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Author: Tinku Tara

Integrate-x-sec-2-x-2-

Question Number 6841 by Tawakalitu. last updated on 30/Jul/16 $${Integrate}:\:\:{x}\:{sec}^{\mathrm{2}} \left({x}^{\mathrm{2}} \right) \\ $$$$ \\ $$ Commented by Tawakalitu. last updated on 30/Jul/16 $${I}\:{have}\:{solve}\:{this}\:{one}.\:{i}\:{got}\:…\:\:\:\frac{\mathrm{1}}{\mathrm{2}}\:{tan}\left({x}^{\mathrm{2}} \right)\:+\:{C}…

a-Z-2a-3-3a-2-3a-7-a-2-a-2-1-a-3k-1-k-Z-

Question Number 6834 by nburiburu last updated on 30/Jul/16 $${a}\in\mathbb{Z},\:\left(\mathrm{2}{a}^{\mathrm{3}} +\mathrm{3}{a}^{\mathrm{2}} −\mathrm{3}{a}+\mathrm{7}\::\:{a}^{\mathrm{2}} +{a}−\mathrm{2}\right)\neq\mathrm{1}\:\Leftrightarrow\:{a}=\mathrm{3}{k}+\mathrm{1},\:{k}\in\mathbb{Z} \\ $$ Commented by Yozzii last updated on 30/Jul/16 $${All}\:{integers}\:{can}\:{be}\:{written}\:{in}\:{one} \\ $$$${of}\:{the}\:{following}\:{forms}\:{since}…

Question-137907

Question Number 137907 by peter frank last updated on 08/Apr/21 Answered by EnterUsername last updated on 08/Apr/21 $$\int_{\mathrm{1}} ^{{e}} \frac{\mathrm{1}+{lnx}}{{x}}{dx}=\int_{\mathrm{1}} ^{{e}} \left(\frac{\mathrm{1}}{{x}}+\frac{{lnx}}{{x}}\right){dx} \\ $$$$=\left[{lnx}+\frac{{ln}^{\mathrm{2}} {x}}{\mathrm{2}}\right]_{\mathrm{1}}…