answer is pretty simple...
Int(0--->1) x.(2n)**n. n(n-1)(n-2)....1
= Int(0-->1)2**n. x**(n+1). !n
=2**n . !n / n+2