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Author: Tinku Tara

e-x-sin2x-dx-

Question Number 23108 by Kathie last updated on 26/Oct/17 $$\int\mathrm{e}^{−\mathrm{x}} \mathrm{sin2x}\:\mathrm{dx} \\ $$ Answered by sma3l2996 last updated on 26/Oct/17 $${I}=\int{e}^{−{x}} {sin}\mathrm{2}{xdx} \\ $$$${u}={sin}\mathrm{2}{x}\Rightarrow{u}'=\mathrm{2}{cos}\mathrm{2}{x} \\…

m-2-n-2-2mn-m-2-n-2-is-pythagorean-triplet-for-all-m-n-N-This-can-be-proved-easily-Is-the-vice-versa-of-the-statement-is-also-true-I-E-If-for-a-b-c-N-a-2-b

Question Number 23105 by Rasheed.Sindhi last updated on 26/Oct/17 $$\left(\mid\mathrm{m}^{\mathrm{2}} −\mathrm{n}^{\mathrm{2}} \mid,\mathrm{2mn},\mathrm{m}^{\mathrm{2}} +\mathrm{n}^{\mathrm{2}} \right)\:\mathrm{is}\:\mathrm{pythagorean} \\ $$$$\mathrm{triplet}\:\mathrm{for}\:\mathrm{all}\:\mathrm{m},\mathrm{n}\in\mathbb{N}.\:\mathrm{This}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{proved}\:\mathrm{easily}.\mathrm{Is}\:\mathrm{the}\:\mathrm{vice}\:\mathrm{versa}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{statement}\:\mathrm{is}\:\mathrm{also}\:\mathrm{true}? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}-\mathrm{E} \\ $$$$\mathrm{If}\:\:\mathrm{for}\:\mathrm{a},\mathrm{b},\mathrm{c}\in\mathbb{N}\:,\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}}…

show-tht-the-curve-with-parametric-equcations-x-t-2-y-t-3-9t-intersect-at-the-point-9-0-

Question Number 23104 by lizan 123 last updated on 26/Oct/17 $${show}\:{tht}\:{the}\:{curve}\:{with}\:{parametric}\:{equcations} \\ $$$${x}={t}^{\mathrm{2}} \:,{y}={t}^{\mathrm{3}} \:−\mathrm{9}{t}\:{intersect}\:{at}\:{the}\:{point}\:\left(\mathrm{9},\mathrm{0}\right). \\ $$ Answered by ajfour last updated on 26/Oct/17 $${y}={t}\left({t}^{\mathrm{2}}…

Question-154175

Question Number 154175 by daus last updated on 15/Sep/21 Commented by daus last updated on 15/Sep/21 integrate it Answered by EDWIN88 last updated on 15/Sep/21 $$\int\:\frac{\mathrm{32}{x}}{\left(\mathrm{2}{x}−\mathrm{1}\right)\left(\mathrm{2}{x}\:−\mathrm{3}\:\:\right)\left(\mathrm{2}{x}−\mathrm{5}\right)}\:{dx}…

Solve-3-x-27-x-18-

Question Number 23096 by tawa tawa last updated on 26/Oct/17 $$\mathrm{Solve}:\:\:\mathrm{3}^{\mathrm{x}\:} =\:\frac{\mathrm{27}}{\mathrm{x}}\:+\:\mathrm{18} \\ $$ Commented by Physics lover last updated on 26/Oct/17 $${i}\:{just}\:{used}\:{hit}\:{and}\:{trial}\:{method} \\ $$$${and}\:{got}\:{x}\:=\:\mathrm{3}…