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Question Number 76575 by Rio Michael last updated on 28/Dec/19 $${define}\:{the}\:{concept}\:{of}\:{a}\:\boldsymbol{{contingency}} \\ $$$${Which}\:{of}\:{the}\:{following}\:{is}\:{a}\:{contingency}\: \\ $$$${and}\:{which}\:{is}\:{a}\:{tautology} \\ $$$$\left.\mathrm{1}\right)\:\left({P}\:\Rightarrow\sim{P}\right)\:\vee\:{Q}\:\: \\ $$$$\left.\mathrm{2}\right)\:\left({P}\:\Rightarrow\:\sim{P}\right)\:\Rightarrow\:{Q} \\ $$ Answered by benjo 1/2…

Question Number 142100 by ZiYangLee last updated on 26/May/21 $$\:\:\:\:\:\:\int^{\:} \:\frac{\mathrm{1}}{\mathrm{1}+\sqrt{\mathrm{1}+{t}}\:}\:{dt}=? \\ $$ Answered by iloveisrael last updated on 26/May/21 $${I}=\int\:\frac{{dt}}{\mathrm{1}+\sqrt{\mathrm{1}+{t}}}\:=\:\int\:\frac{\mathrm{1}−\sqrt{\mathrm{1}+{t}}}{−{t}}\:{dt} \\ $$$${I}=\int\:\frac{\sqrt{\mathrm{1}+{t}}}{{t}}\:{dt}\:−\mathrm{ln}\:{t}\:+{c} \\ $$$${let}\:\sqrt{\mathrm{1}+{t}}\:=\:{u}\Rightarrow{t}={u}^{\mathrm{2}}…

Question Number 11020 by ridwan balatif last updated on 07/Mar/17 Answered by sandy_suhendra last updated on 08/Mar/17 Commented by sandy_suhendra last updated on 08/Mar/17 $$\left.\mathrm{1}\right)\:\mathrm{P}\left(−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{A}\:,\:−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{B}\right)\:=\:\mathrm{P}\left(\mathrm{5},\mathrm{7}\right)…

Question Number 11019 by ridwan balatif last updated on 07/Mar/17 Answered by bahmanfeshki last updated on 07/Mar/17 $${I}=\int_{\mathrm{2}} ^{{n}} {xe}^{−\mathrm{2}{x}+\mathrm{4}} \:{dx}=−\frac{\mathrm{1}}{\mathrm{2}}\left(\left[{xe}^{−\mathrm{2}{x}+\mathrm{4}} \right]_{\mathrm{2}} ^{{n}} −\int_{\mathrm{2}\:\:} ^{{n}}…

Question Number 11011 by madscientist last updated on 06/Mar/17 $${if}\:{tan}\left({xy}\right)={x}\:{then}\:\frac{{dy}}{{dx}}= \\ $$ Answered by mrW1 last updated on 06/Mar/17 $${xy}=\mathrm{tan}^{−\mathrm{1}} \:{x} \\ $$$${y}=\frac{\mathrm{tan}^{−\mathrm{1}} \:{x}}{{x}} \\…