Question Number 161537 by cortano last updated on 19/Dec/21 $$\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \:\frac{\mathrm{1}+\mathrm{tan}\:^{\mathrm{4}} \left({x}\right)}{\mathrm{cot}\:^{\mathrm{2}} \left({x}\right)}\:{dx}\:=? \\ $$ Answered by Ar Brandon last updated on 19/Dec/21 $$=\int_{\mathrm{0}}…
Question Number 30441 by abdo imad last updated on 22/Feb/18 $${prove}\:{that}\:\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−\left[{x}\right]^{\mathrm{2}} } =\:\sum_{{n}\geqslant\mathrm{0}} \:{e}^{−{n}^{\mathrm{2}} } . \\ $$ Answered by alex041103 last updated…
Question Number 30442 by abdo imad last updated on 22/Feb/18 $${prove}\:{that}\:\:\:\frac{\mathrm{1}}{{e}}\:\leqslant\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{−\left({x}−\left[{x}\right]\right)^{\mathrm{2}} } \:{dx}\leqslant\mathrm{1}. \\ $$ Commented by alex041103 last updated on 22/Feb/18 $${You}\:{can}\:{see}\:{that}\:{if}\:{x}\in\left[\mathrm{0},\mathrm{1}\right),\:{then}…
Question Number 30426 by abdo imad last updated on 22/Feb/18 $${find}\:\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}} }\:\:{with}\:{n}\:{integr}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30423 by abdo imad last updated on 22/Feb/18 $${study}\:{the}\:{convergence}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sint}}{{t}^{\alpha} }{dt}\:.\:\alpha{from}\:{R}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30413 by abdo imad last updated on 22/Feb/18 $${study}\:{the}\:{convergence}\:{of}\:\:{A}\left(\alpha\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ln}\left({t}\right)\:{arctant}}{{t}^{\alpha} }{dt} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 95951 by me2love2math last updated on 28/May/20 Commented by me2love2math last updated on 28/May/20 $${pls}\:{help}\:{out}\:{on}\:{this}\: \\ $$ Commented by prakash jain last updated…
Question Number 95949 by Ar Brandon last updated on 28/May/20 $$\int_{\mathrm{0}} ^{+\infty} \frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{e}^{\mathrm{x}^{\mathrm{2}} } −\mathrm{1}}\mathrm{dx} \\ $$ Answered by Sourav mridha last updated on…
Question Number 95943 by mathmax by abdo last updated on 28/May/20 $$\mathrm{f}\:\mathrm{is}\:\mathrm{a}\:\mathrm{integrable}\:\mathrm{function}\:\mathrm{wich}\:\mathrm{verify}\:\mathrm{f}\left(\mathrm{x}+\pi\right)=\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{prove}\:\mathrm{that} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\mathrm{f}\left(\mathrm{x}\right)×\frac{\mathrm{sinx}}{\mathrm{x}}\mathrm{dx}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx} \\ $$ Terms of Service Privacy Policy…
Question Number 161443 by smallEinstein last updated on 18/Dec/21 Answered by mathmax by abdo last updated on 18/Dec/21 $$\mathrm{I}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{log}^{\mathrm{2}} \left(\mathrm{1}+\mathrm{x}\right)}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx}\:\mathrm{letf}\left(\mathrm{a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{a}}…