Question Number 197338 by yusufkhabibulloh last updated on 13/Sep/23 $$\int\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$ Answered by TheHoneyCat last updated on 13/Sep/23 $$=\int\frac{{x}^{\mathrm{2}} +\mathrm{1}−\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}\mathrm{d}{x} \\…
Question Number 197335 by sonukgindia last updated on 13/Sep/23 Answered by witcher3 last updated on 13/Sep/23 $$\mathrm{x}\rightarrow\frac{\mathrm{1}}{\mathrm{x}} \\ $$$$\mathrm{I}=\int_{\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}} ^{\sqrt{\mathrm{3}}} \frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\mathrm{tan}^{−\mathrm{1}} \left(\frac{\sqrt{\mathrm{3}}\mathrm{x}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} +\mathrm{2}}\right)\mathrm{dx}…
Question Number 197325 by sonukgindia last updated on 13/Sep/23 Answered by witcher3 last updated on 13/Sep/23 $$\mathrm{f}\left(\mathrm{f}\left(\mathrm{x}\right)\right)=\mathrm{x}^{\mathrm{2}} −\mathrm{1} \\ $$$$\mathrm{if}\:\mathrm{x}\in\mathbb{R}\:\mid\mathrm{f}^{\mathrm{2}} \left(\mathrm{x}\right)=\mathrm{x}\Rightarrow\mathrm{x}^{\mathrm{2}} −\mathrm{x}−\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{x}\in\left\{\frac{\mathrm{1}−\sqrt{\mathrm{5}}}{\mathrm{2}},\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}\right\} \\…
Question Number 197320 by tri26112004 last updated on 13/Sep/23 $$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\right)^{{k}\left({k}+\mathrm{1}\right)} \\ $$ Answered by Erico last updated on 13/Sep/23 $$\forall\mathrm{k}\in\left[\mathrm{1},\mathrm{n}\right]\:\:\:\:\:\left(−\mathrm{1}\right)^{\mathrm{k}\left(\mathrm{k}+\mathrm{1}\right)} =\mathrm{1} \\ $$$$\Rightarrow\:\underset{\mathrm{k}=\mathrm{1}}…
Question Number 197272 by Erico last updated on 12/Sep/23 $$\mathrm{How}\:\mathrm{to}\:\mathrm{calculate}\:\mathrm{this}\:\mathrm{integral} \\ $$$$\underset{\:\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{ln}\left(\mathrm{1}+{sint}\right)}{{sint}}{dt} \\ $$ Answered by Mathspace last updated on 12/Sep/23 $${tan}\left(\frac{{t}}{\mathrm{2}}\right)={x}\:\Rightarrow \\…
Question Number 197274 by sonukgindia last updated on 12/Sep/23 Commented by TheHoneyCat last updated on 18/Sep/23 Can you please provide the definitions on these factorials? (I only know "n!") Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 197299 by bbbbbbbb last updated on 12/Sep/23 $$\sqrt[{\mathrm{6}}]{−\mathrm{64}}−\sqrt[{\mathrm{10}}]{−\mathrm{10}}=? \\ $$$$\boldsymbol{{I}}\:\boldsymbol{\mathrm{need}}\:\boldsymbol{\mathrm{so}}\:\boldsymbol{\mathrm{much}}\:\boldsymbol{\mathrm{plz}} \\ $$ Answered by Frix last updated on 13/Sep/23 $$\forall{n}\in\mathbb{N}\backslash\left\{\mathrm{0}\right\}:\:−{n}={n}\mathrm{e}^{\mathrm{i}\pi} \:\Rightarrow \\ $$$$\sqrt[{{k}}]{−{n}}=\sqrt[{{k}}]{{n}}\mathrm{e}^{\mathrm{i}\frac{\pi}{{k}}}…
Question Number 197290 by sonukgindia last updated on 12/Sep/23 Commented by mahdipoor last updated on 12/Sep/23 $${log}_{\mathrm{7}} {A}={log}_{\mathrm{7}} \left(\frac{\mathrm{36}}{\mathrm{9}}\right)\Rightarrow{A}=\mathrm{4}\Rightarrow{log}_{\mathrm{2}} {A}=\mathrm{2} \\ $$ Terms of Service…
Question Number 197245 by sonukgindia last updated on 11/Sep/23 Commented by mr W last updated on 26/Sep/23 $${see}\:{Q}#\mathrm{197680} \\ $$ Terms of Service Privacy Policy…
Question Number 197252 by sciencestudentW last updated on 11/Sep/23 $$\mathrm{lo}\underset{{a}} {\mathrm{g}}{x}=\mathrm{30} \\ $$$$\mathrm{lo}\underset{{b}} {\mathrm{g}}{x}=\mathrm{70} \\ $$$$\mathrm{lo}\underset{{ab}} {\mathrm{g}}{x}=?\:\:\: \\ $$ Answered by AST last updated on…