Category: Algebra

Question Number 160398 by HongKing last updated on 29/Nov/21 $$\mathrm{Find}:$$$$\mathbf{\Omega }=\underset{0}{\stackrel{\mathrm{\infty }}{\int }}\frac{\log (\mathrm{x}+1)}{{\mathrm{x}}^3+1}\mathrm{dx}$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 160373 by HongKing last updated on 28/Nov/21 $$\mathrm{Compare}\mathrm{it}:$$$$\frac{1-\sin \left(10°\right)}{\cos \left(10°\right)}\mathrm{and}1$$ Answered by ghimisi last updated on 28/Nov/21 $$\frac{sin90-sin10}{cos10}=\frac{2sin40cos50}{sin80}=$$$$\frac{\mathrm{2}{sin}\mathrm{40}{sin}\mathrm{40}}{\mathrm{2}{sin}\mathrm{40}{cos}\mathrm{40}}={tg}\mathrm{40}<{tg}\mathrm{45}=\mathrm{1} \…

Question Number 94835 by Jidda28 last updated on 21/May/20 $$\mathrm{proof}\mathrm{or}\mathrm{disproof}\mathrm{that}\mathrm{if}\mathrm{a}\mathrm{quotient}$$$$\mathrm{group}\frac{\mathrm{G}}{\mathrm{H}}\mathrm{is}\mathrm{abelian}\mathrm{then}\mathrm{G}\mathrm{must}\mathrm{be}\mathrm{abelian}.$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 94811 by Abdulrahman last updated on 21/May/20 $$\int \frac{\mathrm{dx}}{\mathrm{x}+\sqrt{\mathrm{x}}}(2,3)=?$$ Answered by ElOuafi last updated on 21/May/20 $$\int \frac{dx}{x+\sqrt{x}}=\int \frac{dx}{\sqrt{x}(\sqrt{x}+1)}=\int \frac{\frac{2}{2\sqrt{x}}}{\sqrt{x}+1}dx=2\int \frac{d(\sqrt{x}+1)}{\sqrt{x}+1}$$$$putu=\sqrt{x}+1\Rightarrow =2\int \frac{du}{u}$$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{2}{ln}\left(\sqrt{{x}}+\mathrm{1}\right)+{c} \…

Question Number 160342 by alf123 last updated on 28/Nov/21 Answered by Rasheed.Sindhi last updated on 28/Nov/21 $$4^x=6;\frac{8^x+8^{-x}}{4^x+4^{-x}}=?$$$$\mathrm{8}=\mathrm{4}^{\frac{\mathrm{3}}{\mathrm{2}}} \…