Integrate the functions in Exercises 1 to 22. 1. x sin x 2. x sin 3x 3. x 2 e x 4. x log x 5. x log 2x 6. x 2 log x 7. x sin 1x 8. x tan1 x 9. x cos1 x 10. (sin1x) 2 11. 1 2 cos 1 x x x 12. x sec2 x 13. tan1x 14. x (log x) 2 15. (x 2 + 1) log 16. e x (sinx + cosx) 17. 2 (1 ) x x e x 18. 1 sin 1 cos x x e x 19. 2 1 1 x e x x 20. 3 ( 3) ( 1) x x e x 21. e 2x sin x 22. 1 2 2 sin 1 x x Choose the correct answer in Exercises 23 and 24. 23. 3 2 x x e dx equals (A) 1 3 C 3 x e (B) 1 2 C 3 x e (C) 1 3 C 2 x e (D) 1 2 C 2 x e 24. sec (1 tan ) x e x xd x equals (A) e x cos x + C (B) e x sec x + C (C) e x sin x + C (D) e x tan x + C
Question 1:x sin x
Question 2:x sin 3x
Question 3:x 2 e x
Question 4:x log x
Question 5:x log 2x
Question 6:x 2 log x
Question 7:x sin– 1x
Question 8:x tan–1 x
Question 9:x cos–1 x
Question 10:(sin–1x) 2
Question 11:1 2 cos 1 x x x ✓ ✔
Question 12:x sec2 x
Question 13:tan–1x
Question 14:x (log x) 2
Question 15:(x 2 + 1) log
Question 16:e x (sinx + cosx)
Question 17:2 (1 ) x x e x
Question 18:1 sin 1 cos x x e x
Question 19:2 1 1 – x e x x
Question 20:3 ( 3) ( 1) x x e x
Question 21:e 2x sin x
Question 22:1 2 2 sin 1 – x x ✔ ✓ ✕ Choose the correct answer in Exercises 23 and 24
Question 23:3 2 x x e dx ✖ equals (A) 1 3 C 3 x e ✗ (B) 1 2 C 3 x e ✘ (C) 1 3 C 2 x e ✘ (D) 1 2 C 2 x e ✘
Question 24:sec (1 tan ) x e x xd x ✚ equals (A) e x cos x + C (B) e x sec x + C (C) e x sin x + C (D) e x tan x + C