I don't really understand these calc II questions?

Question

Integrate (2x) / ((x+2)(x+1)) dx.

Let P(x) = 3x^2 - 5x^3 +7x^4 + 3x^5 be the fifth degree Taylor polynomial for the function f(x) about x=0. What is the value of f'''(0)?

Answer 1

2 x/(x+2)((x+1) =2 (A/(x+2) +B/(x+1)) (partial fractions)
so
A(x+1)+B(x+2) = x and A+B=1 and A+2B=0
-2B+B=1 so B=-1 and A =2
The integral is 2( ln(x+2)^2- lnIx+1I)
In the Taylor polynomial you know that the coefficient of
x^3 is f´´´(0)/3! so
-5= f´´´(0)/6 and f´´´(0) =-30

Answer 2

1) Let A/(x+2) + B(x+1) = 2x / (x+2)(x+1)
LHS becomes
A(x+1) + B(x+2) / (x+2)(x+1)
= (A+B)x + (A+2b) / (x+2)(x+1)
Numerator of LHS = numerator of RHS, so
(A+B)x + (A+2B) = 2x + 0
So A+B = 2 and (A+2B) = 0
If A+2B = 0, then A = -2B
and from A+B=2, B = 2-A = 2 +2B
so B = -2
and A = -2B = 4

So original problem can be split up as
integral ( 4/ (x+2)) + integral ( (-2) / (x+1))
Take it from here...
A +4 - 2A = 0
A = -2