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
Question Number 32705 by caravan msup abdo. last updated on 31/Mar/18 $${let}\:{give}\:\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:{ln}\left(\mathrm{1}\:+\frac{{x}}{{t}^{\mathrm{2}} }\right){dt}\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$${find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right). \\ $$ Commented by abdo imad last updated…
Question Number 32704 by caravan msup abdo. last updated on 31/Mar/18 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\left({x}+\mathrm{1}\right)\sqrt{{x}}}{\mathrm{2}+{x}^{\mathrm{2}} }{dx}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 163759 by amin96 last updated on 10/Jan/22 $$\int_{\mathrm{0}} ^{\mathrm{1}} \left(\frac{\boldsymbol{\mathrm{ln}}\left(\mathrm{1}+\boldsymbol{\mathrm{x}}\right)}{\boldsymbol{\mathrm{x}}}\right)^{\mathrm{2}} \boldsymbol{\mathrm{dx}}=? \\ $$$$\boldsymbol{\mathrm{by}}\:\boldsymbol{\mathrm{M}}.\boldsymbol{\mathrm{A}} \\ $$ Answered by Kamel last updated on 10/Jan/22 $$\Omega\overset{{IBP}}…
Question Number 98214 by me2love2math last updated on 12/Jun/20 Commented by mr W last updated on 12/Jun/20 $${A}=\frac{\mathrm{2}}{\mathrm{3}}×\mathrm{4}×\mathrm{4}=\frac{\mathrm{32}}{\mathrm{3}} \\ $$ Commented by mr W last…
Question Number 163751 by amin96 last updated on 10/Jan/22 $$\int_{\mathrm{0}} ^{\mathrm{1}} \boldsymbol{{ln}}\left(\mathrm{1}+\boldsymbol{{x}}\right)\boldsymbol{{ln}}\left(\mathrm{1}−\boldsymbol{{x}}\right)\boldsymbol{{dx}}=? \\ $$$$\boldsymbol{{by}}\:\boldsymbol{{MATH}}.\boldsymbol{{AMIN}} \\ $$$$−−−−−−−−−−−−−−−−−−−− \\ $$ Answered by Kamel last updated on 10/Jan/22…
Question Number 32675 by Cheyboy last updated on 31/Mar/18 Commented by caravan msup abdo. last updated on 31/Mar/18 $${we}\:{have}\:\mathrm{1}+{cos}\left(\mathrm{4}{x}\right)=\mathrm{2}{cos}^{\mathrm{2}} \left(\mathrm{2}{x}\right)\Rightarrow \\ $$$${I}=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\sqrt{\mathrm{1}+{cos}\left(\mathrm{4}{x}\right)}\:{dx} \\…
Question Number 98182 by abdomathmax last updated on 12/Jun/20 $$\mathrm{find}\:\int\:\mathrm{x}^{\mathrm{2}} \sqrt{\frac{\mathrm{2}−\mathrm{x}}{\mathrm{2}+\mathrm{x}}}\mathrm{dx} \\ $$ Answered by MJS last updated on 12/Jun/20 $$\int{x}^{\mathrm{2}} \sqrt{\frac{\mathrm{2}−{x}}{\mathrm{2}+{x}}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{\frac{\mathrm{2}+{x}}{\mathrm{2}−{x}}}\:\rightarrow\:{dx}=\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\left(\mathrm{2}+{x}\right)\left(\mathrm{2}−{x}\right)^{\mathrm{3}} }{dt}\right]…