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Evaluate the following Integrate (x+2)[√(x-3)]I am in class 11 this is a easy question which I can`t solved plz try it and make me know the answer

Evaluate the following Integrate (x+2)[√(x-3)]I am in class 11 this is a easy question which I can`t solved plz try it and make me know the answer

Question Image
Grade:11

1 Answers

Nandana
110 Points
4 years ago
hi ,
     you might go in this way  !
     first ,  seperate the terms in this way  
            ∫x /√(x-3) dx + 2∫ 1/ √(x-3) dx
                 x -3 =u
                dx = du & x= u+3
          2∫ 1/ √(x-3) dx  = 2 u-1/2+1 / ½ = 4√(x-3) +c
           ∫x /√(x-3) dx =    ∫ x√(x-3) / (x-3) dx
                                       x -3 = u
                                      x = u+3
                                     dx = du
                          = ∫(u+3)√u/u du = ∫(√u + 3/√u ) du
                                                      = 2/3 (x-3)3/2 + 6 √(x-3) + k
              finally,
                    ∫(x +2)/√(x-3) dx  = 2/3 (x-3)3/2 + 6 √(x-3) + 4√(x-3) + K
                                                 = 2/3 (x-3)3/2  + 10√(x-3) +K
                                              K – arbitary constant .
                                                                                                Thank you ,  keep learning by questioning !
      

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