Category: Algebra

Question Number 32524 by Bindugirish107@gmail.com last updated on 27/Mar/18 $$\frac{1}{2}{x}^2+\sqrt{2}=$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 163587 by HongKing last updated on 08/Jan/22 Answered by MJS_new last updated on 08/Jan/22 $$\int \frac{x}{(x+1)(x^2+1)(a^2{x}^2+1)}dx=$$$$=−\frac{\mathrm{1}}{\mathrm{2}\left({a}^{\mathrm{2}} +\mathrm{1}\right)}\int\frac{{dx}}{{x}+\mathrm{1}}−\frac{\mathrm{1}}{\mathrm{2}\left({a}^{\mathrm{2}} −\mathrm{1}\right)}\int\frac{{x}+\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}{dx}+\frac{{a}^{\mathrm{2}}…

Question Number 163576 by cortano1 last updated on 08/Jan/22 $$Whatisthecoefficientof{x}^{2020}$$$$in{(1+x+x^2+x^3+\dots +x^{2020})}^{2021}$$ Answered by bobhans last updated on 08/Jan/22 $$\:\:\:\mathrm{f}\left(\mathrm{x}\right)=\left(\mathrm{1}+\mathrm{x}+\mathrm{x}^{\mathrm{2}}…

Question Number 163564 by HongKing last updated on 07/Jan/22 $$\mathrm{Find}\mathrm{the}\mathrm{closed}\mathrm{form}\mathrm{of}\mathrm{a}\mathrm{integral}:$$$$\mathbf{\Omega }=\underset{\frac{\mathit{\pi }}{2}}{\stackrel{\mathit{\pi }}{\int }}\frac{\mathrm{dx}}{{\mathrm{e}}^{\mathbf{x}}+\ln \left(\cos \mathbf{x}\right)}$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 163536 by HongKing last updated on 07/Jan/22 $$\mathrm{Prove}\mathrm{that}:$$$$\underset{9}{\stackrel{1}{\int }}\frac{\ln (1+\mathrm{x})}{1+{\mathrm{x}}^2}\mathrm{dx}=\frac{\pi \cdot \ln \left(2\right)}{8}$$ Answered by Ar Brandon last updated on 07/Jan/22…