Question 4

( 1) ( 2) ( 3) / x x - x - x - 5. 2 3 2 x x x+ + 6. (1 2 ) / - x / x - x 7. 2( 1) ( - 1) x x x+ 8. 2( 1) ( 2) x x - x + 9. 3 2 3 5 x x - x x + − + 10. 2 2 3 ( 1) (2 3) / x / x - x − + 11. 2 ( 1) ( 4) / x x x+ − 12. 3/2 1/1 x x x + + − 13. 2 (1 ) (1 )x x− + 14. 2 3 1 ( 2) / x - / x + 15. 4 1x − 16. ( 1)nx x + [Hint: multiply numerator and denominator by x n - 1 and put xn = t ] 17. cos (1 - sin ) (2 - sin ) / x x x [Hint : Put sin x = t] 18. 2 2 2 2 ( 1) ( 2) ( 3) ( 4) / x x / x x + + + + 19. 2 2 ( 1) ( 3) / x x x+ + 20. 4 ( 1)x x - / 21. ( 1)xe - [Hint : Put ex = t] Choose the correct answer in each of the Exercises 22 and 23. 22. ( 1) ( 2) x dx x x− −∫ equals (A) 2( 1)log C 2 x x − +− (B) 2( 2)log C 1 x x − +− (C) 2 1log C x x −  + −  (D) log ( 1) ( 2) Cx x− − + 23. 2( 1) dx x x +∫ equals (A) 21log log ( +1) + C2x x− (B) 21log log ( +1) + C2x x+ (C) 21log log ( +1) + C2x x− + (D) 21 log log ( +1) + C2 x x+