Question Number 82446 by M±th+et£s last updated on 21/Feb/20 $${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\infty} {x}^{−{log}\left({x}\right)} \:{x}\:{log}\left({x}\right)\:{dx}={e}\sqrt{\pi} \\ $$ Commented by abdomathmax last updated on 21/Feb/20 $${changement}\:{logx}={t}\:{give}\:{x}={e}^{{t}}…
Question Number 82442 by mathmax by abdo last updated on 21/Feb/20 $$\left.\mathrm{1}\right){find}\:\int\:\frac{\sqrt{{x}^{\mathrm{2}} −{x}+\mathrm{1}}}{{x}^{\mathrm{2}} \:+\mathrm{3}}{dx} \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\sqrt{{x}^{\mathrm{2}} −{x}+\mathrm{1}}}{{x}^{\mathrm{2}} \:+\mathrm{3}}{dx} \\ $$ Commented by mathmax…
Question Number 82440 by mathmax by abdo last updated on 21/Feb/20 $${find}\:\int\:\frac{{x}+\mathrm{1}}{{x}+\mathrm{2}}\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}{dx} \\ $$ Commented by abdomathmax last updated on 24/Feb/20 $${let}\:{A}\:=\int\frac{{x}+\mathrm{1}}{{x}+\mathrm{2}}\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}{dx}\:\:{changement}\:\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}={t} \\ $$$${hive}\:\:\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}={t}^{\mathrm{2}} \:\Rightarrow\mathrm{1}−{x}={t}^{\mathrm{2}}…
Question Number 82439 by mathmax by abdo last updated on 21/Feb/20 $${calculate}\:{I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{{n}} \sqrt{\mathrm{1}+{x}+{x}^{\mathrm{2}} }{dx} \\ $$ Commented by abdomathmax last updated on…
Question Number 82435 by mathmax by abdo last updated on 21/Feb/20 $${calculate}\:\int_{\mathrm{4}} ^{+\infty} \:\:\:\:\:\frac{{x}^{\mathrm{3}} }{\left(\mathrm{2}{x}+\mathrm{1}\right)^{\mathrm{3}} \left({x}−\mathrm{3}\right)^{\mathrm{5}} }{dx} \\ $$ Commented by abdomathmax last updated on…
Question Number 82434 by mathmax by abdo last updated on 21/Feb/20 $$\left.\mathrm{1}\right){decompose}\:{inside}\:{C}\left({x}\right){and}\:{R}\left({x}\right)\:{the}\:{fraction} \\ $$$${F}\left({x}\right)=\frac{\mathrm{2}{x}+\mathrm{1}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{3}} \left({x}−\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{3}} ^{+\infty} {F}\left({x}\right){dx} \\ $$ Terms of…
Question Number 82433 by mathmax by abdo last updated on 21/Feb/20 $$\left.\mathrm{1}\right){decompose}\:{inside}\:{C}\left({x}\right){and}\:{R}\left({x}\right)\:{F}=\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Commented by mathmax…
Question Number 16892 by tawa tawa last updated on 27/Jun/17 $$\int_{\:\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{2x}\:+\:\mathrm{4}}\:\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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Question Number 82391 by jagoll last updated on 21/Feb/20 $$\int\:\mathrm{sin}\:{x}\:\mathrm{cos}\:\left(\mathrm{sin}\:{x}\right)\:{dx}\:? \\ $$ Commented by M±th+et£s last updated on 21/Feb/20 $${i}\:{think}\:{that}\:{its}\:{special}\:{integral} \\ $$$${cos}\left({sin}\left({x}\right)\right)=\mathrm{1}−\frac{{sin}^{\mathrm{2}} \left({x}\right)}{\mathrm{2}{i}}+\frac{{sin}^{\mathrm{4}} \left({x}\right)}{\mathrm{4}{i}}−\frac{{sin}^{\mathrm{6}} \left({x}\right)}{\mathrm{6}{i}}+……