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Question Number 116016 by bemath last updated on 30/Sep/20 $$\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}\:\frac{{dx}}{\:\sqrt{\mathrm{6}+{x}−{x}^{\mathrm{2}} }}\:? \\ $$ Answered by bobhans last updated on 30/Sep/20 $${I}=\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}\:\frac{{dx}}{\:\sqrt{\mathrm{6}−\left({x}^{\mathrm{2}}…
Question Number 116014 by mnjuly1970 last updated on 30/Sep/20 $$\:\:\:\:\:\:\:…{nice}\:\:{calculus}\:…\:\:\: \\ $$$$\:{prove}\:: \\ $$$$\:\:\:{i}:\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\left({x}\right)}{\left(\mathrm{1}+{x}^{\sqrt{\mathrm{2}}} \right)^{\sqrt{\mathrm{2}}} }\:=\mathrm{0}\:\:\:\:\:\:\checkmark \\ $$$$\:\:\:{ii}:\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{1}+\sqrt{\mathrm{2}}} \right)^{\mathrm{1}+\sqrt{\mathrm{2}}} }\:=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:\:\checkmark\:\: \\…
Question Number 116000 by frc2crc last updated on 30/Sep/20 $${U}\left({n}\right)=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}−\mathrm{tanh}\:{x}}{\:\sqrt[{{n}}]{\mathrm{tanh}\:{x}}}{dx} \\ $$$${another}\:{way}? \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 115974 by jm2bok last updated on 29/Sep/20 $$\int\frac{{e}^{\mathrm{3}{x}} −{e}^{{x}} }{{x}\left({e}^{\mathrm{3}{x}} +\mathrm{1}\right)\left({e}^{{x}} +\mathrm{1}\right)}{dx}\:=\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 50433 by Abdo msup. last updated on 16/Dec/18 $${find}\:{all}\:{function}\:{f}\:\:{C}^{\mathrm{2}} \:{onR}\:/ \\ $$$${f}\left({x}\right)+\int_{\mathrm{0}} ^{{x}} \left({x}−{t}\right){f}\left({t}\right){dt}\:=\mathrm{1}\:\forall\:{x}\in{R}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 50427 by Abdo msup. last updated on 16/Dec/18 $${let}\:{I}_{{n}} \left(\lambda\right)\:=\int_{\mathrm{0}} ^{\pi} \:\:\frac{{vos}\left({nt}\right)}{\mathrm{1}−\mathrm{2}\lambda{cost}\:+\lambda^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{1}\right){calculate}\:{I}_{\mathrm{0}} \left(\lambda\right)\:{and}\:{I}_{\mathrm{1}} \left(\lambda\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{relation}\:{between}\:{I}_{{n}−\mathrm{1}} ,{I}_{{n}} \:{and}\:{I}_{{n}+\mathrm{1}} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:{I}_{{n}}…
Question Number 50425 by Abdo msup. last updated on 16/Dec/18 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{sin}^{\mathrm{4}} \left({t}\right)}{{t}^{\mathrm{3}} }\:{dt} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 50423 by Abdo msup. last updated on 16/Dec/18 $${find}\:{f}\left({a}\right)\:=\int_{{a}} ^{+\infty} \:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\sqrt{{x}^{\mathrm{2}} −{a}^{\mathrm{2}} }}\:\:{with}\:{a}>\mathrm{0} \\ $$ Commented by Abdo msup. last updated on…
Question Number 50422 by Abdo msup. last updated on 16/Dec/18 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}\left({x}\right)}{\:\sqrt{{x}}\left(\mathrm{1}−{x}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} }{dx} \\ $$ Commented by Abdo msup. last updated on 23/Dec/18 $${changement}\:{x}\:={sin}^{\mathrm{2}}…