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Show-that-1-i-x-2-x-has-no-nonzero-integral-solution-

Question Number 167928 by Mastermind last updated on 29/Mar/22 $${Show}\:{that}\:\mid\mathrm{1}−{i}\mid^{{x}} =\mathrm{2}^{{x}} \:{has}\:{no}\:{nonzero}\:{integral}\:{solution}\: \\ $$ Answered by MJS_new last updated on 30/Mar/22 $$\mid\mathrm{1}−\mathrm{i}\mid=\sqrt{\mathrm{2}};\:\mid\mathrm{1}−\mathrm{i}\mid^{{x}} =\left(\sqrt{\mathrm{2}}\right)^{{x}} =\mathrm{2}^{\frac{{x}}{\mathrm{2}}} \\…

now-the-way-is-clear-also-try-this-one-cos-x-sin-2-x-sin-2x-dx-

Question Number 36814 by MJS last updated on 06/Jun/18 $$\mathrm{now}\:\mathrm{the}\:\mathrm{way}\:\mathrm{is}\:\mathrm{clear},\:\mathrm{also}\:\mathrm{try}\:\mathrm{this}\:\mathrm{one}: \\ $$$$\int\frac{\mathrm{cos}\:{x}}{\mathrm{sin}^{\mathrm{2}} \:{x}\:\sqrt{\mathrm{sin}\:\mathrm{2}{x}}}{dx} \\ $$ Answered by math1967 last updated on 06/Jun/18 $$\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\int\frac{{cosx}}{{sin}^{\mathrm{2}} {x}\sqrt{\mathrm{sin}\:{x}\mathrm{cos}\:{x}}}{dx} \\…

Calculate-I-1-x-1-x-1-x-dx-Indication-poser-t-1-x-1-x-

Question Number 167882 by LEKOUMA last updated on 28/Mar/22 $${Calculate} \\ $$$${I}=\int\frac{\mathrm{1}}{{x}}\left(\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}\right){dx} \\ $$$${Indication}\:{poser}\:{t}=\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}} \\ $$ Answered by ArielVyny last updated on 29/Mar/22 $${t}=\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}\rightarrow{dt}=\frac{−\frac{\mathrm{2}}{\left(\mathrm{1}+{x}\right)^{\mathrm{2}} }}{\mathrm{2}{t}}{dx}=−\frac{\mathrm{1}}{\left(\mathrm{1}+{x}\right)^{\mathrm{2}}…