Question Number 204517 by Lindemann last updated on 20/Feb/24 Answered by witcher3 last updated on 20/Feb/24 $$\left.=\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right)\mathrm{cos}^{−\mathrm{1}} \left(\mathrm{x}\right)\right]_{−\mathrm{1}} ^{\mathrm{1}} +\int_{−\mathrm{1}} ^{\mathrm{1}} \mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right).\frac{\mathrm{dx}}{\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}._{=\mathrm{0}}…
Question Number 204533 by bello6646 last updated on 20/Feb/24 Answered by MM42 last updated on 20/Feb/24 $${ln}\frac{{ax}}{{b}}={u}\Rightarrow{I}={ln}\left({ln}\frac{{a}}{{b}}{x}\right)+{c} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 204472 by mnjuly1970 last updated on 18/Feb/24 $$\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{Calculate}\:… \\ $$$$\:\:\:\:\:\:\:\Omega=\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\lfloor\frac{\:\mathrm{1}}{\:\sqrt[{{k}}]{{e}}\:−\mathrm{1}}\:\rfloor\:=? \\ $$$$ \\ $$ Answered by TonyCWX08 last updated…
Question Number 204409 by mr W last updated on 16/Feb/24 $${find}\:\lfloor\int_{\mathrm{0}} ^{\mathrm{2023}} \frac{\mathrm{2}}{{x}+{e}^{{x}} }{dx}\rfloor=? \\ $$ Commented by witcher3 last updated on 16/Feb/24 $$\mathrm{nice}\:\mathrm{problems}\:\mathrm{sir}\:\:\mathrm{Thanx}\:\mathrm{for}\:\mathrm{share}\:\mathrm{it} \\…
Question Number 204275 by Frix last updated on 11/Feb/24 $$\mathrm{Show}\:\mathrm{that} \\ $$$$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{4}}} {\int}}\sqrt{\mathrm{tan}\:{x}}\:\sqrt{\mathrm{1}−\mathrm{tan}\:{x}}\:{dx}=\left(\frac{\sqrt{\sqrt{\mathrm{2}}−\mathrm{1}}}{\:\sqrt{\mathrm{2}}}−\mathrm{1}\right)\pi \\ $$ Answered by witcher3 last updated on 11/Feb/24 $$\mathrm{nice}\:\mathrm{problem} \\…
Question Number 204233 by Perelman last updated on 09/Feb/24 Answered by Frix last updated on 09/Feb/24 $$\int\frac{{x}^{\frac{\mathrm{1}}{\mathrm{2}}} }{{x}^{\frac{\mathrm{3}}{\mathrm{4}}} +\mathrm{1}}{dx}\:\overset{{t}={x}^{\frac{\mathrm{1}}{\mathrm{4}}} } {=}\:\mathrm{4}\int\frac{{t}^{\mathrm{5}} }{{t}^{\mathrm{3}} +\mathrm{1}}{dt}= \\ $$$$=\mathrm{4}\int{t}^{\mathrm{2}}…
Question Number 204244 by pticantor last updated on 09/Feb/24 Answered by pticantor last updated on 09/Feb/24 $${please}\:{can}\:{some}\:{one}\:{help}\:{me}\:{to}\:{solve}\:{question}\:\mathrm{2}−{b}\: \\ $$$${for}\:{this}\:{exercise}? \\ $$ Answered by witcher3 last…
Question Number 203964 by mnjuly1970 last updated on 03/Feb/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{Advanced}\:\:{calculus}\:… \\ $$$$\:\:{Q}:\:\:\:{If}\:,\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{x}\mathrm{ln}\left({x}\right)\mathrm{ln}^{\mathrm{2}} \left({y}\:\right)}{\mathrm{1}−{xy}}\:{dxdy}\:=\:\lambda\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\mathrm{1}}{{n}^{\:\mathrm{3}} \left(\:{n}+\mathrm{1}\:\right)^{\mathrm{2}} }\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:\:{Find}\:,\:\:\:\:\:\lambda\:=?…
Question Number 203884 by Mathspace last updated on 31/Jan/24 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{x}^{\mathrm{3}} }{\left(\mathrm{1}+{x}\right)^{\mathrm{4}} \left({x}+\mathrm{2}\right)^{\mathrm{5}} }{dx} \\ $$ Answered by Frix last updated on 01/Feb/24 $$\mathrm{Use}\:\mathrm{Ostrogradski}'\mathrm{s}\:\mathrm{Method}\:\mathrm{to}\:\mathrm{get}…
Question Number 203867 by Mathspace last updated on 30/Jan/24 $${find}\:\int\sqrt{\frac{\mathrm{1}−{x}^{\mathrm{3}} }{\mathrm{1}+{x}^{\mathrm{3}} }}{dx} \\ $$ Answered by MathematicalUser2357 last updated on 06/Feb/24 $$\frac{\mathrm{8}{x}\sqrt{\frac{\mathrm{1}−{x}^{\mathrm{3}} }{{x}^{\mathrm{3}} +\mathrm{1}}}{F}_{\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{3}};−\frac{\mathrm{1}}{\mathrm{2}},\frac{\mathrm{1}}{\mathrm{2}};\frac{\mathrm{4}}{\mathrm{3}};{x}^{\mathrm{3}}…