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I have some problems trying to solve this integral:

$$ \ \int^\ \frac{(x^2-1)\,dx}{(x^4+3x^2+1)\cdot\arctan\left(\frac{x^2+1}{x}\right)^{1001}}\,. $$ I can see $$ (x^2+1)^2+(x)^2=x^4+3x^2+1 $$ So i´m thinking in do some trigonometrical substitution, but how I can get the $$x^2-1$$ Every answer helps and sorry for the English.

Przemysław Scherwentke
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TBRB
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1 Answers1

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$$t=\arctan \left(\frac{x^2+1}{x}\right)\Rightarrow dt =\frac{x^2-1}{x^4+3x^2+1}\,dx$$

L. F.
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