Category: Integration

Question Number 7184 by Yozzia last updated on 15/Aug/16 $${Show}\:{that} \\ $$$$\int\frac{\mathrm{2}^{{x}} }{\left(\mathrm{1}+\sqrt{\mathrm{5}}\right)^{{x}} +\left(\mathrm{3}+\sqrt{\mathrm{5}}\right)^{{x}} }{dx}=\frac{\mathrm{1}}{{ln}\left(\mathrm{1}+\sqrt{\mathrm{5}}\right)−{ln}\mathrm{2}}\left({ln}\left[\mathrm{1}+\left(\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{\mathrm{2}}\right)^{{x}} \right]−\left(\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{\mathrm{2}}\right)^{{x}} \right)+{C} \\ $$$$ \\ $$ Terms of Service Privacy…

Question Number 138223 by mnjuly1970 last updated on 11/Apr/21 $$\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:…….{nice}\:…\:…\:…\:{calculus}… \\ $$$$\:\:\:{evaluate}\:::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\Theta}=\underset{{n}=−\infty} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{3}{n}+\mathrm{1}\right)^{\mathrm{3}} }\:=? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:……………………. \\ $$ Answered by…

Question Number 138205 by Bekzod Jumayev last updated on 11/Apr/21 Commented by Jamshidbek last updated on 11/Apr/21 $$\mathrm{Og}'\mathrm{ayni}\:\mathrm{kun}\:\mathrm{savolini}\:\mathrm{oziz}\:\mathrm{yechmasizmi}? \\ $$$$\mathrm{Yoki}\:\mathrm{kechqurun}\:\mathrm{kanalga}\:\mathrm{tashlanadiku}\:\mathrm{yechim}.\mathrm{O}'\mathrm{shanda} \\ $$$$\mathrm{o}'\mathrm{rganib}\:\mathrm{olardizda} \\ $$ Commented…

Question Number 72665 by TawaTawa last updated on 31/Oct/19 $$\int_{\:\mathrm{2}} ^{\:\mathrm{3}} \:\:\frac{\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right)}{\mathrm{1}\:−\:\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx} \\ $$ Commented by mind is power last updated on 31/Oct/19…

Question Number 7096 by Tawakalitu. last updated on 10/Aug/16 Commented by Rasheed Soomro last updated on 10/Aug/16 $${First}\:{vertex}\:{of}\:{a}\:{triangle}\:{can}\:{be} \\ $$$${chosen}\:{in}\:{n}\:{ways}\:{in}\:{a}\:{regular}\:{n}-{gon}. \\ $$$${The}\:{second}\:{vertex}\:{can}\:{be}\:{chosen}\:{in} \\ $$$${n}−\mathrm{1}\:{ways}.\:{The}\:{third}\:{vertex}\:{can}\:{be}\: \\…