bcmhea
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SOLVED
Last edited by bcmhea; 1 month ago
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Lucifer323
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Use a substitution in the integral.
The denominator can be called k
Find what happens in the numerator
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Lucifer323
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(Original post by bcmhea)
I tried doing integration by substitution endless times but always end up with something not looking right...

I am fully confident with b just the first part that I can't wrap my head around
k=x^2+x+2
(k)'=2x+1
See what happens.
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Lucifer323
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(Original post by bcmhea)
I get massive numbers whereas I think they should cancel out and make nice equation to carry on with, I really tried its not like im just asking because I cannot be bothered... if you know to tackle it please give me a hand
When I go home I will do it on paper and write the solution.
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Lucifer323
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(Original post by bcmhea)
I know its crazy late but please don't forget about me :/
Hi, I am trying to do the integral and it seems there is no anti-derivative.

I did the question without the 3/4 and there is an anti-derivate. The solution involves ln and inverse tan + constant of integration.

Are you sure you have the right function?

F(x)= (14x-6)/(x^2+x+2)^3/4

My question: Is the power of 3/4 on the denominator? And is the function correct the way I wrote it?
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RDKGames
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(Original post by bcmhea)
That was my issue as well, so I felt I am trying to solve something that has no solution, here is the screenshot of the question.
The indefinite integral is not in terms of elementary functions.

You have two options;

(a) double check with whoever gave you this whether the power is indeed supposed to be 3/4, or

(b) use numerical methods to approximate this integral
Last edited by RDKGames; 1 month ago
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Lucifer323
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(Original post by RDKGames)
The indefinite integral is not in terms of elementary functions.

You have two options;

(a) double check with whoever gave you this whether the power is indeed supposed to be 3/4, or

(b) use numerical methods to approximate this integral
It's exactly what I said to the user.
The integral doesn't seem to have a solution. I can't find an anti-derivate. Without the 3/4 there is clearly a solution.

The integral however does have a numerical solution.
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4D Chess
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Do you by any chance know what the hypergeometric function is
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Lucifer323
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(Original post by bcmhea)
Is it possible in this case to get the answer without the 3/4 so I can explain this to my teacher and present that I didn't just leave it empty
Yes the answer is

7ln(x^2+x+2) - (26 arctan ((2x+1)/root 7))/root7 + C
Last edited by Lucifer323; 1 month ago
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Lucifer323
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Without the 3/4 you write the function
F(x)=14x-6/x^2+x+2 as
F(x)=7(2x+1)-13 / x^2+x+2

Split the fraction the first part gives you a natural logarithm when you integrate and the second part gives you an inverse tan result.
However to get the second one you need to complete the square and remember that
Int (1/1+x^2) = arctanx + C
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