need some help solving an integral using partial fraction?

Integrate ∫{1/[(x + 7)(x² + 9)]}dx {from 4 to -1}

First rearrange the expression into a form easier to integrate by using partial fractions.

1/[(x + 7)(x² + 9)] = a/(x + 7) + (bx + c)/(x² + 9)

Cross multiplying we get:

1 = a(x² + 9) + (bx + c)(x + 7)

1 = ax² + 9a + bx² + 7bx + cx + 7c

1 = (a + b)x² + (7b + c)x + (9a + 7c)

From this we get

0 = a + b

0 = 7b + c

1 = 9a + 7c

Solving for a, b, and c we get

a = -b

7a = -7b

c = -7b

c = 7a

1 = 9a + 7c = 9a + 49a = 58a

a = 1/58

b = -a = -1/58

c = 7a = 7/58

1/[(x + 7)(x² + 9)] = a/(x + 7) + (bx + c)/(x² + 9)

1/[(x + 7)(x² + 9)] = (1/58)/(x + 7) + [(-1/58)x + (7/58)]/(x² + 9)

Now you can integrate.