Hai

1. I am anitha from chennai. what is integral X^n logX?

anitha

I = xⁿlogx dx

choose logx as first function & xⁿ as second then using integration by parts

I = logx [xⁿdx] - { d/dx (logx) [xⁿdx]}dx

I = logx[xⁿ⁺¹]/n+1 - { xⁿ⁺¹/x(n+1)}dx

I = logx[xⁿ⁺¹]/n+1 - { xⁿ/n+1}dx

I = logx[xⁿ⁺¹]/n+1 - {xⁿ⁺¹}/(n+1)² + C

approve if u like my ans