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    Integ prob but I'm stuck

    I'm trying to do the following: int (3x^3 + 4x)/(x^2+1)^2 dx I let u = x^2+1 and I eventually get: int 3(u-1)+4/u^2 du/2 When I further break this down, I get: 1/2 int 3u^-1 -u^-2 du am I on the right track? When I integrate this, I'm thinking that I have to be doing something...
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    May have copied wrong

    I'm trying to integrate the following: int (x^3 + 4x)/sqrt(x^2-4) dx I let u= x^2-4 so du/2 = xdx granted, the above also gives me x^2=u+4 so, this gives me: 1/2 int u+8 u^-1/2 du but the professor has: 1/2 int [u^1/2+8 u^-1/2] du Did I miss the first u^1/2 somewhere...
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    Limits question

    I'm trying to figure out the following: An=1x3x5.... (2n-1)/(2n)^n and I'm trying to determine if it converges or diverges and if it converges, what the limit is. The answer is 1/2n x 3/2n x 5/2n.... (2n-1)/2n and it converges, but I don't understand what they did or how they got to the...
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    Infinite Series: sigma n^2/(n^2 +1)

    If I take the limit on the sum... I get 1/1 = 1 If the limit does NOT = 0 then sigma f(x) diverges...I'm not quite sure I follow this... Does this mean that in order for the equation to converge, the sum (sigma) must be = to 0?
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    Infinite Series: sigma (2^n)+1/(2^n+1)

    i'm not quiet sure how to attack this problem: sigma (2^n)+1/(2^(n+1)) n->1 If I start plugging in #'s for n, then I get: n=1: 3/4 n=2: 5/8 n=3: 9/16... by this method, I see that it's going to 1/2, but I need another way to 'see' that. Any suggestions?
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    Int x^3 sin x

    I'm trying to integtrate x^3 sin x without using integration by parts. I have set up the equation to either: int x^3 cosx dx = (Ax^3 + Bx^2+Cx+D)cos x + K or int x^3 coxs dx = (Ax^3+Bx)sinx + (Cx^2+D)cosx +K but I'm having trouble... any help would be appreciated!
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    L'Hopital's Lim x->0 tan x / x

    I've done this problem but am not comfortable with the answer. Could someone take a quick look? Limx->0 tan x /x Limx->0 sec^2x ==> 0 I'm just not sure this is right...
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    Integrate 1/(t^2(t-1))dt question

    I've stared at this problem for about 5 minutes and I'm not sure how to start it. I see the function and its derivative, but I'm missing something I suspect is simple. Any suggestions as to how to start?
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    Integrate w/negative exponent

    I need a little 'suggestion' as to how to integrate cos^6x sin^-3x dx. I rewrite to cos^6x/sin^3x dx and let u = sinx but when I'm trying to rewrite integral, what should I do with the ^6? Thanks!
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    L'Hopital's Rule - I'm loosing my hair

    L'Hopital's Rule - I'm loosing my hair!! Ok, I have the following: Lim x->0 sqrt(4-x^2) -2 /x After I change the equation to remove the radicle, I get: Lim x->0 ((4-x^2)^1/2 - 2)/x but when I apply the rule the, I'm loosing it :surprised I thought I should get: 1/2...