integrals!!!!!!!!!!!!!!!!!!!!!!!!

Question

evaluate

             

Answer 1

Let us find factors for x^2 - 6x + 5 = x^2 - x - 5x +5 

                                                            = x(x - 1) - 5(x - 1)

                                                            = (x - 5) (x - 1)

Let us assume

  -> (1)

1 = A(x - 1) + B(x - 5)

If x = 1 then -4B = 1 => B = -1/4

If x = 5 then 4A = 1 => A = 1/4

Substituting A and B values in the equation (1) we get,

Apply integral on both sides we get,

                               

                                                                                3

                                            =(1/4)(ln(x-5)-ln(x-1))

                                                                                0

                                                                               3

                                            =(1/4)(ln(x-5)/(x-1))

                                                                                0

Apply the limits

                                       =(1/4)(ln(-1)-ln5)

                                      =(1/4)(ln(-1/5)