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Category: Integration

Express-f-x-1-x-1-2-x-2-1-into-partial-fractions-hence-evaluate-I-0-4-f-x-dx-

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…

let-f-x-0-tsin-tx-1-t-4-dt-with-x-gt-0-1-find-a-explicit-form-of-f-x-2-find-the-value-of-0-tsin-2t-1-t-4-dt-

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…

nice-calculus-evaluate-I-0-1-li-2-1-x-2-dx-m-n-1970-

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…

x-2-4-x-2-5-dx-

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}}…