Questions 6 (Hints and solutions start on page .)

Q 3.10   Rewrite each of the following in one of the forms X² + A², X² - A², A² - X², - X² - A² or ±X² by completing the square.

9x² + 6x + 5,        4x² - 4x - 3,        9x² - 12x + 4

4x - 2x²,        2 - 4x - 4x²,        x² + x + 2

Now work out the integrals

$$\int$$$${\frac{dx}{\sqrt{2-4x-4x^2}}}$$,        $$\int$$$${\frac{dx}{\sqrt{4x-2x^2}}}$$,        $$\int$$$${\frac{dx}{\sqrt{9x^2+6x+5}}}$$