Menu Close

1-explicite-0-arctan-1-x-2-t-2-2-t-2-dt-withx-gt-0-2-determine-values-of-0-arctan-3-t-2-2-t-2-dt-and-0-arctan-5-2t-2-2-t-2-dt-

Tinku Tara 0 Comments
Pin




Question Number 116586 by Bird last updated on 05/Oct/20
1) explicite ∫_0 ^∞ ((arctan(1+x(2+t^2 )))/(2+t^2 ))dt withx>0 2)determine values of ∫_0 ^∞ ((arctan(3+t^2 ))/(2+t^2 ))dt and ∫_0 ^∞ ((arctan(5+2t^2 ))/(2+t^2 ))dt
$$\left.\mathrm{1}\right)\:{explicite}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{arctan}\left(\mathrm{1}+{x}\left(\mathrm{2}+{t}^{\mathrm{2}} \right)\right)}{\mathrm{2}+{t}^{\mathrm{2}} }{dt} \\ $$$${withx}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right){determine}\:{values}\:{of} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\frac{{arctan}\left(\mathrm{3}+{t}^{\mathrm{2}} \right)}{\mathrm{2}+{t}^{\mathrm{2}} }{dt}\:{and}\: \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\frac{{arctan}\left(\mathrm{5}+\mathrm{2}{t}^{\mathrm{2}} \right)}{\mathrm{2}+{t}^{\mathrm{2}} }{dt} \\ $$

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *