Question Number 19452 by icyfalcon999 last updated on 11/Aug/17 Answered by Tinkutara last updated on 11/Aug/17 $$\int\frac{{dx}}{{x}^{\mathrm{2}} \:+\:\mathrm{1}}\:=\:\mathrm{tan}^{−\mathrm{1}} {x} \\ $$$$\left[\mathrm{tan}^{−\mathrm{1}} {x}\right]_{−\infty} ^{\infty} \:=\:\frac{\pi}{\mathrm{2}}\:−\:\left(−\frac{\pi}{\mathrm{2}}\right)\:=\:\pi \\…
Question Number 84986 by jagoll last updated on 18/Mar/20 $$\mathrm{5}^{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} } \:+\:\mathrm{625}\:\leqslant\:\mathrm{5}^{\mathrm{x}^{\mathrm{2}} +\mathrm{2}} \:+\:\mathrm{5}^{\mathrm{2x}+\mathrm{3}} \: \\ $$ Commented by mr W last updated on 18/Mar/20…
Question Number 84987 by Jidda28 last updated on 18/Mar/20 $$\boldsymbol{{I}}{negrate} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{4}} \left(\varrho^{{t}} \boldsymbol{{B}}_{{n}} \mathrm{sin}\:\frac{{n}\pi}{\mathrm{4}}\right)^{\mathrm{2}} {tdt} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 150517 by ajfour last updated on 13/Aug/21 Commented by ajfour last updated on 13/Aug/21 $${Cannot}\:{OP}\:{be}\:{a}\:{bit}\:{greater} \\ $$$${than}\:{OB}={R}\:\left({radius}\:{of}\:{hemi}-\right. \\ $$$$\left.{sphere}\right)?\:{If}\:{yes}\:{then}\:{for}\:{what} \\ $$$${range}\:{of}\:{semi}-{vertical}\:\angle\:\theta \\ $$$${of}\:{cone}\:\left({right}\right),\:{is}\:{that}\:{so}?…
Question Number 84982 by M±th+et£s last updated on 18/Mar/20 $$\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{{H}_{{n}} \:{H}_{{n}+\mathrm{1}} }{{n}^{\mathrm{3}} −{n}} \\ $$ Answered by Kamel Kamel last updated on 18/Mar/20…
Question Number 150516 by mathdanisur last updated on 13/Aug/21 $$\mathrm{Compare}: \\ $$$$\boldsymbol{\mathrm{x}}\:=\:\mathrm{2}^{\mathrm{3}^{\mathrm{2}^{\mathrm{3}} } } \:\:\:\:\:\mathrm{and}\:\:\:\:\:\boldsymbol{\mathrm{y}}\:=\:\mathrm{3}^{\mathrm{2}^{\mathrm{3}^{\mathrm{2}} } } \\ $$ Commented by mr W last updated…
Question Number 150515 by mathdanisur last updated on 13/Aug/21 Answered by ajfour last updated on 13/Aug/21 $${x}={t}+{h} \\ $$$$\mathrm{7}\sqrt{\mathrm{4}{t}^{\mathrm{2}} +\mathrm{8}{ht}+\mathrm{4}{h}^{\mathrm{2}} +\mathrm{5}{t}+\mathrm{5}{h}−\mathrm{1}} \\ $$$$−\mathrm{7}\sqrt{\mathrm{4}{t}^{\mathrm{2}} +\mathrm{8}{ht}+\mathrm{4}{h}^{\mathrm{2}} −\mathrm{12}{t}−\mathrm{12}{h}+\mathrm{12}}…
Question Number 84976 by jagoll last updated on 18/Mar/20 Commented by jagoll last updated on 18/Mar/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{area}\: \\ $$ Commented by jagoll last updated on…
Question Number 150508 by saly last updated on 13/Aug/21 Commented by saly last updated on 13/Aug/21 $$\:{Do}\:{you}\:{help}\:{me}? \\ $$ Answered by Olaf_Thorendsen last updated on…
Question Number 84970 by Power last updated on 18/Mar/20 Answered by mr W last updated on 18/Mar/20 $$\mathrm{2}{x}+\mathrm{3}{y}=\pi \\ $$$$\Rightarrow{x}=\frac{\pi}{\mathrm{2}}−\frac{\mathrm{3}{y}}{\mathrm{2}} \\ $$$$\frac{{AB}}{\mathrm{sin}\:\left({x}+{y}\right)}=\frac{{BD}}{\mathrm{sin}\:{x}} \\ $$$$\Rightarrow\frac{\mathrm{11}}{\mathrm{cos}\:\frac{{y}}{\mathrm{2}}}=\frac{\mathrm{2}}{\mathrm{cos}\:\frac{\mathrm{3}{y}}{\mathrm{2}}} \\…