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Author: Tinku Tara

Question-125593

Question Number 125593 by shaker last updated on 12/Dec/20 Answered by MJS_new last updated on 12/Dec/20 $$\int\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}\right)^{\mathrm{2}} }= \\ $$$$\:\:\:\:\:\left[\mathrm{Ostrogradski}'\mathrm{s}\:\mathrm{Method}\:\left({search}\:{the}\:{www}\:{for}\:{it}\right)\right] \\ $$$$=\frac{{x}+\mathrm{1}}{\mathrm{2}\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}\right)}+\frac{\mathrm{1}}{\mathrm{2}}\int\frac{{dx}}{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}}=…

Question-60056

Question Number 60056 by bhanukumarb2@gmail.com last updated on 17/May/19 Commented by maxmathsup by imad last updated on 17/May/19 $${we}\:{see}\:{that}\:\:{S}\:=\sum_{{k}=\mathrm{0}} ^{\infty} \:\frac{{sin}\left({k}\theta\right){cos}^{{k}} \theta}{{k}!}\:\Rightarrow{S}\:={Im}\left(\sum_{{k}=\mathrm{0}} ^{\infty} \:\frac{{e}^{{ik}\theta} \:{cos}^{{k}}…

Question-191126

Question Number 191126 by Mingma last updated on 18/Apr/23 Commented by mahdipoor last updated on 18/Apr/23 $$\mathrm{4}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} +\mathrm{1}^{\mathrm{2}} −\frac{\mathrm{4}\left(\mathrm{4}+\mathrm{3}+\mathrm{2}+\mathrm{1}\right)}{\mathrm{2}} \\ $$ Terms of…

1-1-2-1-2-2-1-3-2-1-4-2-1-1-2-1-2-2-1-3-2-

Question Number 125585 by Dwaipayan Shikari last updated on 12/Dec/20 $$\frac{\left(\frac{\mathrm{1}}{\mathrm{1}!}\right)^{\mathrm{2}} −\left(\frac{\mathrm{1}}{\mathrm{2}!}\right)^{\mathrm{2}} +\left(\frac{\mathrm{1}}{\mathrm{3}!}\right)^{\mathrm{2}} −\left(\frac{\mathrm{1}}{\mathrm{4}!}\right)^{\mathrm{2}} +…\:}{\left(\frac{\mathrm{1}}{\mathrm{1}!}\right)^{\mathrm{2}} +\left(\frac{\mathrm{1}}{\mathrm{2}!}\right)^{\mathrm{2}} +\left(\frac{\mathrm{1}}{\mathrm{3}!}\right)^{\mathrm{2}} +……} \\ $$ Commented by Dwaipayan Shikari last…