Question Number 22623 by tawa tawa last updated on 21/Oct/17 $$\mathrm{How}\:\mathrm{is}:\:\:\:\int\:\frac{\mathrm{x}\:+\:\mathrm{sin}\left(\mathrm{x}\right)}{\mathrm{1}\:+\:\mathrm{cos}\left(\mathrm{x}\right)}\:\mathrm{dx}\:=\:\mathrm{xtan}\left(\frac{\mathrm{x}}{\mathrm{2}}\right)\:+\:\mathrm{C} \\ $$ Answered by vajpaithegrate@gmail.com last updated on 21/Oct/17 $$\int\frac{\mathrm{x}+\mathrm{2sin}\:\frac{\mathrm{x}}{\mathrm{2}}\mathrm{cos}\:\frac{\mathrm{x}}{\mathrm{2}}}{\mathrm{2cos}\:^{\mathrm{2}} \frac{\mathrm{x}}{\mathrm{2}}}\mathrm{dx}\:\: \\ $$$$\int\frac{\mathrm{x}}{\mathrm{2cos}^{\mathrm{2}} \frac{\mathrm{x}}{\mathrm{2}}}+\frac{\mathrm{2sin}\:\frac{\mathrm{x}}{\mathrm{2}}\mathrm{cos}\:\frac{\mathrm{x}}{\mathrm{2}}}{\mathrm{2cos}\:^{\mathrm{2}}…
Question Number 22621 by vajpaithegrate@gmail.com last updated on 21/Oct/17 $$\int\frac{\mathrm{dx}}{\left(\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }−\mathrm{x}\right)^{\mathrm{n}} }\left(\mathrm{n}\neq\mathrm{1}\right)=\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{z}^{\mathrm{n}+\mathrm{1}} }{\mathrm{n}+\mathrm{1}}+\frac{\mathrm{z}^{\mathrm{n}−\mathrm{1}} }{\mathrm{n}−\mathrm{1}}\right)+\mathrm{cccccc} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{where}\:\:\mathrm{z}=? \\ $$$$ \\ $$ Terms of Service Privacy Policy…
Question Number 22618 by Tinkutara last updated on 21/Oct/17 $${If}\:\left(\mathrm{1}\:+\:{x}\right)^{{n}} \:=\:{C}_{\mathrm{0}} \:+\:{C}_{\mathrm{1}} {x}\:+\:{C}_{\mathrm{2}} {x}^{\mathrm{2}} \:+\:{C}_{\mathrm{3}} {x}^{\mathrm{3}} \\ $$$$+\:…\:+\:{C}_{{n}} {x}^{{n}} ,\:{prove}\:{that} \\ $$$$\frac{\mathrm{2}^{\mathrm{2}} }{\mathrm{1}.\mathrm{2}}{C}_{\mathrm{0}} \:+\:\frac{\mathrm{2}^{\mathrm{3}} }{\mathrm{2}.\mathrm{3}}{C}_{\mathrm{1}}…
Question Number 88153 by Chi Mes Try last updated on 08/Apr/20 Commented by Prithwish Sen 1 last updated on 08/Apr/20 $$\mathrm{sin}^{−\mathrm{1}} \mathrm{e}^{\mathrm{x}} \:+\:\mathrm{sec}^{−\mathrm{1}} \left(\mathrm{e}^{−\mathrm{x}} \right)\:=\:\mathrm{sin}^{−\mathrm{1}}…
Question Number 153685 by roxceefocus last updated on 09/Sep/21 Commented by liberty last updated on 09/Sep/21 $${f}\left({x}\right)=\mathrm{2}{x}^{\mathrm{3}} +\mathrm{5}{x}^{\mathrm{2}} +\mathrm{7}{x}+\mathrm{11} \\ $$$${divided}\:{by}\:{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{1} \\ $$$${By}\:{Horner} \\…
Question Number 22612 by Tinkutara last updated on 21/Oct/17 $${In}\:{the}\:{binomial}\:{expasion}\:{of}\:\left({a}\:−\:{b}\right)^{\mathrm{5}} , \\ $$$${the}\:{sum}\:{of}\:\mathrm{2}^{{nd}} \:{and}\:\mathrm{3}^{{rd}} \:{term}\:{is}\:{zero}, \\ $$$${then}\:\frac{{a}}{{b}}\:{is} \\ $$ Answered by ajfour last updated on…
Question Number 153681 by EDWIN88 last updated on 09/Sep/21 $$\:\:\mathrm{24}^{\mathrm{log}\:_{\mathrm{10}} \left({x}\right)} −\mathrm{26}^{\mathrm{log}\:_{\mathrm{10}} \left({x}\right)} =\mathrm{1} \\ $$$$\:{x}=? \\ $$ Answered by MJS_new last updated on 09/Sep/21…
Question Number 153682 by EDWIN88 last updated on 09/Sep/21 $$\:\left(\sqrt[{{i}}]{{i}}\:\right)^{{xi}} \:=\:{i}^{{x}} \: \\ $$$$\:\:{x}=?\: \\ $$ Answered by MJS_new last updated on 09/Sep/21 $$\mathrm{lhs}\:\mathrm{i}=\mathrm{e}^{\mathrm{i}\frac{\pi}{\mathrm{2}}} \:\Rightarrow\:\sqrt[{\mathrm{i}}]{\mathrm{i}}=\mathrm{e}^{\frac{\pi}{\mathrm{2}}}…
Question Number 153676 by SANOGO last updated on 09/Sep/21 Answered by som(math1967) last updated on 09/Sep/21 $$\mathrm{1}.\:\boldsymbol{{a}}>\mathrm{0},\boldsymbol{{b}}>\mathrm{0} \\ $$$$\:\left(\boldsymbol{{a}}−\boldsymbol{{b}}\right)^{\mathrm{2}} \geqslant\mathrm{0}\:\:\:\left[\boldsymbol{{if}}\:\boldsymbol{{a}}=\boldsymbol{{b}}\:\boldsymbol{{then}}\left(\boldsymbol{{a}}−\boldsymbol{{b}}\right)=\mathrm{0}\right] \\ $$$$\Rightarrow\left(\boldsymbol{{a}}+\boldsymbol{{b}}\right)^{\mathrm{2}} −\mathrm{4}\boldsymbol{{ab}}\geqslant\mathrm{0} \\ $$$$\Rightarrow\:\left(\frac{\boldsymbol{{a}}+\boldsymbol{{b}}}{\mathrm{2}}\right)^{\mathrm{2}}…
Question Number 153679 by liberty last updated on 09/Sep/21 $${Find}\:{the}\:{constant}\:{of}\:{polynom} \\ $$$$\:{P}\left(\mathrm{11}{x}−\mathrm{2}\right)\:{if}\:{given}\:{the}\:{equation} \\ $$$$\mathrm{3}{P}\left({x}+\mathrm{2}\right)−{P}\left(\mathrm{2}{x}+\mathrm{3}\right)=−\mathrm{4}{x}^{\mathrm{2}} −{x}+\mathrm{3} \\ $$ Answered by EDWIN88 last updated on 09/Sep/21 Commented…