Question Number 79500 by ubaydulla last updated on 25/Jan/20 $$\int\left(\mathrm{cot}\:^{\mathrm{2}} {x}+\mathrm{cot}\:^{\mathrm{4}} {x}\right){dx} \\ $$ Answered by john santu last updated on 25/Jan/20 $$\int\mathrm{cot}\:^{\mathrm{2}} {x}\left(\mathrm{1}+\mathrm{cot}\:^{\mathrm{2}} {x}\right){dx}\:=…
Question Number 13960 by tawa tawa last updated on 25/May/17 $$\int_{\:\:\:\mathrm{0}} ^{\:\frac{\mathrm{a}}{\mathrm{2}}} \:\:\:\mathrm{x}^{\mathrm{2}} \left(\mathrm{a}^{\mathrm{2}} \:−\:\mathrm{x}^{\mathrm{2}} \right)^{−\mathrm{3}/\mathrm{2}} \:\:\mathrm{dx} \\ $$ Answered by ajfour last updated on…
Question Number 79485 by ubaydulla last updated on 25/Jan/20 $$\int\left(\mathrm{tan}\:^{\mathrm{2}} {x}+\mathrm{tan}\:^{\mathrm{4}} {x}\right){dx} \\ $$ Answered by jagoll last updated on 25/Jan/20 $$\int\:\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}\left(\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}\right)\mathrm{dx}= \\…
Question Number 144997 by qaz last updated on 01/Jul/21 $$\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{x}\right)\mathrm{ln}\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}}\mathrm{dx}=\frac{\pi}{\mathrm{2}}\mathrm{G}−\frac{\mathrm{33}}{\mathrm{32}}\zeta\left(\mathrm{3}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 144985 by imjagoll last updated on 01/Jul/21 $$\:\int\:\frac{\left(\mathrm{2}+\sqrt{\mathrm{x}}\right)}{\left(\mathrm{x}+\mathrm{1}+\sqrt{\mathrm{x}}\right)^{\mathrm{2}} }\:\mathrm{dx}\:=? \\ $$ Answered by mathmax by abdo last updated on 01/Jul/21 $$\mathrm{f}\left(\mathrm{a}\right)=\int\:\:\:\frac{\mathrm{2}+\sqrt{\mathrm{x}}}{\mathrm{x}+\mathrm{a}+\sqrt{\mathrm{x}}}\:\:\:\mathrm{with}\:\mathrm{a}>\frac{\mathrm{1}}{\mathrm{4}}\:\Rightarrow\mathrm{f}^{'} \left(\mathrm{a}\right)=−\int\:\:\frac{\mathrm{2}+\sqrt{\mathrm{x}}}{\left(\mathrm{x}+\mathrm{a}+\sqrt{\mathrm{x}}\right)^{\mathrm{2}} }\mathrm{dx}\:\Rightarrow…
Question Number 144975 by mim24 last updated on 01/Jul/21 Answered by ArielVyny last updated on 01/Jul/21 $$\int{u}'×{u}^{{n}} {du}=\frac{\mathrm{1}}{{n}+\mathrm{1}}{u}^{{n}+\mathrm{1}} +{cte} \\ $$$$\int\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)\left({x}+{ln}\left({x}\right)\right){dx}=\frac{\mathrm{1}}{\mathrm{2}}\left({x}+{lnx}\right)^{\mathrm{2}} \\ $$ Answered by…
Question Number 79413 by rajesh4661kumar@gmail.com last updated on 25/Jan/20 Commented by john santu last updated on 25/Jan/20 $$\left(\frac{\mathrm{cos}\:{x}\mathrm{sin}\:{x}}{\mathrm{cos}\:\mathrm{2}{x}\left(\mathrm{cos}^{\mathrm{2}} {x}−\mathrm{sin}\:^{\mathrm{2}} {x}\right)\:}\right)^{\mathrm{2}} = \\ $$$$\frac{\mathrm{1}}{\mathrm{4}}.\frac{\mathrm{sin}\:^{\mathrm{2}} \mathrm{2}{x}}{\mathrm{cos}\:^{\mathrm{4}} \mathrm{2}{x}}\:=\frac{\mathrm{1}}{\mathrm{4}}\mathrm{tan}\:^{\mathrm{2}}…
Question Number 144939 by yoba last updated on 30/Jun/21 $$ \\ $$$$\boldsymbol{\mathrm{resoudre}} \\ $$$$\boldsymbol{\mathrm{I}}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \boldsymbol{\mathrm{tan}}\left(\boldsymbol{\mathrm{nx}}\right)\boldsymbol{\mathrm{tan}}^{\boldsymbol{\mathrm{n}}} \left(\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{dx}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 144925 by qaz last updated on 30/Jun/21 $$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(\mathrm{2n}\right)!!}{\mathrm{2}^{\mathrm{n}} \centerdot\left(\mathrm{n}+\mathrm{1}\right)\centerdot\left(\mathrm{2n}+\mathrm{1}\right)!!}=? \\ $$ Answered by Ar Brandon last updated on 30/Jun/21 $$\left(\mathrm{2n}\right)!!=\mathrm{2n}\left(\mathrm{2n}−\mathrm{2}\right)\left(\mathrm{2n}−\mathrm{4}\right)…=\mathrm{2}^{\mathrm{n}} \mathrm{n}\left(\mathrm{n}−\mathrm{1}\right)\left(\mathrm{n}−\mathrm{2}\right)…=\mathrm{2}^{\mathrm{n}}…
Question Number 144926 by ArielVyny last updated on 30/Jun/21 $$\int_{\mathrm{0}} ^{\infty} {x}^{{n}} \left({e}^{{ix}} \right)^{{z}} {dx}=???\:\:\:\left({z}\in\mathbb{C}\right) \\ $$ Answered by mathmax by abdo last updated on…