Question Number 188470 by aleks041103 last updated on 01/Mar/23 $$\underset{\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}{arctan}\left(\sqrt{\frac{\mathrm{1}−{tan}^{\mathrm{2}} {x}}{\mathrm{2}}}\right){dx}\:=\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 122927 by bemath last updated on 21/Nov/20 Commented by liberty last updated on 21/Nov/20 $$\mu\left({x}\right)=\int\:\sqrt{\frac{\mathrm{1}−\sqrt{{x}}}{\mathrm{1}+\sqrt{{x}}}}\:{dx}\: \\ $$$$\:\left[\:{let}\:\sqrt{{x}}\:=\:\mathrm{sin}\:{z}\:\Rightarrow\:{dx}\:=\:\mathrm{sin}\:\mathrm{2}{z}\:{dz}\:\right] \\ $$$$\mu\left({x}\right)=\int\:\sqrt{\frac{\mathrm{1}−\mathrm{sin}\:{z}}{\mathrm{1}+\mathrm{sin}\:{z}}}\:\left(\mathrm{sin}\:\mathrm{2}{z}\:{dz}\:\right)\: \\ $$$$\mu\left({x}\right)=\int\:\frac{\sqrt{\left(\mathrm{1}−\mathrm{sin}\:{z}\right)^{\mathrm{2}} }}{\mathrm{cos}\:{z}}\:\left(\mathrm{2sin}\:{z}\:\mathrm{cos}\:{z}\:\right)\:{dz} \\…
Question Number 57388 by Joel578 last updated on 03/Apr/19 $$\mathrm{Given}\:{f}\left({x}\right)\:=\:{f}\left({x}\:+\:\mathrm{2016}\right),\:\:\forall{x}\:\in\:\mathbb{R} \\ $$$$\mathrm{If}\:\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\:{f}\left({x}\right)\:=\:\mathrm{30},\:\mathrm{then}\:\underset{\mathrm{3}} {\overset{\mathrm{5}} {\int}}\:{f}\left({x}\:+\:\mathrm{2016}\right)\:=\:… \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 122922 by bemath last updated on 21/Nov/20 $$\:\:\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\:\frac{\mathrm{cos}\:{x}+\mathrm{sin}\:{x}}{\mathrm{16sin}\:\mathrm{2}{x}+\mathrm{9}}\:{dx}\: \\ $$ Answered by liberty last updated on 21/Nov/20 $$\varsigma\:=\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\frac{\mathrm{cos}\:{x}+\mathrm{sin}\:{x}}{\mathrm{16sin}\:\mathrm{2}{x}+\mathrm{9}}\:{dx}\: \\…
Question Number 57385 by Tinkutara last updated on 03/Apr/19 Commented by Tinkutara last updated on 03/Apr/19 How to prove d? Answered by einsteindrmaths@hotmail.fr last updated on 03/Apr/19 $${S}_{{n}}…
Question Number 122919 by bemath last updated on 20/Nov/20 Answered by Dwaipayan Shikari last updated on 20/Nov/20 $$\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \frac{{xe}^{\mathrm{2}{x}} }{\left(\mathrm{1}+\mathrm{2}{x}\right)^{\mathrm{2}} }{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{4}}\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 122885 by CanovasCamiseros last updated on 20/Nov/20 Commented by CanovasCamiseros last updated on 20/Nov/20 $$\boldsymbol{{Please}}\:\boldsymbol{{help}} \\ $$ Answered by ebi last updated on…
Question Number 122884 by CanovasCamiseros last updated on 20/Nov/20 Commented by CanovasCamiseros last updated on 20/Nov/20 $$\boldsymbol{{Need}}\:\boldsymbol{{help}}\:\boldsymbol{{for}}\:\boldsymbol{{this}}\:\boldsymbol{{please}} \\ $$ Answered by MJS_new last updated on…
Question Number 122882 by mnjuly1970 last updated on 20/Nov/20 $$\:\:\:\:\:\:\:\:\:…\:\:{nice}\:\:{calculus}… \\ $$$$\:\:\:\:{prove}\:{that}\:::: \\ $$$$\:\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \left(\frac{{x}^{\varphi} −\mathrm{1}}{{ln}\left({x}\right)}\right)^{\mathrm{2}} {dx}=\sqrt{\mathrm{5}}\:{ln}\left(\varphi\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.{m}.{n}. \\ $$ Answered by TANMAY…
Question Number 122875 by pipin last updated on 20/Nov/20 $$\:\int\frac{\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{1}\right)\boldsymbol{\mathrm{dx}}}{\boldsymbol{\mathrm{x}}^{\mathrm{4}} +\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{1}}\:=\:… \\ $$$$\: \\ $$ Answered by som(math1967) last updated on 20/Nov/20 $$\int\frac{\frac{\mathrm{x}^{\mathrm{2}}…