Question Number 17514 by sma3l2996 last updated on 07/Jul/17 $${S}\left({n}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\mathrm{2}{n}} {sin}\left(\mathrm{2}{n}\pi{x}\right){dx} \\ $$ Commented by alex041103 last updated on 07/Jul/17 $$\mathrm{Is}\:{n}\:\mathrm{a}\:\mathrm{whole}\:\mathrm{number}? \\ $$…
Question Number 17512 by tawa tawa last updated on 06/Jul/17 $$\int\:\frac{\mathrm{e}^{−\mathrm{t}} \:\mathrm{ln}\left(\mathrm{1}\:+\:\mathrm{e}^{−\mathrm{t}} \right)}{\mathrm{1}\:+\:\mathrm{e}^{−\mathrm{t}} }\:\mathrm{dt} \\ $$ Answered by sma3l2996 last updated on 07/Jul/17 $${I}=\int\frac{{e}^{−{t}} {ln}\left(\mathrm{1}+{e}^{−{t}}…
Question Number 17506 by tawa tawa last updated on 06/Jul/17 $$\int\:\mathrm{tan}^{−\mathrm{1}} \left(\sqrt{\frac{\mathrm{x}\:+\:\mathrm{1}}{\mathrm{x}\:−\:\mathrm{1}}}\right)\:\mathrm{dx} \\ $$ Answered by sma3l2996 last updated on 06/Jul/17 $${u}={tan}^{−\mathrm{1}} \left(\sqrt{\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}}\right)\Rightarrow{u}'=\frac{−\mathrm{1}}{\mathrm{2}{x}\sqrt{\left({x}−\mathrm{1}\right)\left({x}+\mathrm{1}\right)}}=\frac{−\mathrm{1}}{\mathrm{2}{x}\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}} \\…
Question Number 148565 by mathmax by abdo last updated on 29/Jul/21 $$\mathrm{calculate}\:\int_{−\infty} ^{+\infty} \:\:\frac{\mathrm{x}^{\mathrm{2}} \mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{x}+\mathrm{1}\right)} \\ $$ Answered by Ar Brandon last updated…
Question Number 148570 by mathmax by abdo last updated on 29/Jul/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{logx}}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{x}+\mathrm{1}}\mathrm{dx} \\ $$ Answered by Ar Brandon last updated on 29/Jul/21…
Question Number 148567 by mathmax by abdo last updated on 29/Jul/21 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{x}^{\mathrm{2}} \:\mathrm{logx}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{3}} }\mathrm{dx} \\ $$ Answered by Ar Brandon last updated…
Question Number 148566 by mathmax by abdo last updated on 29/Jul/21 $$\mathrm{calculate}\:\:\mathrm{U}_{\mathrm{n}} =\int\int_{\left[\frac{\mathrm{1}}{\mathrm{n}},\mathrm{n}\left[\right.\right.} \:\:\:\frac{\mathrm{cos}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{y}^{\mathrm{2}} }\mathrm{dxdy} \\ $$$$\mathrm{and}\:\mathrm{determine}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \mathrm{U}_{\mathrm{n}} \\ $$$$\mathrm{nature}\:\mathrm{of}\:\Sigma\:\mathrm{U}_{\mathrm{n}} ? \\…
Question Number 17480 by Arnab Maiti last updated on 06/Jul/17 $$\mathrm{why}\:\:\frac{\mathrm{d}}{\mathrm{dx}}\left(\int_{\mathrm{0}} ^{\:\:\mathrm{y}} \mathrm{e}^{\mathrm{t}} \mathrm{dt}\right)=\mathrm{e}^{\mathrm{y}} \frac{\mathrm{dy}}{\mathrm{dx}} \\ $$ Answered by mrW1 last updated on 06/Jul/17 $$\mathrm{let}\:\mathrm{F}\left(\mathrm{y}\right)=\int_{\mathrm{0}}…
Question Number 17479 by Arnab Maiti last updated on 06/Jul/17 $$\mathrm{If}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{periodic}\:\mathrm{function}\:\mathrm{with}\:\mathrm{period} \\ $$$$\mathrm{time}\:\mathrm{t}\:;\:\mathrm{prove}\:\mathrm{that}\int_{\mathrm{a}} ^{\:\mathrm{a}+\mathrm{t}} {f}\left({x}\right)\mathrm{d}{x}\:\mathrm{is}\:\mathrm{a}\:\mathrm{indipendent}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 83010 by mathmax by abdo last updated on 26/Feb/20 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ch}\left({cos}\left(\mathrm{2}{x}\right)\right)}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com