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Author: Tinku Tara

I-Find-Fun-integral-problem-x-dx-1-note-I-already-know-that-integral-Solution-Try-integral-problem-Product-Integral-Integral-

Question Number 218534 by SdC355 last updated on 11/Apr/25 $$\mathrm{I}\:\mathrm{Find}\:\mathrm{Fun}\:\mathrm{integral}\:\mathrm{problem}! \\ $$$$\int\:\:{x}^{\mathrm{d}{x}} −\mathrm{1}\:=??\: \\ $$$$\left.\mathrm{note}\right)\:\:\mathrm{I}\:\mathrm{already}\:\mathrm{know}\:\mathrm{that}\:\mathrm{integral}\:\mathrm{Solution} \\ $$$$\:\mathrm{Try}\:\mathrm{integral}\:\mathrm{problem}! \\ $$$$\left(#\:\mathrm{Product}\:\mathrm{Integral}\:,\:#\mathrm{Integral}\right) \\ $$ Terms of Service Privacy…

Question-218494

Question Number 218494 by Spillover last updated on 10/Apr/25 Answered by vnm last updated on 10/Apr/25 $$\frac{{R}}{\:\sqrt{{R}^{\mathrm{2}} +\left(\mathrm{2}{R}\right)^{\mathrm{2}} }}=\frac{{r}}{\:\sqrt{{R}^{\mathrm{2}} +\left(\mathrm{2}{R}\right)^{\mathrm{2}} }−\left({R}+{r}\right)} \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}}}=\frac{{r}}{\:{R}\sqrt{\mathrm{5}}−{R}−{r}}=\frac{{r}/{R}}{\:\sqrt{\mathrm{5}}−\mathrm{1}−{r}/{R}} \\ $$$$\sqrt{\mathrm{5}}=\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{{r}/{R}}−\mathrm{1}…

solve-for-real-x-3-x-5-5x-4-10x-3-10x-2-5x-x-2-2x-1-x-4-4x-2-4-3-

Question Number 218482 by Nicholas666 last updated on 10/Apr/25 $$ \\ $$$$\:\:\:\:{solve}\:{for}\:{real}\:\boldsymbol{{x}}; \\ $$$$ \\ $$$$\underset{\:\:\:\mathrm{3}\sqrt{\frac{\boldsymbol{{x}}^{\mathrm{5}} −\mathrm{5}\boldsymbol{{x}}^{\mathrm{4}} +\mathrm{10}\boldsymbol{{x}}^{\mathrm{3}} −\mathrm{10}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{5}\boldsymbol{{x}}}{\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{2}\boldsymbol{{x}}+\mathrm{1}}+\sqrt{\boldsymbol{{x}}^{\mathrm{4}} +\mathrm{4}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{4}}}=\sqrt{\mathrm{3}\:}\:\:\:} {\:} \\…

Solve-the-following-equation-for-the-real-x-value-x-4-4x-3-6x-2-4x-2-2x-4-8x-3-12x-2-8x-5-

Question Number 218473 by Nicholas666 last updated on 10/Apr/25 $$ \\ $$$$\:{Solve}\:{the}\:{following}\:{equation}\:{for}\:{the}\:{real}\:\boldsymbol{{x}}\:{value}; \\ $$$$\:{x}^{\mathrm{4}} −\mathrm{4}{x}^{\mathrm{3}} +\mathrm{6}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{2}\:=\:\sqrt{\mathrm{2}{x}^{\mathrm{4}} −\mathrm{8}{x}^{\mathrm{3}} +\mathrm{12}{x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{5}}\:\:\:\: \\ $$$$ \\ $$ Answered…