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Question-129378

Question Number 129378 by BHOOPENDRA last updated on 15/Jan/21 Answered by Dwaipayan Shikari last updated on 15/Jan/21 $$\mathscr{L}\left({ut}^{\mathrm{2}} {e}^{−\mathrm{2}{t}} −{ute}^{−\mathrm{2}{t}} \right)={u}\int_{\mathrm{0}} ^{\infty} {t}^{\mathrm{2}} {e}^{−\left({s}+\mathrm{2}\right){t}} −{u}\int_{\mathrm{0}}…

0-1-e-x-2-dx-1-1-1-2-3-2-7-10-2-32-42-2-174-216-2-1196-1312-2-

Question Number 129376 by Dwaipayan Shikari last updated on 15/Jan/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} {e}^{−{x}^{\mathrm{2}} } {dx}=\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{3}^{\mathrm{2}} }{\mathrm{7}+\frac{\mathrm{10}^{\mathrm{2}} }{\mathrm{32}+\frac{\mathrm{42}^{\mathrm{2}} }{\mathrm{174}+\frac{\mathrm{216}^{\mathrm{2}} }{\mathrm{1196}+\frac{\mathrm{1312}^{\mathrm{2}} }{….}}}}}}} \\ $$ Commented by Dwaipayan…

x-x-1-dx-

Question Number 129377 by pipin last updated on 15/Jan/21 $$\int\frac{\:\sqrt{\boldsymbol{\mathrm{x}}}}{\:\sqrt{\boldsymbol{\mathrm{x}}-\mathrm{1}}}\mathrm{dx}\:=\:… \\ $$ Answered by Ar Brandon last updated on 15/Jan/21 $$\mathcal{I}=\int\frac{\sqrt{\mathrm{x}}}{\:\sqrt{\mathrm{x}−\mathrm{1}}}\mathrm{dx}\:,\:\mathrm{x}=\mathrm{t}^{\mathrm{2}} \:\Rightarrow\mathrm{dx}=\mathrm{2tdt} \\ $$$$\:\:\:=\mathrm{2}\int\frac{\mathrm{t}^{\mathrm{2}} }{\:\sqrt{\mathrm{t}^{\mathrm{2}}…

Question-129364

Question Number 129364 by shaker last updated on 15/Jan/21 Answered by mindispower last updated on 15/Jan/21 $${let}\:\alpha={e}^{{i}\frac{\pi}{\mathrm{4}}} \\ $$$$\alpha,\alpha^{\mathrm{3}} ,\alpha^{\mathrm{5}} ,\alpha^{\mathrm{7}} \:{are}\:{roots}\:{of}\:{x}^{\mathrm{4}} +\mathrm{1}=\mathrm{0} \\ $$$$\frac{{x}^{\mathrm{2}}…

sin-a-sin-b-1-3-cos-a-cos-b-5-3-cos-2-a-b-

Question Number 129360 by bramlexs22 last updated on 15/Jan/21 $$\begin{cases}{\mathrm{sin}\:{a}\:+\:\mathrm{sin}\:{b}\:=\:\frac{\mathrm{1}}{\mathrm{3}}}\\{\mathrm{cos}\:{a}+\mathrm{cos}\:{b}\:=\:\frac{\mathrm{5}}{\mathrm{3}}}\end{cases} \\ $$$$\:\:\:\:\mathrm{cos}^{\mathrm{2}} \:\left({a}+{b}\right)\:=?\: \\ $$ Commented by bramlexs22 last updated on 15/Jan/21 $$\:\mathrm{nice}\:\mathrm{trigonometry} \\ $$…