Question Number 123793 by liberty last updated on 28/Nov/20 $$\:\:\int\:\frac{\mathrm{4}{x}−\mathrm{1}}{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}}\:{dx}\:? \\ $$ Answered by Dwaipayan Shikari last updated on 28/Nov/20 $$\int\frac{\mathrm{4}{x}−\mathrm{3}}{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}}+\mathrm{2}\int\frac{\mathrm{1}}{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}}{dx} \\…
Question Number 189325 by mnjuly1970 last updated on 14/Mar/23 $$ \\ $$$$\:\:\:\:\:{prove} \\ $$$$ \\ $$$$\:\:\Omega=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{\:{cos}\left({x}\right)+{cos}\left(\mathrm{5}{x}\right)}{\mathrm{1}+\:\mathrm{2}{sin}\left({x}\right)}\:\overset{\:?} {=}\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$ \\ $$ Answered by…
Question Number 189323 by mnjuly1970 last updated on 14/Mar/23 Answered by witcher3 last updated on 14/Mar/23 $$\Leftrightarrow\Sigma\frac{\Gamma\left(\mathrm{n}\right)\Gamma\left(\mathrm{n}\right)}{\Gamma\left(\mathrm{2n}\right).\mathrm{2}^{−\mathrm{n}} }=\underset{\mathrm{n}\geqslant\mathrm{1}} {\sum}\frac{\beta\left(\mathrm{n},\mathrm{n}\right)}{\mathrm{2}^{−\mathrm{n}} } \\ $$$$=\underset{\mathrm{n}\geqslant\mathrm{1}} {\sum}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{x}^{\mathrm{n}−\mathrm{1}}…
Question Number 58250 by Tawa1 last updated on 20/Apr/19 $$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\:\left(\frac{\mathrm{3x}^{\mathrm{3}} \:−\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{2x}\:−\:\mathrm{4}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{3x}\:+\:\mathrm{2}}}\right)\:\mathrm{dx} \\ $$ Answered by MJS last updated on 21/Apr/19 $$\underset{\mathrm{0}}…
Question Number 58249 by tanmay last updated on 20/Apr/19 $$\overset{} {{I}}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {cos}^{{n}} {xcos}\left({nx}\right){dx} \\ $$$${then}\:{show}\:{that}\:{I}_{\mathrm{1}} ,{I}_{\mathrm{2}} ,{I}_{\mathrm{3}} ….{are}\:{in}\:{G}.{P} \\ $$ Terms of Service…
Question Number 58240 by salaw2000 last updated on 20/Apr/19 $$\mathrm{i}=\int\mathrm{dx}/\left(\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} \\ $$ Commented by maxmathsup by imad last updated on 21/Apr/19 $${let}\:{I}\:=\int\:\:\frac{{dx}}{\left({ax}^{\mathrm{2}} \:+{bx}\:+{c}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} }\:\:{let}\:{p}\left({x}\right)={ax}^{\mathrm{2}}…
Question Number 58238 by Tawa1 last updated on 20/Apr/19 $$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\:\left(\frac{\mathrm{3}\boldsymbol{\mathrm{x}}^{\mathrm{3}} \:−\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:+\:\mathrm{2}\boldsymbol{\mathrm{x}}\:−\:\mathrm{4}}{\:\sqrt{\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:−\:\mathrm{3}\boldsymbol{\mathrm{x}}\:+\:\mathrm{2}}}\right)\:\:\boldsymbol{\mathrm{dx}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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Question Number 123769 by oustmuchiya@gmail.com last updated on 28/Nov/20 Commented by oustmuchiya@gmail.com last updated on 17/Dec/20 $$ \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 123764 by mnjuly1970 last updated on 28/Nov/20 $$\:\:\:\:\:\:\:\:\:\:\:\:….\:{advanced}\:\:{calculus}\:… \\ $$$$\:\:\:\:\:\:\:{prove}\:\:{that}:::: \\ $$$$\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left\{\frac{\zeta\left(\mathrm{2}{n}+\mathrm{1}\right)}{\mathrm{4}^{{n}\:} \:\left(\mathrm{2}{n}+\mathrm{1}\right)}\right\}={ln}\left(\mathrm{2}\right)−\gamma \\ $$$$\:\:\:\:\:\:\:\:\gamma::\:\:{euler}−{mascheroni} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{constant} \\ $$ Answered by…