Question Number 226819 by Spillover last updated on 16/Dec/25
$${Evaluate} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$
Answered by AgniMath last updated on 16/Dec/25
![∫_0 ^∞ (dx/(1+x^2 )) = [tan^(−1) (x)]_0 ^∞ = (π/2)](Q226825.png)
$$\int_{\mathrm{0}} ^{\infty} \frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}} }\:=\:\left[{tan}^{−\mathrm{1}} \left({x}\right)\right]_{\mathrm{0}} ^{\infty} \:=\:\frac{\pi}{\mathrm{2}} \\ $$
Commented by Spillover last updated on 16/Dec/25
$${thanks} \\ $$