How to calculate the antiderivative of: [sqrt(t^4 + t^2 + 1)]/(t^2 + 1)

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Anybodys knows how to resolve the problem of the subject.
I am working in it for three hours. I am desperated.

I have tried all the subtitutions of "Calculus. Schaum. Ayres&Mendelson". Whithout suceeds.

Thank you.


Diego.
 
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Well, I'm sorry to disappoint you, but it's simply impossible to calculate it. Just try typing it into wolfram alpha, mathematica or whatever: http://integrals.wolfram.com/index.jsp?expr=Sqrt[x^4+%2B+x^2+%2B+1]/(x^2+%2B+1)&random=false

See what you get? Three different elliptic functions, that are not elementary functions. Hence, this function doesn't have an antiderivative that could be written down using elementary functions only.
 
Where in your homework is it?
I mean, can we see the full problem?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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