If `m=n`, then `x^(m)/x^(n)=` ______.

x^(m+n)/x^(n)= _________.

If I_(m,n)=int (x^(m))/((log x)^(n))dx then (m+1)I_(m,n)-n.I_(m,n+1)=

If m, n in N , then l_(m n) = int_(0)^(1) x^(m) (1-x)^(n) dx is equal to

If I_(m,n) - int (x^(m) (logx)^(n) dx then I_(m,n) - (x^(m+1))/((m + 1)) (logx)^(n) =

Find the nature of the roots of the quadratic equations. If the real roots exist, find them :- (m+n)^2x^2+ (m+n)x-2=0 .

if I_(m,n)=int(x^(m))/((log x)^(n))dx, then (m+1)I_(m,n)-nI_(m,n+1) is

Evaluate for m in N , int(x^(3m)+x^(2n)+x^m)(2x^(2m)+3x^m+6)^(1/m)dx ,x >0

Use the identity (1+x)^(m)(1+x)^(n)=(1+x)^(m+n) to prove Vandermonde's theorem, ""^(m)C_(r ) +""^(m)C_(r-1). ""^(n)C_( 1)+""^(m)C_(r -2) *""^(n)C_(2) +….+""^(n)C_(r )=""^((m+n))C_(r )

If m and n are +ve integers and m>n and if (1+x)^(m+n)(1-x)^(m-n) is expanded as a polynomial in x ,then the coefficient of x^(2) is