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If-213-4x-2-2-12-x-2-11-find-the-value-of-213-4x-2-2-12-x-2-

Question Number 124423 by ZiYangLee last updated on 03/Dec/20 $$\mathrm{If}\:\sqrt{\mathrm{213}−\mathrm{4}{x}^{\mathrm{2}} }−\mathrm{2}\sqrt{\mathrm{12}−{x}^{\mathrm{2}} }=\mathrm{11}, \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\sqrt{\mathrm{213}−\mathrm{4}{x}^{\mathrm{2}} }+\mathrm{2}\sqrt{\mathrm{12}−{x}^{\mathrm{2}} }. \\ $$ Commented by ZiYangLee last updated on 03/Dec/20…

Question-124406

Question Number 124406 by joki last updated on 03/Dec/20 Answered by Bird last updated on 03/Dec/20 $${let}\:{decompose}\:{F}\left({x}\right)=\frac{{x}+\mathrm{3}}{\left({x}−\mathrm{1}\right)^{\mathrm{2}} \left({x}+\mathrm{4}\right)} \\ $$$${F}\left({x}\right)=\frac{{a}}{{x}−\mathrm{1}}+\frac{{b}}{\left({x}−\mathrm{1}\right)^{\mathrm{2}} }+\frac{{c}}{{x}+\mathrm{4}} \\ $$$${b}=\left({x}−\mathrm{1}\right)^{\mathrm{2}} {F}\left({x}\right)\mid_{{x}=\mathrm{1}} \:\:=\frac{\mathrm{4}}{\mathrm{5}}…

2xdx-1-x-4-

Question Number 124398 by bounhome last updated on 03/Dec/20 $$\int\frac{\mathrm{2}{xdx}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{4}} }}=? \\ $$ Answered by Dwaipayan Shikari last updated on 03/Dec/20 $$\int\frac{\mathrm{2}{xdx}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{4}} }}\:\:\:\:\:\:\:{x}^{\mathrm{2}} ={t}\Rightarrow\mathrm{2}{x}=\frac{{dt}}{{dx}} \\…