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**Am I integrating this right: (x^2 + 3x + 11)/(x+2)^4 ???**

1. ∫(x

^{2}+ 3x + 4)/(x+2)

^{4}dx

2. With these sorts of problems, I think about integration by partial fractions.

So in this case, the denominator factors are all the same, so I have to make each one with different exponents.

I wrote:

A/(x + 2) + B/(x + 2)

^{2}+ C/(x + 2)

^{3}+ D/(x + 2)

^{4}

I multiplied to get common denominators:

A(x + 2)

^{3}+ B(x + 2)

^{2}+ C(x + 2) + D = x

^{2}+ 3x + 11

Now I need to figure out what A, B, C, and D equal.

When I substitute x=-2, D=9

A(x + 2)

^{3}+ B(x + 2)

^{2}+ C(x + 2) + 9 = x

^{3}+ 3x + 11

I think I am supposed to take the derivative now to figure out the other values.

2x + 3 = 3A(x + 2)

^{2}+ 2B(x + 2) + C

When I substitute x=-2, C= -1

Now, am I able to take the derivative again?

That's what I did next:

Substituting x=-2,

2 = 6A(x + 2) + 2B

B=1

If x=1,

2 = 6A(x + 2) + 2(1)

A=0

...Am I even doing this right? :/

I don't want to go on if I'm not even doing this part right!

Thank you very much! :D