Integrate the functions in Exercises 1 to 37: 1. 2 2 1 x x 2. 2 log x x 3. 1 x x x log 4. sin sin (cos ) x x 5. sin ( ) cos ( ) ax b ax b 6. ax b 7. x x 2 8. 2 x 1 2 x 9. 2 (4 2) 1 x xx 10. 1 x x 11. 4 x x , x > 0 12. 1 3 5 3 ( 1 x x ) 13. 2 3 3 (2 3 ) x x 14. 1 (log )m x x , x > 0 15. 2 9 4 x x 16. 2 3 x e 18. 1 2 1 tan x e x 19. 2 2 1 1 x x e e 20. 2 2 2 2 x x x x e e e e 21. tan2 (2x 3) 22. sec2 (7 4x) 23. 1 2 sin 1 x x 24. 2cos 3sin 6cos 4sin x x x x 25. 2 2 1 cos (1 tan ) x x 26. cos x x 27. sin 2 cos 2 x x 28. cos 1 sin x x 29. cot x log sin x 30. sin 1 cos x x 31. 2 sin 1 cos x x 32. 1 1 cot x 33. 1 1 tan x 34. tan sin cos x x x 35. 2 1 log x x 36. 2 ( 1) log x x x x 37. 3 1 4 sin tan 1 x x x Choose the correct answer in Exercis
Question 1:2 2 1 x x
Question 2: 2 log x x
Question 3:1 x x x log
Question 4:sin sin (cos ) x x
Question 5:sin ( ) cos ( ) ax b ax b
Question 6:ax b
Question 7:x x 2
Question 8:2 x 1 2 x
Question 9:2 (4 2) 1 x xx
Question 10:1 x – x
Question 11:4 x x , x > 0
Question 12:1 3 5 3 ( 1 x – x )
Question 13:2 3 3 (2 3 ) x x
Question 14:1 (log )m x x , x > 0
Question 15:2 9 4 x – x
Question 16:2 3 x e
Question 18:1 2 1 – tan x e x
Question 19:2 2 1 1 x x e – e
Question 20:2 2 2 2 x – x x – x e –e e e
Question 21:tan2 (2x – 3)
Question 22:sec2 (7 – 4x)
Question 23:1 2 sin 1 – x – x
Question 24:2cos 3sin 6cos 4sin x – x x x
Question 25:2 2 1 cos (1 tan ) x – x
Question 26:cos x x
Question 27:sin 2 cos 2 x x
Question 28:cos 1 sin x x
Question 29:cot x log sin x
Question 30:sin 1 cos x x
Question 31: 2 sin 1 cos x x
Question 32:1 1 cot x
Question 33:1 1 tan – x
Question 34:tan sin cos x x x
Question 35: 2 1 log x x
Question 36: 2 ( 1) log x x x x
Question 37: 3 1 4 sin tan 1 – x x x Choose the correct answer in Exercises 38 and 39
Question 38:10 9 10 10 10 log 10 x e x x dx x equals (A) 10x – x 10 + C (B) 10x + x 10 + C (C) (10x – x10) –1 + C (D) log (10x + x10) + C
Question 39:2 2 equals sin cos dx x x (A) tan x + cot x + C (B) tan x – cot x + C (C) tan x cot x + C (D) tan x – cot 2x +