Evaluate `I=int_(0)^(infty) xe^(-x)dx`

Evaluate int_(0)^(infty) e^(-x)x^(3)dx .

int xe^(-x)dx

int xe^(-2x)dx

int xe^(3x)dx

The value of int_(0)^(infty)[2e^(-x)] dx (where ,[.] denotes the greatest integer function of x) is equal to S

int xe^(x^(2))dx

int xe^(x^2+2)dx