Question Number 151415 by ArielVyny last updated on 20/Aug/21 $$\int_{\mathrm{0}} ^{\infty} \frac{{ln}\left({x}\right){arctg}\left({x}\right)}{{x}\left({x}^{\mathrm{2}} +\mathrm{1}\right)}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 20309 by NECC last updated on 25/Aug/17 $$\int{x}^{{x}} {dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 151376 by liberty last updated on 20/Aug/21 $$\:\:\:\:\int\:\frac{\mathrm{x}^{\mathrm{8}} +\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{9}} −\mathrm{2x}^{\mathrm{8}} +\mathrm{1}}}\:\mathrm{dx}\:?\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 151374 by mnjuly1970 last updated on 20/Aug/21 $$ \\ $$$$\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{ln}\:\left(\frac{\mathrm{1}}{{x}}\:\right)}{\mathrm{1}\:+{e}^{\:\mathrm{2}{x}} }\:{dx}\:\overset{?} {=}\:\frac{\mathrm{3}}{\mathrm{2}}\:{ln}^{\:\mathrm{2}} \left(\:\mathrm{2}\:\right) \\ $$$$\:\:{m}.{n} \\ $$ Terms of Service Privacy…
Question Number 85839 by sahnaz last updated on 25/Mar/20 $$\int\mathrm{x}×\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}}\mathrm{dx} \\ $$ Commented by jagoll last updated on 25/Mar/20 $$\int\:\frac{\mathrm{x}\:\mathrm{dx}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\int\:\frac{\mathrm{d}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{1}/\mathrm{2}} }…
Question Number 20293 by tammi last updated on 25/Aug/17 $$\int\sqrt{\frac{{a}+{x}}{{x}}{dx}} \\ $$ Answered by $@ty@m last updated on 25/Aug/17 $$=\int\frac{{a}+{x}}{\:\sqrt{{x}\left({a}+{x}\right)}}{dx} \\ $$$$=\int\frac{{a}+{x}}{\:\sqrt{{ax}+{x}^{\mathrm{2}} }}{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{2}{x}+{a}+{a}}{\:\sqrt{{ax}+{x}^{\mathrm{2}}…
Question Number 85828 by M±th+et£s last updated on 25/Mar/20 $$\int\frac{\mathrm{1}}{{x}+{cot}\left({x}\right)}\:{dx} \\ $$ Answered by mind is power last updated on 26/Mar/20 $${not}\:{found}\:\:{only}\:{withe}\:{Series}\: \\ $$$${have}\:{you}\:{a}\:{solutions}\:{sir}\:? \\…
Question Number 20292 by tammi last updated on 25/Aug/17 $$\int\frac{{dx}}{\left({x}+\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} +\sqrt{{x}−\mathrm{1}}} \\ $$ Answered by $@ty@m last updated on 25/Aug/17 $$=\int\frac{{dx}}{\:\sqrt{{x}+\mathrm{1}}+\sqrt{{x}−\mathrm{1}}} \\ $$$$=\int\frac{\sqrt{{x}+\mathrm{1}}−\sqrt{{x}−\mathrm{1}}}{\left({x}+\mathrm{1}\right)−\left({x}−\mathrm{1}\right)}{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int\sqrt{{x}+\mathrm{1}}{dx}−\frac{\mathrm{1}}{\mathrm{2}}\int\sqrt{{x}−\mathrm{1}}{dx}…
Question Number 20291 by tammi last updated on 25/Aug/17 $$\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\:{dx}} \\ $$ Answered by $@ty@m last updated on 25/Aug/17 $$=\int\frac{\mathrm{1}−{x}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx} \\ $$$$=\int\frac{{dx}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}+\frac{\mathrm{1}}{\mathrm{2}}\int\frac{−\mathrm{2}{x}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx}…
Question Number 151360 by talminator2856791 last updated on 20/Aug/21 $$\: \\ $$$$\:\:\mathrm{find}\:\mathrm{max}\left(\Re\left(\mathrm{I}\right)+\Im\left(\mathrm{I}\right)\right)\:\mathrm{for}\:\mathrm{the}\:\mathrm{integral} \\ $$$$\:\:\mathrm{I}\:=\:\int_{{z}} ^{\:{z}+\mathrm{1}} \:\mathrm{cos}\left(\mathrm{cos}\left(\mathrm{cos}\left({x}^{\mathrm{cos}\left(\mathrm{cos}\left(\mathrm{cos}\left({x}\right)\right)\right)} \right)\right)\right){dx} \\ $$$$\:\:{z}\:\in\:\mathbb{R} \\ $$$$\: \\ $$ Terms of…