Question Number 34260 by math khazana by abdo last updated on 03/May/18 $${let}\:{give}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:\:{F}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{lnt}}{{t}^{\mathrm{2}} \:+{a}^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:{G}\left({a}\right)=\int_{\mathrm{0}} ^{\infty} \:\frac{{aln}\left({t}\right)}{\left({t}^{\mathrm{2}} \:+{a}^{\mathrm{2}} \right)^{\mathrm{2}}…
Question Number 34261 by math khazana by abdo last updated on 03/May/18 $${study}\:{the}\:{convergence}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\frac{{t}−{sint}}{{t}^{{a}} }{dt}\:{with}\:{a}\:{real}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 165329 by mnjuly1970 last updated on 30/Jan/22 $$ \\ $$$$\:\:\:\:{prove}\:\:\:\:\:\:\:\:\:\:\left(\:{n}\in\:\mathbb{N}\:\right) \\ $$$$\:\:\:\:\mathrm{3}\left({n}+\mathrm{1}\right)\:\mid\:{n}^{\:\mathrm{3}} \:+\:\left({n}+\mathrm{1}\right)^{\:\mathrm{3}} +\:\left({n}+\mathrm{2}\:\right)^{\:\mathrm{3}} \\ $$$$ \\ $$ Answered by Rasheed.Sindhi last updated…
Question Number 34257 by math khazana by abdo last updated on 03/May/18 $${find}\:{f}\left({x}\right)=\:\int_{\mathrm{1}} ^{{x}} \:\:\:\:\frac{{dt}}{{t}\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{I}\:=\int_{\mathrm{1}} ^{+\infty} \:\:\:\:\frac{{dt}}{{t}\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }} \\ $$ Terms of…
Question Number 34254 by math khazana by abdo last updated on 03/May/18 $${find}\:{I}\left({x}\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{xt}^{\mathrm{2}} \right)}{{t}^{\mathrm{2}} }{dt}\:\:. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 34255 by math khazana by abdo last updated on 03/May/18 $${find}\:\:{g}\left({x}\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ln}\left(\mathrm{1}+{xt}^{\mathrm{2}} \right)}{{t}^{\mathrm{2}} }\:{dt} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ln}\left(\mathrm{1}+\mathrm{3}{t}^{\mathrm{2}} \right)}{{t}^{\mathrm{2}} }{dt}\:. \\ $$…
Question Number 34253 by math khazana by abdo last updated on 03/May/18 $$\:{let}\:{F}\left({x}\right)=\:\int_{\mathrm{0}} ^{{x}} \:\:\frac{{ln}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}{{t}^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{F}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ln}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}{{t}^{\mathrm{2}} }{dt}…
Question Number 165320 by mnjuly1970 last updated on 29/Jan/22 $$ \\ $$$$\Omega\:=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \:{cos}\:\left(\mathrm{2}{x}\:\right).{e}^{\:\lfloor\:{sin}\left({x}\right)+\:{cos}\left({x}\right)\:\rfloor} {dx} \\ $$$$\:\:\:\lfloor\:{x}\:\rfloor=\:{max}\:\left\{\:{m}\:\in\:\mathbb{Z}\:\mid\:\:{m}\:\leqslant\:{x}\:\right\} \\ $$$$\:\:\:\:\:\:\:\:−−−− \\ $$ Answered by mahdipoor last…
Question Number 99779 by john santu last updated on 23/Jun/20 Commented by Dwaipayan Shikari last updated on 23/Jun/20 $$\int{tan}^{\mathrm{6}} {xsec}^{\mathrm{2}} {xsec}^{\mathrm{2}} {xdx}=\int{t}^{\mathrm{6}} \left(\mathrm{1}+{t}^{\mathrm{2}} \right){dt}=\frac{{t}^{\mathrm{7}} }{\mathrm{7}}+\frac{{t}^{\mathrm{9}}…
Question Number 34237 by abdo mathsup 649 cc last updated on 03/May/18 $${find}\:\:\int\:\:\:\frac{{dx}}{{x}^{\mathrm{2}} \:−{a}}\:\:{with}\:{a}\:\in\:{C}\:. \\ $$ Commented by Joel578 last updated on 04/May/18 $${thank}\:{you}\:{for}\:{correction}\:{Sir} \\…