Question Number 119335 by physicstutes last updated on 23/Oct/20 $$\:\mathrm{Express}\:{f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\left({x}−\mathrm{1}\right)^{\mathrm{2}} \left({x}^{\mathrm{2}} +\mathrm{1}\right)}\:\:\mathrm{into}\:\mathrm{partial}\:\mathrm{fractions}. \\ $$$$\mathrm{hence}\:\mathrm{evaluate}\:{I}\:=\:\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\:{f}\left({x}\right)\:{dx} \\ $$ Answered by floor(10²Eta[1]) last updated on 23/Oct/20…
Question Number 119323 by mnjuly1970 last updated on 23/Oct/20 Commented by Dwaipayan Shikari last updated on 23/Oct/20 $${What}\:{is}\:\eta\left(\mathrm{2}{n}+\mathrm{1}\right)? \\ $$ Commented by mnjuly1970 last updated…
Question Number 53785 by maxmathsup by imad last updated on 25/Jan/19 $${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\frac{{tsin}\left({tx}\right)}{\mathrm{1}+{t}^{\mathrm{4}} }{dt}\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{tsin}\left(\mathrm{2}{t}\right)}{\mathrm{1}+{t}^{\mathrm{4}} }{dt}. \\ $$ Commented…
Question Number 53783 by maxmathsup by imad last updated on 25/Jan/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{t}^{\mathrm{2}} }{{e}^{{t}} −\mathrm{1}}{dt}\:{interms}\:{of}\:\xi\left(\mathrm{3}\right) \\ $$ Answered by Smail last updated on 26/Jan/19…
Question Number 119318 by Bird last updated on 23/Oct/20 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{lnx}}{{x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{2}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 53782 by maxmathsup by imad last updated on 25/Jan/19 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{3}} }{dt} \\ $$ Answered by Smail last updated on 26/Jan/19…
Question Number 119317 by Bird last updated on 23/Oct/20 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{{d}\theta}{\left({x}^{\mathrm{2}} −\mathrm{2}{cos}\theta\:{x}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 119306 by yahyajan last updated on 23/Oct/20 Answered by TANMAY PANACEA last updated on 23/Oct/20 $${x}={dtana} \\ $$$$\int_{\frac{−\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{dsec}^{\mathrm{2}} {da}}{{d}^{\mathrm{2}} {sec}^{\mathrm{2}} {a}}…
Question Number 119282 by mnjuly1970 last updated on 23/Oct/20 $$\:\:\:\:\:\:\:\:…\:\:{nice}\:\:{calculus}… \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{evaluate}:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {li}_{\mathrm{2}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right){dx}=?? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.{m}.{n}.\mathrm{1970}. \\ $$$$\:\:\:\:\:\:\:\: \\ $$ Answered…
Question Number 119262 by bemath last updated on 23/Oct/20 $$\:\int\:\frac{{x}^{\mathrm{2}} }{\:\sqrt{\left(\mathrm{4}−{x}^{\mathrm{2}} \right)^{\mathrm{5}} }}\:{dx}\: \\ $$ Answered by benjo_mathlover last updated on 23/Oct/20 $${set}\:{x}\:=\:\mathrm{2sin}\:{r}\:\Rightarrow\:{dx}\:=\:\mathrm{2cos}\:{r}\:{dr}\: \\ $$$$\int\:\frac{\mathrm{4sin}\:^{\mathrm{2}}…