Question Number 37343 by math khazana by abdo last updated on 12/Jun/18 $${let}\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{xt}^{\mathrm{2}} \right){dt}\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{2}+{t}^{\mathrm{2}} \right){dt}\:. \\ $$…
Question Number 37338 by math khazana by abdo last updated on 12/Jun/18 $${calculate}\:\:{B}_{{n}} \:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:{sh}^{{n}} {xdx}\:. \\ $$ Commented by prof Abdo imad last…
Question Number 37337 by math khazana by abdo last updated on 12/Jun/18 $${calculate}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{ch}^{{n}} {xdx}\:. \\ $$ Commented by math khazana by abdo…
Question Number 37317 by rahul 19 last updated on 11/Jun/18 $$\int\:\frac{\mathrm{acos}\:{x}+{b}}{\left({a}+{b}\mathrm{cos}\:{x}\right)^{\mathrm{2}} }{dx}\:=\:? \\ $$ Commented by math khazana by abdo last updated on 12/Jun/18 $${changement}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)\:=\:{t}\:{give}\:…
Question Number 37316 by rahul 19 last updated on 11/Jun/18 $$\int\:\frac{{x}^{\mathrm{2}} }{\left({x}\mathrm{sin}\:{x}+\mathrm{cos}\:{x}\right)^{\mathrm{2}} }{dx}\:=\:? \\ $$ Answered by ajfour last updated on 11/Jun/18 $${let}\:{x}\mathrm{sin}\:{x}+\mathrm{cos}\:{x}=\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\mathrm{sin}\:\left({x}+\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{{x}}\right)…
Question Number 37310 by math khazana by abdo last updated on 11/Jun/18 $${calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+\mathrm{4}\right)\left({x}^{\mathrm{2}} \:+\mathrm{9}\right)}\:. \\ $$ Commented by math khazana by…
Question Number 37307 by math khazana by abdo last updated on 11/Jun/18 $${calculate}\:\:\:\int_{\gamma} \:\:\:\:\frac{{dz}}{{z}}\:\:\:{with}\:\gamma\:=\left\{{z}\in{C}\:/\mid{z}\mid=\mathrm{1}\right\}\:. \\ $$ Commented by prof Abdo imad last updated on 15/Jun/18…
Question Number 37309 by math khazana by abdo last updated on 11/Jun/18 $${calculate}\:\:\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{x}^{\mathrm{2}} }{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{3}} }\:{dx}\:. \\ $$ Commented by abdo.msup.com last updated…
Question Number 37306 by math khazana by abdo last updated on 11/Jun/18 $${calculate}\:\int_{−\infty} ^{+\infty} \:\:\:{e}^{{ix}} \:\:\:\frac{{x}−{i}}{\left({x}+{i}\right)\left({x}^{\mathrm{2}} \:+\mathrm{3}\right)}\:{dx}\:. \\ $$$$ \\ $$ Commented by prof Abdo…
Question Number 37304 by math khazana by abdo last updated on 11/Jun/18 $${calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{\mathrm{5}+{e}^{{ix}} }{\left(\mathrm{3}+{e}^{{ix}} \right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{dx}\:. \\ $$ Commented by prof Abdo imad…