Integrate 2x-2/(x^2-2x-15)(X+2)

Question



Answer 1

desmos.com/calculator/3dlpwighkb

Answer 2

Using partial fraction methods solve for a, b, and c

One method is to get a common denominator:

(x+2)(x+3)a + (x-5)(x+2)b + (x-5)(x+3)c results in these three equations:

For the x²'s: a + b + c = 0

For the x's: 5a - 3b - 2c = 1

For the constants: 6a - 10b - 15c = -1

Solving results in a = 1/14, b = -1/2, and c = 3/7

The integral becomes:

Which integrates to