`int_0^oox^n e^(-x)dx` (n is a + ve integer) is equal to

int_(0)^( pi)cos^(n)x backslash dx(n is even integer) is equal to

Prove that int_0^oo[n e^(-x)]dx=1n((n^n)/(n !)),w h e r en is a natural number greater than 1 and [.] denotes the greatest integer function..

Prove that int_0^oo[n e^(-x)]dx=ln((n^n)/(n !)),w h e r en is a natural number greater than 1 and [.] denotes the greatest integer function..

Prove that int_0^oo[n e^(-x)]dx=ln((n^n)/(n !)),w h e r en is a natural number greater than 1 and [.] denotes the greatest integer function..

Prove that int_(0)^(infty)x^n e^(-x) dx=n!., Where n is a positive integer.

If int_0^af(2a-x)dx=m and int_0^af(x)dx=n, then int_0^(2a) f(x) dx is equal to

Prove that: I_n=int_0^oox^(2n+1) e^ (-x^2) dx=(n !)/2,n in N .

Prove that: I_n=int_0^oox^(2n+1) e^ (-x^2) dx=(n !)/2,n in N .