Calculate: $$\int \frac{\sqrt{1 + x^4}}{1 - x^4} dx$$
I've been thinking about a good substitution, but I haven't found any yet. Integration by parts doesn't gave me anything meaningful.
Thank you!
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3According to WA, it seems that your integral cannot be computed in terms of elementary functions. – Crostul Dec 20 '16 at 17:29
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this integral leads to an elliptc integral – Dr. Sonnhard Graubner Dec 20 '16 at 17:43
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do you need the solution? – Dr. Sonnhard Graubner Dec 20 '16 at 17:43
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Yes, I need a way to calculate it. – George R. Dec 20 '16 at 17:50
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@GeorgeR.: If you need to calculate it, you can use the form given by Wolfram Alpha. Lots of numerical packages support various hypergeometric functions. Alternatively, you could just quadrature to compute the integral directly. – parsiad Dec 20 '16 at 17:52
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@Crostul: There is an elementary form; see the duplicate that I've linked to. – Hans Lundmark Dec 20 '16 at 19:42