Category: Algebra

Question Number 211879 by Spillover last updated on 23/Sep/24 Answered by BHOOPENDRA last updated on 23/Sep/24 $$=\:\frac{\left({x}−\mathrm{4}\right)}{\mathrm{10}\left({x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{5}\right)}\:+\frac{\mathrm{1}}{\mathrm{10}}\int\:\frac{{x}−\mathrm{4}}{{x}^{\mathrm{3}} −\mathrm{4}{x}^{\mathrm{2}} +\mathrm{5}{x}}\:\left({by}\:{ostrogradsky}'{s}\:{method}\right) \\ $$$$\:\:=\frac{{x}−\mathrm{4}}{\mathrm{10}\left({x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{5}\right)}+\frac{\mathrm{1}}{\mathrm{10}}\left[\int\frac{\mathrm{4}{x}−\mathrm{11}}{\mathrm{5}\left({x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{5}\right)}{dx}−\int\frac{\mathrm{4}}{\mathrm{5}{x}}\:{dx}\right] \\…

Question Number 211859 by xumoyiddin last updated on 22/Sep/24 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 211796 by Spillover last updated on 21/Sep/24 Answered by Ghisom last updated on 21/Sep/24 $$\int\sqrt{\frac{\mathrm{cos}\:\left({x}−{a}\right)}{\mathrm{sin}\:\left({x}+{a}\right)}}{dx}= \\ $$$$=\int\sqrt{\frac{\mathrm{cos}\:{a}\:\mathrm{cos}\:{x}\:+\mathrm{sin}\:{a}\:\mathrm{sin}\:{x}}{\mathrm{sin}\:{a}\:\mathrm{cos}\:{x}\:+\mathrm{cos}\:{a}\:\mathrm{sin}\:{x}}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{tan}\:{x}\right] \\ $$$$=\int\sqrt{\frac{{t}\mathrm{sin}\:{a}\:+\mathrm{cos}\:{a}}{{t}\mathrm{cos}\:{a}\:+\mathrm{sin}\:{a}}}×\frac{{dt}}{{t}^{\mathrm{2}} +\mathrm{1}}= \\…

Question Number 211797 by Spillover last updated on 21/Sep/24 Answered by Ghisom last updated on 21/Sep/24 $$\int\frac{\sqrt{\mathrm{cot}\:{x}}−\sqrt{\mathrm{tan}\:{x}}}{\mathrm{1}+\mathrm{3sin}\:\mathrm{2}{x}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{\mathrm{tan}\:{x}}\right] \\ $$$$=−\mathrm{2}\int\frac{{t}^{\mathrm{2}} −\mathrm{1}}{{t}^{\mathrm{4}} +\mathrm{6}{t}^{\mathrm{2}} +\mathrm{1}}{dt}= \\…

Question Number 211793 by Abelrodas last updated on 20/Sep/24 Terms of Service Privacy Policy Contact: info@tinkutara.com