Let I = dx/x 2 4x + 8. (a) Complete the square to show that x

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Let I = ∫dx/√x− 4x + 8.
(a) Complete the square to show that x2 − 4x + 8 = (x − 2)2 + 4.
(b) Use the substitution u = x − 2 to show that I =du/√u+ 22. Evaluate the u-integral.

(c) Show that I = ln Ι√(x − 2)2 + 4 + x − 2Ι + C.

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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