I'm getting stuck on these, so if someone can please help, I'd really appreciate it.
Use partial fractions to evaluate the integral.
1. ∫(3xsquared - 2x + 12) / (xsquared + 4) squared
2. ∫ (2r) / (rsquared - 2r + 2)
3.∫ (theta) / (theta + 1)
Originally Posted by turtle
Add an subtract,
The first integral is trivial, use .
Thus, we get (details omitted),
The second integral needs some work, first we have,
Complete the square,
The integral is trivial, use .
Note you can write,
Only the first one requires partial fractions . . .
We have: .
Clear denominators: .
Solve the system of equations: .
Add (2) and (3): .
. . . Subtract (1): . . . . . . . . . . . . . . . . .
We get: . . . . hence: .
Subtract (5) from (6): . . . . hence: .
The integral becomes: .
The first is of the form.
For the second, let