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Form Five                                                            Form Five



                                              2
             (b) 2e  x− 2  + c        (c)  −       +  c
                                            3 ln3
                                              x
                 1                        1            1     1   x 
                                                  1
                                               2
                      2
                              5
             (d)  ln x + 2x ++   c    (e)  ln x ++       tan −      + c
         FOR ONLINE READING ONLY
                 2                        2            2        2 
                 x 2
             (f)    ++   2ln x + 2 +  ln x − + c
                                          3
                      x
                 2
                       1
                                        2
                                           1 tan xc
             (g) ln x −+    1   −  1  ln x + +    − 1  +
                           x − 1 2
                              1                   1  sin − 1   x + 3   + c
             (h) tan ( )x −  − 1   +  c       (i)              
                              2
                           2(x + 1)               2        4 
                                                      2
             (j) 1 ln x+  −  ln 1 ln x+  +  c  (k)  −  3(x + 1)  +  c
                                                      3
                 1       3  1       3               1
                                                        2x
             (l)   ( x +  ) 1  2 +  ( x −  ) 1  2 +  c  (m)  7 + c
                 3          3                     2ln 7
                                                           θ
                13       11           1                  1 
          16.  (a)   ln3+   π      (b)  ln θ 2  +  16 +  8tan −   +  c
                10       20           2                   
                                                            4
                 1
             (c)  ln sec4 +  θ  tan 4 +  θ  c
                 4
                                                     x
                                                 tan  − 1+  2 
                 3                 1                         
                                                     2
                                                   
             (d)  ln cos x +  sin x +  x +  4 2 ln               +  c
                 2                 2                         
                                                     x
                                                   tan  − 1+  2   
                                                     2
                                                   
                 35               128
          17. (a)   π         (b)
                256               315
                1328 3            17   3
          19. (a)             (b)    +    ln3
                  2835            36   32
                1
          21. (b)                          22.   ln(1+  2)units
                3
          23.   (a) 1 squareunit    (b)   (eπ− 1) cubic units

                                  207
                                             Mathematics for Advanced Secondary Schools



                                                                        30/06/2024   18:02:56
   ADVANCED MATH F.5 TG CHAPTERS.indd   207                             30/06/2024   18:02:56
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