determine the following integrals

Question

∫(12)/(x^2 - 9) dx

Answer 1

Using partial fractions, 12/(x²-9) = 12/[(x+3)(x-3)]

 

                                              = A/(x+3) + B/(x-3)

 

Multiply by the LCD to get 12 = A(x-3) + B(x+3)

 

If x = 3, then B = 2

If x = -3, then A = -2

 

So, the given integral is equivalent to ∫(-2/(x+3))+2/(x-3))dx

 

                                               = -2lnlx+3l + 2lnlx-3l + C