<s>[INST] Integral of $\int \frac{x^4+2x+4}{x^4-1}dx$ I am trying to solve this integral and I need your suggestions.
$$\int \frac{x^4+2x+4}{x^4-1}dx$$
Thanks
 [/INST] welcome to math.stackexchange this question were answered already.
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use polynomial division, we get $$\int \frac{x^4+2x+4}{x^4-1} dx = \int 1 + \frac{2x+5}{(x^2 - 1)(x^2 + 1)}dx
 = \int 1 + \frac{2x+5}{(x+1)(x-1)(x^2+1)} dx  $$ 
Expressing this as partial fractions, we need only find $A, B, C$
$$=  \int \left(1 + \frac{A}{x+1} + \frac B{x-1} +\frac{CX+D}{x^2 + 1}\right)\,dx$$
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