- #1
Lo.Lee.Ta.
- 217
- 0
Am I integrating this right: (x^2 + 3x + 11)/(x+2)^4 ?
1. ∫(x2 + 3x + 4)/(x+2)4dx
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 = x2 + 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 = x3 + 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
1. ∫(x2 + 3x + 4)/(x+2)4dx
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 = x2 + 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 = x3 + 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