(68) Z e -ax 2 dx = √ π 2 √ a erf ( x √ a ) (69) Z xe -ax 2 dx = - 1 2a e -ax 2 (70) Z x 2 e -ax 2 dx = 1 4 r π a 3 erf(x √ a) - x 2a e -ax 2 Integrals with Trigonometric Functions (71) Z sin ax dx = - 1 a cos ax (72) Z sin 2 ax dx = x 2 - sin 2ax 4a (73) Z sin 3 ax dx = - 3 cos ax 4a + cos 3ax 12a (74) Z sin n ax dx = - 1 a cos ax 2 F 1  1 2 , 1 - n 2 , 3 2 , cos 2 ax  (75) Z cos ax dx = 1 a sin ax (76) Z cos 2 ax dx = x 2 + sin 2ax 4a (77) Z cos 3 axdx = 3 sin ax 4a + sin 3ax 12a 8