The question is:

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Consider the integral

$\displaystyle I=\int \frac{x}{\sqrt{7+8x+x^2}}dx$

(i) Use the substitution u = x +4 to transform the integral into one for which trigonometric substitution is appropriate. (You will need to start by first completing the square under the root sign.)

The second part of this is: (ii) Now use a suitable trignometric substitution on the integral in (i) to find I.

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I think I'll be able to do the second part once I get the first bit sorted.

My problem is basically that I don't know how to deal with the x on the top.

What I have done so far(which may or may not be correct):

I completed the square, and ended up with $\displaystyle (x +4)^2-9$ under the square root sign. I substituted u into that, as per the question, but what I'm left with is in terms of both x and u, as well as not being in the form for trigonometric substituion - the form I'm thinking I should be getting is

$\displaystyle \int \frac{1}{\sqrt{u^2-a^2}}du$

Any ideas on this question? (I would appreciate ideas as opposed to solutions.)

Thank you.