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Question-136283

Question Number 136283 by JulioCesar last updated on 20/Mar/21 Answered by Ar Brandon last updated on 20/Mar/21 $$\int\mathrm{e}^{\mathrm{g}\left(\mathrm{x}\right)} \left[\mathrm{f}\left(\mathrm{x}\right)\mathrm{g}'\left(\mathrm{x}\right)+\mathrm{f}\:'\left(\mathrm{x}\right)\right]\mathrm{dx}=\mathrm{e}^{\mathrm{g}\left(\mathrm{x}\right)} \mathrm{f}\left(\mathrm{x}\right) \\ $$ Terms of Service…

Prove-that-f-x-x-a-cos-x-b-has-at-least-one-real-root-for-a-b-R-

Question Number 70742 by Joel122 last updated on 07/Oct/19 $$\mathrm{Prove}\:\mathrm{that}\:{f}\left({x}\right)\:=\:{x}\:−\:{a}\:\mathrm{cos}\:\left({x}\right)\:−\:{b} \\ $$$$\mathrm{has}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one}\:\mathrm{real}\:\mathrm{root}\:\mathrm{for}\:\forall{a},{b}\:\in\:\mathbb{R} \\ $$ Commented by kaivan.ahmadi last updated on 07/Oct/19 $${x}−{acosx}−{b}=\mathrm{0}\Rightarrow{x}−{b}={acosx} \\ $$$${y}_{\mathrm{1}} ={x}−{b}…

lim-n-S-i-1-n-i-n-1-L-S-R-S-gt-0-What-can-we-tell-about-L-Does-there-exist-a-limit-Is-it-positive-negative-

Question Number 5207 by FilupSmith last updated on 30/Apr/16 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{{S}−\left(\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}{i}!\right)}{{n}}−\mathrm{1}={L} \\ $$$${S}\in\mathbb{R},\:\:{S}>\mathrm{0} \\ $$$$ \\ $$$$\mathrm{What}\:\mathrm{can}\:\mathrm{we}\:\mathrm{tell}\:\mathrm{about}\:{L}? \\ $$$$ \\ $$$$\mathrm{Does}\:\mathrm{there}\:\mathrm{exist}\:\mathrm{a}\:\mathrm{limit}? \\ $$$$\mathrm{Is}\:\mathrm{it}\:\mathrm{positive}/\mathrm{negative}?…

Question-136279

Question Number 136279 by aupo14 last updated on 20/Mar/21 Answered by mindispower last updated on 20/Mar/21 $$=\int{e}^{{x}+\frac{\mathrm{1}}{{x}}} {dx}+\int{x}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right){e}^{{x}+\frac{\mathrm{1}}{{x}}} {dx}={A} \\ $$$$\mathrm{2}{nd}\:{by}\:{part} \\ $$$$\int{x}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right){e}^{{x}+\frac{\mathrm{1}}{{x}}}…