Question Number 151037 by qaz last updated on 17/Aug/21 $$\underset{\mathrm{r}=\mathrm{1},\mathrm{r}\neq\mathrm{s}} {\overset{\mathrm{n}} {\sum}}\:\:\underset{\mathrm{s}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{rs}}{\mathrm{n}\left(\mathrm{n}−\mathrm{1}\right)}\overset{?} {=}\frac{\left(\mathrm{n}+\mathrm{1}\right)\left(\mathrm{3n}+\mathrm{2}\right)}{\mathrm{12}} \\ $$ Answered by mindispower last updated on 17/Aug/21 $$=\underset{{r}=\mathrm{1}}…
Question Number 85488 by john santu last updated on 22/Mar/20 $$\int\:\frac{{dx}}{\left({x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{4}}} } \\ $$ Answered by MJS last updated on 22/Mar/20 $$\mathrm{trying}\:\mathrm{around}\:\mathrm{I}\:\mathrm{landed}\:\mathrm{on} \\…
Question Number 151026 by qaz last updated on 17/Aug/21 $$\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{0}^{\mathrm{n}} }{\mathrm{n}!}=? \\ $$ Answered by ArielVyny last updated on 17/Aug/21 $${according}\:{to}\:{the}\:\:{definition}\: \\ $$$${e}^{{t}}…
Question Number 85480 by M±th+et£s last updated on 22/Mar/20 $$\int\frac{{csc}\left({x}\right)}{{cos}\left({x}\right)+{cos}^{\mathrm{3}} \left({x}\right)+…+{cos}^{\mathrm{2}{n}+\mathrm{1}} \left({x}\right)}{dx} \\ $$$$\forall{x}\in{n} \\ $$ Answered by mind is power last updated on 22/Mar/20…
Question Number 151017 by talminator2856791 last updated on 17/Aug/21 $$\: \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \:\left(\mathrm{ln}\left({x}^{\sqrt{{x}}} −\mathrm{1}\right)\right)^{−{x}} \:{dx}\:=\:? \\ $$$$\: \\ $$$$\: \\ $$ Terms…
Question Number 85468 by M±th+et£s last updated on 22/Mar/20 $$\int{ln}\left(\mathrm{1}−{e}^{{x}} \right)\:{dx} \\ $$ Answered by mind is power last updated on 22/Mar/20 $$={xln}\left(\mathrm{1}−{e}^{{x}} \right){dx}+\int\frac{{xe}^{{x}} }{\mathrm{1}−{e}^{{x}}…
Question Number 150993 by talminator2856791 last updated on 17/Aug/21 $$\: \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{ln}\left({x}+\mathrm{1}\right)}{{x}^{\mathrm{2}} +\mathrm{1}}\:{dx}\:=\:? \\ $$$$\: \\ $$$$\: \\ $$ Commented by…
Question Number 85456 by jagoll last updated on 22/Mar/20 $$\int\:\sqrt{\mathrm{csc}\:\mathrm{x}\:}\:\mathrm{dx}? \\ $$ Commented by jagoll last updated on 22/Mar/20 $$\mathrm{thank}\:\mathrm{sir} \\ $$ Commented by MJS…
Question Number 150992 by talminator2856791 last updated on 17/Aug/21 $$\: \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{{x}}{{e}^{{x}} −\mathrm{1}}\:{dx}\:=\:? \\ $$$$\: \\ $$$$\: \\ $$ Commented by…
Question Number 150994 by talminator2856791 last updated on 17/Aug/21 $$\: \\ $$$$\:\:\:\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{improper}\:\mathrm{integral} \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\:\underset{{B}\rightarrow\infty} {\mathrm{lim}}\:\:\int_{\mathrm{0}} ^{\:{B}} \:\mathrm{sin}\left({x}\right)\mathrm{sin}\left({x}^{\mathrm{2}} \right){dx} \\ $$$$\:\: \\ $$$$\:\:\:\mathrm{converges} \\…