Question Number 154318 by liberty last updated on 17/Sep/21 Answered by MJS_new last updated on 17/Sep/21 $$\mathrm{sin}\:{x}\:+\mathrm{cos}\:{x}\:=\sqrt{\mathrm{2}}\mathrm{sin}\:\frac{\mathrm{4}{x}+\pi}{\mathrm{4}}\:= \\ $$$$\:\:\:\:\:\left[\mathrm{sin}\:\theta\:=\mathrm{1}−\mathrm{2sin}^{\mathrm{2}} \:\frac{\mathrm{2}\theta−\pi}{\mathrm{4}}\right] \\ $$$$=\sqrt{\mathrm{2}}\left(\mathrm{1}−\mathrm{2sin}^{\mathrm{2}} \:\frac{\mathrm{4}{x}−\pi}{\mathrm{8}}\right) \\ $$$$\int\sqrt{\mathrm{sin}\:{x}\:+\mathrm{cos}\:{x}}{dx}=…
Question Number 154309 by liberty last updated on 17/Sep/21 Answered by EDWIN88 last updated on 17/Sep/21 $${max}\:{f}\left({x}\right)=\mathrm{22}\:….\left({C}\right) \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 154280 by EDWIN88 last updated on 16/Sep/21 $$\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:{z}^{\mathrm{2}} } \int_{\mathrm{0}} ^{\:\mathrm{3}} {y}\:\mathrm{cos}\:\left({z}^{\mathrm{5}} \right){dxdydz}\:=? \\ $$ Terms of Service Privacy Policy…
Question Number 154281 by rexford last updated on 16/Sep/21 $$\int_{\mathrm{1}} ^{\mathrm{3}} \lfloor{x}−\mathrm{3}\rfloor{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 88710 by jagoll last updated on 12/Apr/20 $$\underset{−\sqrt{\mathrm{3}}\:} {\overset{\sqrt{\mathrm{3}}} {\int}}\underset{\mathrm{1}} {\overset{\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }} {\int}}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)^{\mathrm{3}/\mathrm{2}} \:{dydx} \\ $$ Commented by mathmax by abdo…
Question Number 154235 by mnjuly1970 last updated on 15/Sep/21 $$ \\ $$$$\:\:\:\:{prove}\:{that}: \\ $$$$\:\:\:\:\:\mathrm{I}{m}\left(\:\psi\:\left(\:{i}\:\right)\:\right)=\:\frac{\:\mathrm{1}}{\:\mathrm{2}}\:+\:\frac{\:\pi}{\mathrm{2}}\:{coth}\left(\pi\:\right) \\ $$$$\:\:\:\:\:\:\:\:{m}.{n} \\ $$ Answered by mindispower last updated on 16/Sep/21…
Question Number 154223 by mnjuly1970 last updated on 15/Sep/21 $$ \\ $$$$\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{x}^{\:{i}+\mathrm{1}} }{\mathrm{1}−{x}}\:{dx}\:=\:\left[−{ln}\left(\mathrm{1}−{x}\right){x}^{\:{i}+\mathrm{1}} \right]_{\mathrm{0}} ^{\:\mathrm{1}} \\ $$$$\:\:\:+\:\left(\mathrm{1}+{i}\right)\int_{\mathrm{0}} ^{\:\mathrm{1}} {x}^{\:{i}} \:{ln}\:\left(\mathrm{1}−{x}\:\right){dx} \\ $$$$\:\:\:=\:\left(\mathrm{1}+{i}\:\right)\:\int_{\mathrm{0}} ^{\:\mathrm{1}}…
Question Number 154208 by amin96 last updated on 15/Sep/21 $$\because\therefore\because\therefore{prove}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \frac{{log}\left(\mathrm{1}−{e}^{−{x}} \right)\left({yLi}_{\mathrm{2}} \left({e}^{−{x}−{y}} \right)+{Li}_{\mathrm{3}} \left({e}^{−{x}−{y}} \right)\right.}{\mathrm{1}−{e}^{{x}+{y}} }{e}^{{x}+{y}} {dxdy}=\frac{\mathrm{21}}{\mathrm{8}}\zeta\left(\mathrm{6}\right)+\zeta^{\mathrm{2}} \left(\mathrm{3}\right) \\…
Question Number 154192 by mnjuly1970 last updated on 15/Sep/21 $$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\Omega\::=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{x}.{sin}\left({ln}\left({x}\right)\right)}{\mathrm{1}−{x}}{dx} \\ $$$$\:\:\:\:\:\:\:\:\:{method}\:\mathrm{1} \\ $$$$\:\:\:\:\:\Omega=\:\mathrm{I}{m}\left[\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\:{x}^{\:{i}+\mathrm{1}} }{\mathrm{1}−{x}}\:{dx}=\Phi\right] \\ $$$$\:\:\:\:\:\:\:\:\:\Phi\:=\:\int_{\mathrm{0}}…
Question Number 154195 by rexford last updated on 15/Sep/21 $$\int\frac{{x}+{sinx}}{\mathrm{1}+{cosx}}{dx}\:\:\:\: \\ $$$${please},{help}\:{me} \\ $$ Answered by qaz last updated on 15/Sep/21 $$\because\:\left(\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{1}+\mathrm{cos}\:\mathrm{x}}\right)'=\frac{\mathrm{1}}{\mathrm{1}+\mathrm{cos}\:\mathrm{x}} \\ $$$$\therefore\int\frac{\mathrm{x}+\mathrm{sin}\:\mathrm{x}}{\mathrm{1}+\mathrm{cos}\:\mathrm{x}}\mathrm{dx} \\…