Question Number 151447 by mnjuly1970 last updated on 21/Aug/21 $$ \\ $$$$\:\:\:\:\:\:{prove}\:{that}… \\ $$$$\:\:\:\mathrm{I}:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{ln}\:\left({x}\:\right)}{\mathrm{1}+\:{e}^{\:{x}} }\:{dx}=\:\frac{−\mathrm{1}}{\mathrm{2}}\:{ln}^{\:\mathrm{2}} \left(\mathrm{2}\right)\:..\blacksquare \\ $$ Answered by Lordose last updated…
Question Number 85896 by ar247 last updated on 25/Mar/20 Commented by abdomathmax last updated on 25/Mar/20 $${I}=\int\:\:\frac{\mathrm{5}{x}−\mathrm{5}}{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{8}{x}−\mathrm{3}}{dx} \\ $$$$\mathrm{3}{x}^{\mathrm{2}} −\mathrm{8}{x}−\mathrm{3}=\mathrm{0}\:\rightarrow\Delta^{'} =\mathrm{4}^{\mathrm{2}} −\left(\mathrm{3}\right)\left(−\mathrm{3}\right)\:=\mathrm{16}+\mathrm{9}=\mathrm{25} \\ $$$${x}_{\mathrm{1}}…
Question Number 151425 by peter frank last updated on 21/Aug/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{dx}}{\left(\mathrm{cos}\:\mathrm{x}+\sqrt{\mathrm{3}}\:\mathrm{sin}\:\mathrm{x}\right)^{\mathrm{2}} }\mathrm{dx}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}} \\ $$ Answered by Olaf_Thorendsen last updated on 21/Aug/21 $$\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…
Question Number 151428 by peter frank last updated on 21/Aug/21 $$\int\frac{\mathrm{x}+\mathrm{2}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{3x}+\mathrm{3}\right)\sqrt{\mathrm{x}+\mathrm{1}}}\mathrm{dx} \\ $$$$ \\ $$ Answered by MJS_new last updated on 21/Aug/21 $$\left(\mathrm{1}\right)\:\mathrm{trying}\:\mathrm{something} \\…
Question Number 151429 by peter frank last updated on 21/Aug/21 $$\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{xdx}}{\left(\mathrm{a}^{\mathrm{2}} \mathrm{cos}\:^{\mathrm{2}} \mathrm{x}+\mathrm{b}^{\mathrm{2}} \mathrm{sin}\:^{\mathrm{2}} \mathrm{x}\right)^{\mathrm{2}} } \\ $$ Answered by Olaf_Thorendsen last updated…
Question Number 85890 by frc2crc last updated on 25/Mar/20 $${Is}\:{there}\:{a}\:{sum}\:{for}\:\psi\left(\frac{{p}}{{q}}\right)\:{or}\:{an}\:{integral} \\ $$$${for}\:{any}\:{fraction}\:{p}/{q} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 151421 by peter frank last updated on 21/Aug/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \mathrm{log}\:\left(\mathrm{1}+\mathrm{tan}\:\mathrm{x}\right)\mathrm{dx} \\ $$ Commented by puissant last updated on 21/Aug/21 $${x}=\frac{\pi}{\mathrm{4}}−{t}\:\rightarrow\:{dx}=−{dt} \\ $$$${Q}=\int_{\frac{\pi}{\mathrm{4}}}…
Question Number 151426 by peter frank last updated on 21/Aug/21 $$\mathrm{Express}\:\frac{\mathrm{1}}{\mathrm{5}×\mathrm{9}}\:\mathrm{in}\:\mathrm{partial}\:\mathrm{fraction} \\ $$ Answered by liberty last updated on 21/Aug/21 $$\:\frac{\mathrm{1}}{\mathrm{n}\left(\mathrm{n}+\mathrm{4}\right)}=\frac{\mathrm{a}}{\mathrm{n}}+\frac{\mathrm{b}}{\mathrm{n}+\mathrm{4}}\: \\ $$$$\mathrm{a}=\:\left[\frac{\mathrm{1}}{\mathrm{n}+\mathrm{4}}\:\right]_{\mathrm{n}=\mathrm{0}} =\frac{\mathrm{1}}{\mathrm{4}} \\…
Question Number 151423 by peter frank last updated on 21/Aug/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{dx}}{\mathrm{1}+\mathrm{tan}\:^{\mathrm{5}} \mathrm{x}} \\ $$ Answered by Olaf_Thorendsen last updated on 21/Aug/21 $$\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…
Question Number 85875 by sakeefhasan05@gmail.com last updated on 25/Mar/20 $$\int\left(\frac{\mathrm{1}}{\mathrm{7}\left[\mathrm{1}−\frac{\mathrm{1}}{\mathrm{7}}\mathrm{e}^{\mathrm{x}} \right]}\right)\:\mathrm{dx} \\ $$ Answered by TANMAY PANACEA. last updated on 25/Mar/20 $$\frac{\mathrm{1}}{\mathrm{7}}\int\frac{{e}^{−{x}} {dx}}{{e}^{−{x}} −\frac{\mathrm{1}}{\mathrm{7}}}\:\left(\boldsymbol{{multiply}}\:\boldsymbol{{N}}_{{r}} {and}\:{D}_{{r}}…