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I'm wondering how shall I solve this primitive/integral

[tex]\int\frac{\cos^3 x}{x^6+1}dx[/tex]

I really don't know how to start... which substitution shall I take or if I shall solve it by parts...

Any hints or tips will be very appreciated

Thanks in advance

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# P(cos(x)^3)/(x^6+1) very hard

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