Find the integrals of the functions in Exercises 1 to 22: 1. sin2 (2x + 5) 2. sin 3x cos 4x 3. cos 2x cos 4x cos 6x 4. sin3 (2x + 1) 5. sin3 x cos3 x 6. sin x sin 2x sin 3x 7. sin 4x sin 8x 8. 1 cos 1 cos x x 9. cos 1 cos x x 10. sin4 x 11. cos4 2x 12. 2 sin 1 cos x x 13. cos 2 cos 2 cos cos x x 14. cos sin 1 sin 2 x x x 15. tan3 2x sec 2x 16. tan4 x 17. 3 3 2 2 sin cos sin cos x x x x 18. 2 2 cos 2 2sin cos x x x 19. 3 1 sin cos x x 20. 2 cos 2 cos sin x x x 21. sin 1 (cos x) 22. 1 cos ( ) cos ( ) x a xb Choose the correct answer in Exercises 23 and 24. 23. 2 2 2 2 sin cos is equal to sin cos x x dx x x (A) tan x + cot x + C (B) tan x + cosec x + C (C) tan x + cot x + C (D) tan x + sec x + C 24. 2 (1 ) equals cos ( ) x x e x dx e x (A) cot (exx ) + C (B) tan (xex ) + C
Question 1:sin2 (2x + 5)
Question 2:sin 3x cos 4x
Question 3:cos 2x cos 4x cos 6x
Question 4:sin3 (2x + 1)
Question 5:sin3 x cos3 x
Question 6:sin x sin 2x sin 3x
Question 7:sin 4x sin 8x
Question 8:1 cos 1 cos – x x
Question 9:cos 1 cos x x
Question 10:sin4 x
Question 11:cos4 2x
Question 12:2 sin 1 cos x x
Question 13:cos 2 cos 2 cos cos x – x –
Question 14:cos sin 1 sin 2 x – x x
Question 15:tan3 2x sec 2x
Question 16:tan4 x
Question 17:3 3 2 2 sin cos sin cos x x x x
Question 18:2 2 cos 2 2sin cos x x x
Question 19:3 1 sin cos x x
Question 20: 2 cos 2 cos sin x x x
Question 21:sin – 1 (cos x)
Question 22:1 cos ( ) cos ( ) x –a x–b Choose the correct answer in Exercises 23 and 24
Question 23:2 2 2 2 sin cos is equal to sin cos x x dx x x (A) tan x + cot x + C (B) tan x + cosec x + C (C) – tan x + cot x + C (D) tan x + sec x + C
Question 24:2 (1 ) equals cos ( ) x x e x dx e x (A) – cot (exx ) + C (B) tan (xex ) + C (C) tan (e x ) + C (D) cot (e x )