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anonymous
 5 years ago
Find the antiderivative of
f(x)= (x^3+cube root of x+3)/(3)
anonymous
 5 years ago
Find the antiderivative of f(x)= (x^3+cube root of x+3)/(3)

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0f'(x)= (x^3+cube root of x+3)/(3)  forgot the prime

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Distribute the 3 into both components of the numerator and integrate the two parts separately like so: \[F(x)=\int\limits_{}^{}(x^3/3)dx+\int\limits_{}^{}(\sqrt{x+3}/3)dx\] The first integral is fairly straightforward. To do the second one, you have to choose a substitution u = x + 3, find that du = dx and make the substitution to find the antiderivative of sqrt(u)/3. In the end, you should get: \[F(x)=x^4/12+2/9(x+3)^{3/2}+C\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it says math processing error so i cant see your work

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Okay, I tried doing it with a square root anyway, so it is incorrect. I'll work on it.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thank you. Im workin on it too

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0If f'(x) = (x^3 + cuberoot(x + 3))/3, then... f(x) = integral(x^3 / 3)dx + integral(cuberoot(x + 3) / 3)dx Find the antiderivative of each of these. The second one you must use a usubstitution of u = x + 3. f(x) = x^4 / 12 + (x + 3)^(4/3) / 4 + C However, the problem wants the antiderivative of f, so we have to take another antiderivative. I'll put the second part of the integral back into the usubstitution to get: F(x) = integral(x^4 / 12)dx + integral(u^(4/3) / 4)du + C F(x) = x^5 / 60 + 3u^(7/3) / 28 + Cx + D I hope I did that right... :/

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ha, silly me. You don't need to do the part of finding the antiderivative of the antiderivative, I don't think.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh yea thats right, its just one antiderivative

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0f(x) = [x^3 + cbrt(x+3)]  3 is this the equation?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0please explain an easier way of looking at antiderivatives. My teacher just wants us to do trial and error. I know all the derivative rules by the way

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0(1/3)x^3 + (1/3)(x+3)^(1/3) sound good?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0no thats a modified version of f(x); trying to get it to look more "doable"

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so now you take it backwards?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0as much as you can :) the first term is easy... (1/3)(1/4) x^4

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0the second one we want to make sure we get all the parts right: (S) (1/3)(x+3)^(1/3) dx (1/3) (S) (x+3)^(1/3) dx lets try to put this into a (S) u du type format.. u = x+3 du = 1 dx which is good, it means that we aint got to add nothing fancy to it :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0(1/3) (S) u^(1/3) du (1/3) (4/3)(x+3)^(4/3) does that make sense?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0lol .... the integral sign is a deformed "S" so I just use that to indicate the integral sign :) (S) = integral sign... thats all

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0and it should be (3/4)(x+3)^(4/3) thats better

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0check to make sure that derives down to our intended form...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thats the 2nd term right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so the first term is 1/12 (x^4)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.02nd term: (1/3)(3/4) (x+3)^(4/3) right? clean it up some....

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0youre keeping good track of this stuff :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i can do the chain rule to clean that up?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0no chain rule needed, just squish it all together to get something resembling one term :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0(x+1) cbrt(x+1)  is what I get for the 2nd term 4

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0we cant get rid of the cbrt?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0nope, its stuck there :) but we were aboe to pull out a chunk of that (x+3)^4 :) namely that (x+3)^3 its fine, unless we missed something. better double check our work to make sure :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yea let me do the derivative of it

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0im gonna go get a coffee while you whittle away :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0this is what i got: F'(x)= x^3+1/4[(x+1)[1/3(x+1)^2/3+(x+1)^1/3]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0that doesnt seem like the original

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0let me do this on paper to check your work...and mine :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0x^4 (x+3)^(4/3) F(x) =  +  12 4 This is what I want to "derive" to get back to our original equation....

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0I get: 4x^3 4 (x+3)^(1/3) f(x) =  +  (4)(3) (4)(3) Do you see that it works? or did I miss something?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0its not working for me

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0check my work, and se if its right :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0k the first term def works

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the second term would be 1/12(4) 1/3(x+3)^2/3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so that is 1/3* (1/3(x+3)^2/3

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0remember to take the (1/4) to the side and derive the rest of it, dont try to confuse this with the quotient rule

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0the only thing to chain would be the derivative of (x+3) which equals 1 :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i dont see how that makes the original

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0cross your 4s, and whats left?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yea but its x^3 on the bottom

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0(x+3)^(1/3) = cbrt(x+3) right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the 3 isnt in the cbrt. Its not suppose to be

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0theres no x term on the bottom.... clean it up so you can see what your looking at :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but f(x) is (x^3+cbrt(x)+3)/x^3

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0now now, I asked you if I had the equation right to begin with.... and now you wanna change it on me? .... :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0lol .... well it does make it easier

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i wrote it wrong its my fault

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0integratings integrating, doesnt matter if its the right one or not, well get it done :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0f(x) = (x^3+cbrt(x)+3)/x^3 we good with this one then?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0just remember, you start at the beginning, and when you get to the end....stop :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0thats from alice in wonderland, through the looking glass :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0can we set it up like this x^3*(x)^1/3+3*x^3

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0x^3 +x^(1/3) +3 f(x) =    x^3 x^3 x^3

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0f(x) = 1 + x^(8/3) + 3x^(3) right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0which form are you using

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0the rest is cake walk :) f(x) =1 + x^(8/3) + 3x^(3) F(x) = [x] + [3x^(5/3)]/5  [3x^(2)]/2 + C good?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0let me take the derivative

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0second term should be () not (+)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0why negatives, everything needs to be positive that wont make sense

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0for instance, take the last term: (S) 3x^(3) dx 3 x^2  do you see why its negative now? 2 < makes a difference

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.02nd term: (S) x^(8/3) dx x^[(8/3 + 3/3)] x^(5/3) 3x^(5/3)  =  =  (8/3 + 3/3) 5/3 5

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sounds good. lol it was so confusing im sorry

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0usually when I miss something on a test, its cause I forgot to keep track of me signs :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so it the F(x)=x1/5*(3x)^5/3[3x)^2]+c

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0it looks good except for this: ....[3x)^2]___+c somethings missing :) can you tell me what you left out? and its prolly just a typo error...

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0thats what I was looking for :) good job, now get the derivative and see if it matches....which it will :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0lol my brain isnt working forwards now

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0F(x) = x  [3x^(5/3)]/5  [3x^2]/2 + C f(x) = 1  [(3/5)(5/3) x^(8/3)]  [(3/2)(2) x^3 ] f(x) = 1 + x^(8/3) +3x^(3) which we can modify back to your original stuff....

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0does it make sense to you? or are you just agreeing with me :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how does x^(8/3) become cbrt of x?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0never mind, you divide everything by x^3

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0put all your negative exponents underneath again.... but make sure you take out the x^(3) from x^(8/3) remember when bases multiply together, their exponents "add" up. to split them simply undo the process like this: x^(8/3) = x^(1/3) x^(9/3)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yes, in essense, yes :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how does the 1 become x^3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.01/x^3=x^3 with the common denomonator

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0omg i am acting dumb, sorry

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0(x^3)/(x^3) = 1 right? thats where we got it from

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yea thats right 1/x^3= x^3+1/x^3

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0had to go hunt down which version we were using :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yea it works out, complicated but works out

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0its easier with a fresh pair of eyes :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yea thank you sooooooo much

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Have a good night, ill ttyl
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