`int_(0)^(1) x (1 -x)^(n) dx=?`

int_(0)^(1) x dx

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

int_(0)^(1)(1-x^(3))^(n)dx=

evaluate int_(0)^(1)x^(2)(1-x)^(n)dx

Statement-1: (C_(0))/(2.3)- (C_(1))/(3.4) +(C_(2))/(4.5)-.............+............+(-1)^(n) (C_(n))/((n+2)(n+3))= (1)/((n+1)(n+2)) Statement-2: (C_(0))/(k)- (C_(1))/(k+1) +(C_(2))/(k+3)+............+(-1)^(n) (C_(n))/(k+n)=int_(0)^(1)x^(k-1) (1 - x)^(n) dx

int_(0)^(a) x (1-x)^(5)dx=........

int_(0)^(1)x e^(x)dx=

U_(n)=int_(0)^(1)x^(n)(2-x)^(n)dx and V_(n)=int_(0)^(1)x^(n)(1-x)^(n)dx,n in N and if (V_(n))/(U_(n))=1024, then the value of n is