Question

quick integral question!

Answer 1

Question: \[\int\limits_{?}^{?}\frac{ 2 }{ x ^{2}+6x+11 }dx\]

Answer 2

My Approach:

Answer 3

\[\int\limits_{?}^{?}\frac{ 2 }{ (x ^{2}+6x+9)+2 }\]

Answer 4

those are question marks on the limits right? they are not 2s are they?

Answer 5

\[\int\limits_{}^{}\frac{ 2 }{ (x+3)^{2}+2}dx\]

Answer 6

Let u = x + 3
\[\frac{ du }{ dx } = 1\]
\[du = dx\]

Answer 7

Sub u into integral
\[\int\limits_{}^{}\frac{ 2 }{ u ^{2}+2}du\]

Answer 8

Then I'm not sure where to go from there...got any ideas?

Answer 9

you probably need to use trig substituion

Answer 10

I can't seem figure out a trig substitution that would fit...:/

Answer 11

ah

\[\int\limits_{}^{}\frac{ 2 }{ u ^{2}+\sqrt{2}^{2} }du\]

Answer 12

Still looks hairy though with that sqrt 2

Answer 13

it's really not so bad\[u=\sqrt 2\tan\theta\]\[\int\frac{2\sqrt2\sec^2\theta d\theta}{2\tan^2\theta+2}=\sqrt2\int\frac{\sec^2\theta d\theta}{\tan^2\theta+1}\]

Answer 14

then do I apply trig substitution?

Answer 15

why not just use the integral formulas?
first page, second to the last of the formulas for common integrals.....
http://tutorial.math.lamar.edu/pdf/Calculus_Cheat_Sheet_Integrals.pdf