Question
Asked Dec 2, 2019
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Find or evaluate the integral by completing the square. (Use C for the constant of integration.)

dx
9x2- 18x 36
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dx 9x2- 18x 36

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Expert Answer

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Step 1

Let's look at the denominator.

The denominator = 9x2 – 18x + 36 = 9x2 – 18x + 9 + 27 = (9x2 – 18x + 9) + 27 = 9[(x2 – 2x + 1) + 3] = 9[(x – 1)2 + 3]

Step 2

Please see the white board. Let x - 1 = z; hence, dx = dz

The integral therefore takes the shape as shown in the last expression on the white board.

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dax dx 9x- 1)2+3 9x2-18x36 dz

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Step 3

Recall the standard integration ...

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dar du a2+ x2 1+ u2 a 1 arctan uC 1 arctan C =

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Math

Calculus

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