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}}\:. \\ $$ Commented by abdo imad last updated on 03/Apr/18…
Question Number 98249 by mathmax by abdo last updated on 12/Jun/20 $$\mathrm{explicit}\:\mathrm{A}\left(\theta\right)\:=\int_{\mathrm{1}} ^{+\infty} \:\frac{\mathrm{ln}\left(\mathrm{lnx}\right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{2xcos}\theta\:+\mathrm{1}}\mathrm{dx}\:\:\:\mathrm{with}\:−\pi<\theta<\pi \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32708 by abdo imad last updated on 31/Mar/18 $${let}\:{give}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{ln}\left(\mathrm{1}+{xtant}\right)}{{tant}}{dt} \\ $$$${find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{ln}\left(\mathrm{1}+\mathrm{2}{tant}\right)}{{tant}}{dt}\:. \\ $$ Commented by abdo imad…
Question Number 98245 by M±th+et+s last updated on 12/Jun/20 $$\underset{{k}\rightarrow\mathrm{0}} {{lim}}\int_{\mathrm{0}} ^{{k}} \frac{\mathrm{1}}{\:\sqrt{{cos}\left({x}\right)−{cos}\left({k}\right)}}{dx}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com