(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find [tex]\int[/tex][tex]\frac{x+2}{x^{2}+2*x+10}[/tex]*dx

You are given that [tex]\int[/tex][tex]\frac{du}{u^{2}+a^{2}}[/tex] = [tex]\frac{1}{a}[/tex]tan[tex]^{-1}[/tex] [tex]\frac{u}{a}[/tex] + C fora not equal to 0

2. Relevant equations

None.

3. The attempt at a solution

I'm not entirely too sure how to go about doing this. I first thought of integration by parts, but given that this is a 3 mark question it seems quite long winded.

I split up the expression:

1/x^2+2*x+10*x+2*dx

Then I set u = x+2, du = 1, dv =1/x^2+2*x+10, v = (1/3)*arctan((1/3)*x+1/3)

I have no idea how to get v, that was calculated using Maple, so how is that arctan component calculated by hand?

Using the uv - int(vdu) formula for the rest of it results in some bizarre answers, which might be right but seems altogether too long and complex for a 3 mark answer.

The final answer as calculated by Maple is:

(1/2)*ln(x^2+2*x+10)+(1/3)*arctan((1/3)*x+1/3)

Any help and direction greatly appreciated.

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# Homework Help: How do I go about integrating this?

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