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

int_(0)^(oo)x^(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.

int_0^1(dx)/(e^x+e^(-x)) is equal to

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