(78) Z cos p axdx = - 1 a(1 + p) cos 1+p ax × 2 F 1  1+ p 2 , 1 2 , 3+ p 2 , cos 2 ax  (79) Z cos x sin x dx = 1 2 sin 2 x + c 1 = - 1 2 cos 2 x + c 2 = - 1 4 cos 2 x + c 3 (80) Z cos ax sin bx dx = cos[(a - b)x] 2(a - b) - cos[(a + b)x] 2(a + b) ,a 6= b (81) Z sin 2 ax cos bx dx = - sin[(2 a - b)x] 4(2 a - b) + sin bx 2 b - sin[(2 a + b)x] 4(2 a + b) (82) Z sin 2 x cos x dx = 1 3 sin 3 x (83) Z cos 2 ax sin bx dx = cos[(2 a - b)x] 4(2 a - b) - cos bx 2 b - cos[(2 a + b)x] 4(2 a + b) (84) Z cos 2 ax sin ax dx = - 1 3 a cos 3 ax (85) Z sin 2 ax cos 2 bxdx = x 4 - sin 2 ax 8 a - sin[2(a - b)x] 16(a - b) + sin 2 bx 8 b - sin[2(a + b)x] 16(a + b) (86) Z sin 2 ax cos 2 ax dx = x 8 - sin 4 ax 32 a (87) Z tan ax dx = - 1 a ln cos ax 9