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CHAPTER 27
27.48
27.49
27.50
27.51
27.52
27.53
27.54
From the formula in Problem 27.46, we get
From the formula in Problem 27.46, we obtain
From the formula in Problem 27.39, we get
By completing the square,
Then
From the formula in Problem 27.41, we get
Now,
Note that
(The second integral was evaluated in Problem 27.51; the first integral was found by the formula of Problem 19.1.)
By completing the square, x
2 + 8x + 20 = (x + 4)
2 +4. Let u = x + 4, du = dx. Then
Dividing x
3 by x
2 - 2x + 4, we obtain
Hence,
Let x=u2, dx=2u du. Then
Let x=u2, dx=2u du. Then