Integrals with Exponentials (58) Z e ax dx = 1 a e ax (59) Z √ xe ax dx = 1 a √ xe ax + i √ π 2a 3/2 erf ( i √ ax ) , where erf(x)= 2 √ π Z x 0 e -t 2 dt (60) Z xe x dx =(x - 1)e x (61) Z xe ax dx =  x a - 1 a 2  e ax (62) Z x 2 e x dx = ( x 2 - 2x +2 ) e x (63) Z x 2 e ax dx =  x 2 a - 2x a 2 + 2 a 3  e ax (64) Z x 3 e x dx = ( x 3 - 3x 2 +6x - 6 ) e x (65) Z x n e ax dx = x n e ax a - n a Z x n-1 e ax dx (66) Z x n e ax dx = (-1) n a n+1 Γ[1 + n, -ax], where Γ(a, x)= Z ∞ x t a-1 e -t dt (67) Z e ax 2 dx = - i √ π 2 √ a erf ( ix √ a ) 7