- #1
JFonseka
- 117
- 0
Homework Statement
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 for a not equal to 0
Homework Equations
None.
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.