Question Number 145775 by Engr_Jidda last updated on 08/Jul/21 $$\int\frac{\mathrm{2}{x}+\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{5}}}{dx} \\ $$ Answered by mathmax by abdo last updated on 08/Jul/21 $$\Upsilon=\int\:\:\frac{\mathrm{2x}+\mathrm{4}−\mathrm{3}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} \:+\mathrm{4x}+\mathrm{5}}}\mathrm{dx}\:=\int\:\:\frac{\mathrm{2x}+\mathrm{4}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} \:+\mathrm{4x}+\mathrm{5}}}\mathrm{dx}−\mathrm{3}\int\:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{x}^{\mathrm{2}}…
Question Number 80227 by jagoll last updated on 01/Feb/20 $${how}\:{to}\:{prove} \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:{x}^{{n}} \:\left(\mathrm{1}−{x}\right)^{{m}\:} \:{dx}\:=\:\frac{{m}!\:×{n}!}{\left({m}+{n}\right)!} \\ $$$${via}\:{Gamma}\:{function} \\ $$ Commented by john santu last…
Question Number 14688 by tawa tawa last updated on 03/Jun/17 $$\int\:\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{x}\right)\:\mathrm{cos}^{\mathrm{2}} \left(\mathrm{x}\right)}\:\mathrm{dx} \\ $$ Answered by ajfour last updated on 03/Jun/17 $$\int\frac{\mathrm{4}}{\left(\mathrm{2sin}\:{x}\mathrm{cos}\:{x}\right)^{\mathrm{2}} }{dx}\:\:=\mathrm{4}\int\frac{{dx}}{\left(\mathrm{sin}\:\mathrm{2}{x}\right)^{\mathrm{2}} }…
Question Number 145745 by mathmax by abdo last updated on 07/Jul/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{cos}\left(\mathrm{2x}\right)}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{4}\right)}\mathrm{dx} \\ $$ Answered by mathmax by abdo last…
Question Number 14667 by Umar math last updated on 03/Jun/17 Commented by prakash jain last updated on 03/Jun/17 $$\frac{\mathrm{1}}{\left({x}^{\mathrm{3}} −\mathrm{1}\right)^{\mathrm{3}} }=\frac{\mathrm{1}}{\left({x}−\mathrm{1}\right)^{\mathrm{3}} \left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{3}} } \\…
Question Number 145723 by madwdah last updated on 07/Jul/21 Answered by bramlexs22 last updated on 07/Jul/21 $$\int\:\mathrm{x}.\mathrm{e}^{\mathrm{2x}} \:\mathrm{dx}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{xe}^{\mathrm{2x}} −\frac{\mathrm{1}}{\mathrm{2}}\int\mathrm{e}^{\mathrm{2x}} \:\mathrm{dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\frac{\mathrm{1}}{\mathrm{4}}\mathrm{e}^{\mathrm{2x}} \left(\mathrm{2x}−\mathrm{1}\right)+\mathrm{c} \\ $$…
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Question Number 14646 by tawa tawa last updated on 03/Jun/17 $$\mathrm{Prove}\:\mathrm{that}:\:\:\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\mathrm{sin}\left(\mathrm{x}\right)\:\mathrm{cos}^{−\mathrm{1}} \left(\mathrm{x}\right)\:\mathrm{dx}\:>\:\frac{\mathrm{1}}{\mathrm{e}^{\mathrm{2}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 145676 by mnjuly1970 last updated on 07/Jul/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{advanced}\:……{calculus}… \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{prove}\:{that}:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} }{{n}^{\:\mathrm{3}} \:\begin{pmatrix}{\:\mathrm{2}{n}}\\{\:\:\:{n}}\end{pmatrix}}\:=\:\frac{\mathrm{2}}{\mathrm{5}}\:\zeta\:\left(\mathrm{3}\:\right) \\ $$$$ \\ $$ Answered by Kamel…
Question Number 145671 by mathlove last updated on 07/Jul/21 Commented by mathlove last updated on 07/Jul/21 $${pleas}\:{help}\:{me} \\ $$ Answered by imjagoll last updated on…