∫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

Question

∫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

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

wiat...-9 lol

amistre64 · Answer

your right there...good job :)

anonymous · Answer

lols amistre, "good job" :P

amistre64 · Answer

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

amistre64 · Answer

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

anonymous · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

x = sqrt(3) sec(t)

amistre64 · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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 ;)

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

you sure you posted the question right?

cherrilyn · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

cherrilyn · Answer

No conclusion ? :(

amistre64 · Answer

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