int_(0)^(1)x(1-x)^(x)dx

Evaluate : (i) int_(0)^(1)x(1-x)^(n)dx (ii) int_(0)^(1)x(1-x)^(3//2)dx

int_(0)^(1)x(1-x)^(4)dx=(1)/(30)

Evaluate :int_(0)^(1)(1-x)/(1+x)(dx)/(sqrt(x+x^(2)+x^(3)))

int_(0)^(1)(x)/(x+1)dx=

int_(0)^(1)x sin(x-1)dx+int_(0)^(1)(1-x)sin xdx=

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

" (iii) "1=int_(0)^(1)(x-1)(x+2)dx

int_(0)^(1)e^(x)(x^(x)+1)^(3)dx=

Let I= int_(0)^(1) (x^(x))/( x+1) dx, then the vlaue of the intergral int_(0)^(1) (xe^(x^(2)))/( x+1) dx, is

If int_(0)^(1)f(x)dx=1, int_(0)^(1)x f(x)dx=a and int_(0)^(1)x^(2)f(x)dx=a^(2) , then : int_(0)^(1)(a-x)^(2)f(x)dx=