Question Number 32717 by caravan msup abdo. last updated on 31/Mar/18 $${finf}\:\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}} \:+{x}^{\mathrm{4}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32718 by caravan msup abdo. last updated on 31/Mar/18 $${find}\:\:\int_{\mathrm{0}} ^{\infty} \:{arctan}\left(\mathrm{2}{x}\right)\:\frac{{e}^{−{tx}} }{{x}}\:{dc}\:{with}\:{t}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left(\mathrm{2}{x}\right)}{{x}}\:{e}^{−{x}} \:{dx}. \\ $$ Terms of Service…
Question Number 163785 by amin96 last updated on 10/Jan/22 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{x}}−\mathrm{1}\right)\boldsymbol{\mathrm{ln}}\left(\mathrm{1}−\boldsymbol{\mathrm{x}}\right)}{\boldsymbol{\mathrm{x}}}\boldsymbol{\mathrm{dx}}=? \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{x}}−\mathrm{1}\right)\boldsymbol{\mathrm{ln}}\left(\mathrm{1}+\boldsymbol{\mathrm{x}}\right)}{\boldsymbol{\mathrm{x}}}\boldsymbol{\mathrm{dx}}=? \\ $$$$\boldsymbol{\mathrm{by}}\:\boldsymbol{\mathrm{M}}.\boldsymbol{\mathrm{A}} \\ $$ Terms of Service Privacy Policy…
Question Number 32716 by caravan msup abdo. last updated on 31/Mar/18 $${find}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{cos}^{\mathrm{2}} {x}}{\mathrm{1}+\mathrm{3}{sin}^{\mathrm{2}} {x}}{dx}\:. \\ $$ Answered by Joel578 last updated on 02/Apr/18…
Question Number 32715 by caravan msup abdo. last updated on 31/Mar/18 $${calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{dt}}{\left(\mathrm{1}+{it}\right)\left(\mathrm{1}+{it}^{\mathrm{2}} \right)}\:\:. \\ $$ Commented by abdo imad last updated on 03/Apr/18…
Question Number 98248 by mathmax by abdo last updated on 12/Jun/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{\mathrm{ln}\left(\mathrm{lnx}\right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}}\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32714 by caravan msup abdo. last updated on 31/Mar/18 $${calculate}\:\:\int_{\mathrm{1}} ^{+\infty} \:\:\frac{{dt}}{{t}^{\mathrm{2}} \sqrt{\mathrm{1}+{t}^{\mathrm{2}} }}\:. \\ $$ Commented by abdo imad last updated on…
Question Number 163786 by mnjuly1970 last updated on 10/Jan/22 Answered by cortano1 last updated on 11/Jan/22 $$\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{{ax}−\sqrt{{ax}}−{x}+{b}\sqrt{{x}}}{\:\sqrt{{ax}−\sqrt{{ax}}}+\sqrt{{x}−{b}\sqrt{{x}}}}\:=\:\mathrm{5} \\ $$$$\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left({a}−\mathrm{1}\right){x}+\sqrt{{x}}\:\left({b}−\sqrt{{a}}\right)}{\:\sqrt{{x}}\:\left({a}−\sqrt{\frac{{a}}{{x}}}\right)+\sqrt{{x}}\:\left(\mathrm{1}−\frac{{b}}{\:\sqrt{{x}}}\right)}\:=\:\mathrm{5} \\ $$$$\:\begin{cases}{{a}−\mathrm{1}=\mathrm{0}\Rightarrow{a}=\mathrm{1}}\\{\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{{b}−\sqrt{{a}}}{{a}+\mathrm{1}}\:=\:\mathrm{5}\Rightarrow{b}−\mathrm{1}=\mathrm{10}\:;\:{b}=\mathrm{11}}\end{cases} \\…
Question Number 98246 by M±th+et+s last updated on 12/Jun/20 $$\int\frac{{x}}{{sin}^{\mathrm{2}} \left({x}−\mathrm{3}\right)}{dx} \\ $$ Answered by smridha last updated on 13/Jun/20 $$=\int\boldsymbol{{xcosec}}^{\mathrm{2}} \left(\boldsymbol{{x}}−\mathrm{3}\right)\boldsymbol{{dx}} \\ $$$$=−\boldsymbol{{xcot}}\left(\boldsymbol{{x}}−\mathrm{3}\right)+\int\frac{{d}\boldsymbol{{sin}}\left(\boldsymbol{{x}}−\mathrm{3}\right)}{\boldsymbol{{sin}}\left(\boldsymbol{{x}}−\mathrm{3}\right)} \\…
Question Number 32712 by caravan msup abdo. last updated on 31/Mar/18 $${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\frac{{dt}}{\mathrm{1}+{a}\:{cos}^{\mathrm{2}} {t}}\:. \\ $$ Commented by abdo imad last updated on 03/Apr/18…