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Question Number 159477 by HongKing last updated on 17/Nov/21

$$\mathrm{Find}:\mathrm{\Omega }=\int \frac{1}{{(\mathrm{x}+\frac{1}{\mathrm{x}})}^2}\mathrm{dx}$$

Answered by MJS_new last updated on 17/Nov/21

$$t=\arctan x$$$$\Rightarrow$$$$\int {\sin }^{2}tdt=\frac{1}{2}\int (1-\cos 2t)dt=$$$$=\frac{t}{2}-\frac{\sin 2t}{4}=$$$$=\frac{1}{2}\arctan x-\frac{x}{2(x^2+1)}+C$$

Commented by HongKing last updated on 17/Nov/21

$$\mathrm{thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{my}\mathrm{dear}\mathrm{Ser}$$

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