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anonymous
 5 years ago
find the intergral of 1/((1+9(x^2))^2)
anonymous
 5 years ago
find the intergral of 1/((1+9(x^2))^2)

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0factor out the 9, youre going to get arctan something

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0alright i know what i need to do i need to use trig subsitution and i wasn't sure 1/((1+9(x^2))^4/2) or should i just use tan i mean what is going to be the coeffiecinet but that seems incorrect

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh nevermind, i didnt see the square . you can do trig substitution

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ohk i can factor out the 9 that seems a good think thanks i just wasn't doing that : i guess

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0whoa, where did 4/2 come from?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.04/2 is the same thing as 2 so when i see all the examples in book they have roots under the section of trig subsitution

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0dont use 4/2, thats weird

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It is weird. Very weird. Use a tan sub, as above.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if youre using an integral table look for 1 / ( x^2 + a^2)^2 dx

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yup i am using a tan sub just sure what to put as a coefficient for tan

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Integral tables are for babies.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes that i what i am following cantroset but in that the a will 1/3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0errr you can have 1 / ( ax^2 + b^2) ^2 dx,

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i know that formula :P

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0:) so 1/3 should be my coefficient right :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0lets use trig sub just to be thorough, i use pauls online math course, here one sec i will post link

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\text{Let } x = \frac{1}{3}\cdot \tan \alpha\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Paul is the man!! http://tutorial.math.lamar.edu/Classes/CalcII/TrigSubstitutions.aspx scroll down

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes why is that a 1/3 that is what i am lost about shouldn't it be 1/9

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok one sec, i hate this thing it keeps freezing. yeesh why doesnt google help with the appearance of this

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the 1/3 is squared to 1/9

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ohk so it is (1+ 1/3 tan (theta))^2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0(1+ 1/3 tan (theta)^2)^2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh i think i see what youre doing, youre forcing it to be a square root ok sqrt a^2 + b^2x^2 , let x = a/b tan t

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[1+9x^2 = 1+ 9\left(\frac{1}{3}\tan \alpha \right)^2 = 1+\tan^2 \alpha\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so you want ( 1 + 9x^2)^2 = [ (1+9x^2)^4] ^1/2 ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i think newton thats simpler,

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0paul seems to say you want a square root though

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh that makes so much more sense :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you don't really need to have it i guess you can force it but you don't need it you need it for inital i guess it won't really change anything ( i am referring to the square root)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0xD how on earth does that make more sense. Crazy Americans.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you can also do partial fractions i bet

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i mean what you wrote.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah i can do partial fraction, but i am required to do trig :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh, good. And you can't split it in to partial fractions (I don't think).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0here integrals involving quadratics http://tutorial.math.lamar.edu/Classes/CalcII/IntegralsWithQuadratics.aspx

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Because it's the same term squared on the bottom and no others.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0But assuming you could put it into partial fractions, it would not simplify it at all.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so those are your factors irreducible quadratic

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0(9x^2+1)^2 = (tan(a)^2+1) = sec(a)^4 is this correct

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but probably not the easiest approach. youre tan sub is fine , one sec

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0No, because it would be \[\frac{ax + b}{1+9x^2} + \frac{cx + d}{\left(1+9x^2\right)^2}\] But they all equal 0 except fro d = 1, because ... etc

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Now include the change of what you are integrating with respect to and go from there.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ohk so next 1/sec(a)^4 = cos(a)^4

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yes, but\[\frac{\mathbb{d}\alpha}{\mathbb{d}x}\] don't forget to include

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0not if you use complex root factoring

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0avnis just talking to newton

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh, OK, you can;t split it up into partial fractions in a way which would make it a retardedly different problem  is that better?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0newton, it would be like partial decomp'ing 1/(x^2 + 1) = A/ (x+i) + B/ ( x i)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i prefer approaches , one size fits all. hehe, the one size hammer that is

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how do i solve the rest of it

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0@anvis If you are now integrating with respect something other than x, you need to account for that. Note: \[x = \frac{1}{3}\tan\alpha \implies \frac{\mathbb{d}x}{\mathbb{d}\alpha} = \frac{1}{3}\sec^2 \alpha\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i see which will make a equal to tan^1(3x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so i wll be left with 1/3 integral of cos^2(a)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It will, but you don't need to include that yet. \[\int\limits \frac{1}{(1+9x^2)^2} \mathbb{d}x\] becomes \[\int\limits \frac{1}{(1+\tan^2\alpha)^2} \cdot \frac{1}{3} \sec^2 \alpha \cdot \mathbb{d}a = \int \frac{1}{3} \cos^2\alpha\ \cdot \mathbb{d}a\] yes.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Now do whatever you feel like with cos^2 to make it easier to integrate, sub back in x with the tan^(1) thing you had above and you're done.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.01/3inetgarl (1/2 (cos 2(a)+1/2) du

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you have an extra 1/2 there

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Sorry gang, got to go. But here's a nice one for you to try if you feel up to it: By finding constants a, b, c and d such that: \[\frac{ax+b}{x^2+2x+2} + \frac{cx+d}{x^22x+2} \equiv \frac{1}{x^4+4} \] Show \[\int_0^1\frac{1}{x^4+4} = \frac{1}{16}\ln 5 + \frac{1}{8}\tan^{1}2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hmm so i got a/6 + (sin 2a)+12 and i know that a= tan^1(3x) how i do i solve that

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what would the side be would one side be 3x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but there is this online answer from wolfaram and it doesn't match it so i am so lost

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0What did you get as sin(2x) ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0OK, what what did you get as sin(x) and cos(x)? Hint, use the trinagle I uploaded, with the facts opp/hyp = sin(x) and adj/hpy = cos(x) NOTE these should all be as, NOT xs, sorry for the confusion.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ya that is why i was thinking i don't have x:

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sin(a) =3x/ sqrt (9x^2+1)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yeah the typing on my diagram should be a, too. Indeed. And cos(a)? And then 2sin(2a) ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sorry, only sin(2a), not 2 sin(2a)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0cos (a)= 1/ sqrt(9x^2+1)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i have learnt alot today :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Good to hear. Goodbye.
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