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Question Number 98821 by bramlex last updated on 16/Jun/20

$$\int {\stackrel{\mathrm{\infty }}{}}_0\frac{dx}{a^2+x^2}=?$$

Answered by Ar Brandon last updated on 16/Jun/20

$$\mathcal{I}=\frac{1}{\mathrm{a}}{\left[\arctan \left(\frac{\mathrm{x}}{\mathrm{a}}\right)\right]}_0^{\mathrm{\infty }}=\frac{1}{\mathrm{a}}[\frac{\pi }{2}-0]\{\begin{array}{l}\\ \end{array}\mathrm{since}\tan \left[\frac{\pi }{2}\right]=+\mathrm{\infty }\}$$$$\Rightarrow \int {\stackrel{\mathrm{\infty }}{}}_0\frac{dx}{a^2+x^2}=\frac{\pi }{2\mathrm{a}}$$

Commented by bramlex last updated on 16/Jun/20

$$thanks$$

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