How i should deal with it, i’ve tried fraction decomposition, but haven’t worked so far. $$\lim_{n\to \infty} \int_{\frac 1n}^n \frac {1}{(x^2+1)(x^7+1)} \, dx$$
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1@MaximilianJanisch my bad, that’s right. I ve edited. – benj2k1 Dec 26 '19 at 19:35
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5The answer is $\frac\pi4$ as is proven here: Computing $\int_0^\infty\frac{1}{(1+x^{2015})(1+x^2)}$ – Maximilian Janisch Dec 26 '19 at 19:37
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Yes, it worked, thanks. – benj2k1 Dec 26 '19 at 19:46
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The substitution $x=\tan\theta$ also works here. – bjorn93 Dec 26 '19 at 20:33