## cherrilyn 5 years ago ∫dx/(x^2+6x+6)^2 Evaluate the integral by completing the square and using trig substitution. After completing the square I got (x+3)^2-3 but I don't know what to do next

1. amistre64

your good with the completing the square part: [(x+3)^2 +6+9)]^2

2. amistre64

you are adding +9 inside; so you add +9 outside as well....

3. amistre64

wiat...-9 lol

4. amistre64

5. anonymous

lols amistre, "good job" :P

6. amistre64

you need to substitute the trig..... x^2 -1 thing....

7. amistre64

tan = x^2 + 1 sin = 1 - x^2 whats the other one? sec?

8. anonymous

don't trig sub needed amistre what is with you and trig subbing!?!?! those are the worst!!! just to regular subbing

9. amistre64

its in the prob itself...use trig sub lol :) not my fault this time lol

10. amistre64

sec^2 - 1 = tan...i think thats the one...

11. amistre64

x = sqrt(3) sec(t)

12. amistre64

err.... (x+3) = sqrt(3)sec(t) 3sec^2(t) -3 = 3(sec^2(t)-1) [3tan^2(t)]^2 = 9 tan^4(t)

13. anonymous

the integral of (x+3)^2-3 is $\frac{1}{3}(x + 3)^3 - 3x$

14. anonymous

oy i should learn to read the question... amistre, i take everything back...

15. anonymous

...but what i did was right...why do you need trig id?

16. amistre64

d(sqrt(3) sec(t))/dt = ....everything? even the ceramic unicorn you gave me for my birthday?

17. amistre64

d(sqrt(3) sec(t))/dt = d(x+3)/dx sqrt(3) sec(t)tan(t) dt = dx [sqrt(3) sec(t)tan(t) dt]/[9 tan^4(t)] is this looking right ;)

18. amistre64

$\int\limits_{} \frac{\sqrt{3} \sec(t) \tan(t)}{9 \tan^4 (t)}dt$

19. amistre64

we can ignore for the moment the sqrt(3)/9 reduce to: sec(t)/tan^3(t) = sin(t)/cos^4(t)

20. amistre64

you sure you posted the question right?

21. cherrilyn

yeah I just don't know how to add the division bar . lol . "Evaluate the integral by completing the square and using trigonometric substitution"

22. amistre64

frac{top}{bottom} in the editor :)

23. amistre64

any ideas how to integrate: sin(t) ----- ?? cos^4

24. amistre64

sin(t) = sqrt(1-cos^2) sqrt(1-cos^2) ------------ doesnt seem to make it easier cos^4

25. amistre64

cos^2 = 1-sin^2 (1-sin^2)(1-sin^2) = sin^4 -2sin^2 +1...... hmmm

26. amistre64

D(tan^4) = 4 tan^3 sec^2....dont see that helping lol

27. cherrilyn

No conclusion ? :(

28. amistre64

i couldnt get to a result.....at leaast not without pencil and paper to do it with.... and a lot more braincells :)