Question Number 83115 by 09658867628 last updated on 28/Feb/20 $$\int\mathrm{cos}\:{xe}^{\mathrm{sin}\:{x}} {dx} \\ $$ Commented by niroj last updated on 28/Feb/20 $$ \\ $$$$\:\int\boldsymbol{\mathrm{cos}}\:\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{sin}}\:\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{dx}} \\…
Question Number 83108 by M±th+et£s last updated on 28/Feb/20 $${prove}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{{cos}\left({nx}\right)}{{cos}^{{n}} \left({x}\right)}\:{dx}\:=\mathrm{2}^{{n}} \left[\frac{\pi}{\mathrm{8}}−\underset{{k}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\sum}}\frac{{sin}\left(\frac{{k}\pi}{\mathrm{4}}\right)}{\mathrm{2}{k}\left(\sqrt{\mathrm{2}}\right)^{{k}} }\right]\:{n}\in{N}^{\ast} \\ $$ Answered by mind is…
Question Number 83110 by 09658867628 last updated on 28/Feb/20 $${bounded}\:{by}\:{the}\:{curve}\:{y}=\sqrt{\mathrm{4}-{x}}\:{y}=\mathrm{0}\:{y}=\mathrm{1} \\ $$ Commented by jagoll last updated on 28/Feb/20 $$\mathrm{Area}\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{4}−\mathrm{y}^{\mathrm{2}} \right)\:\mathrm{dy}\: \\ $$$$=\:\mathrm{4y}\:−\:\frac{\mathrm{y}^{\mathrm{3}}…
Question Number 83104 by 09658867628 last updated on 28/Feb/20 $$\int\frac{{e}^{{x}} {dx}}{\mathrm{3}+{e}^{{x}} } \\ $$ Answered by MJS last updated on 28/Feb/20 $$\int\frac{\mathrm{e}^{{x}} }{\mathrm{3}+\mathrm{e}^{{x}} }{dx}= \\…
Question Number 83109 by 09658867628 last updated on 28/Feb/20 $$\int_{\mathrm{1}/\boldsymbol{{e}}} ^{{e}} \frac{\boldsymbol{{dt}}}{\boldsymbol{{t}}} \\ $$ Commented by jagoll last updated on 28/Feb/20 $$=\:\mathrm{ln}\:\left(\mathrm{t}\right)\:\mid_{\frac{\mathrm{1}}{\mathrm{e}}} ^{\mathrm{e}} \:=\:\mathrm{1}−\left(−\mathrm{1}\right)\:=\:\mathrm{2} \\…
Question Number 83096 by 09658867628 last updated on 28/Feb/20 $$\int\mathrm{tan}\:{x}^{\mathrm{4}} {dx} \\ $$ Commented by jagoll last updated on 28/Feb/20 $$??? \\ $$ Terms of…
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Question Number 83093 by 09658867628 last updated on 28/Feb/20 $$\int\mathrm{cosec}\:{x}^{\mathrm{5}} {dx} \\ $$ Commented by jagoll last updated on 28/Feb/20 $$??? \\ $$ Terms of…