Use partial Fraction Decomposition calculate∫ 2 dx / [(x-4)(x^2+2x+6)]?

Question

Hi,
I'm trying to understand how to solve this review problem. I can't figure out how they reached their answer.

∫ 2 dx / [(x-4)(x^2+2x+6)]

The farthest I managed to reach is that
A = 1/17
B = -1/17
C = 6/17

(1/17) / (x-4) + (-1/17x + 6/17) / (x^2+2x+6)

Answer 1

Now find partial decomposition

 

 

Equate the   coefficients

Equate the x coefficients

Equate the constants

From (1)

Substitute B value in equation (2).

To eliminate the A variable subtrct equation (3)  from

Substitute C value in

Substitute A,C values in equation (2)

 

Substitute A, B, C values in equation (i)

 

 

 

 

Answer 2

Comtinuous...

Now the integral becomes  

Now

 

Now   

Now

Apply the formula