Multiply through by dx



Separate the variables:



Integrating the left side using formula  = 

 =  = 

To integerate the right side, we must first complete the
square on the denominator:

x² - 8x + 15

multiply -8 by 1/2, get -4, then square, getting +16
Add 16 then subtract 16

x² - 8x + 16 - 16 + 15

Factor first three terms as square of a binomian, combine last two terms:

(x - 4)² - 1

 = 

We use formula  = 

 =  = 

So we have:

 = 

Let arbitrary constant 

 = 

Multiply through by 6

 = 

Use the coefficient/exponent rule of logarithms and 
write arbitrary constant  as ,
choosing C > 0.

 = 

Use the sum/product rule of logarithms on the right:

 = 


 = 

If the arbitrary constant is chosen properly we may 
erase the absolute values:

 = 

or if we like:

 = 

Edwin