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Author: Tinku Tara

Question-84496

Question Number 84496 by bshahid010@gmail.com last updated on 13/Mar/20 Commented by mathmax by abdo last updated on 13/Mar/20 $${I}\:=\int\:\:\frac{{arcsinx}}{{x}^{\mathrm{2}} }{dx}\:\:{by}\:{parts}\:\:{u}^{'} =\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\:{and}\:{v}={arcsinx}\:\Rightarrow \\ $$$${I}\:=−\frac{{arsinx}}{{x}}\:−\int−\frac{\mathrm{1}}{{x}}\:×\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx}…

Find-a-closed-form-a-R-and-a-0-a-0-x-4-1-x-2-1-a-4-x-4-dx-

Question Number 150034 by mathdanisur last updated on 08/Aug/21 $$\mathrm{Find}\:\boldsymbol{\mathrm{a}}\:\mathrm{closed}\:\mathrm{form}:\:\:\boldsymbol{\mathrm{a}}\in\mathbb{R}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{a}}\neq\mathrm{0} \\ $$$$\Omega\left(\mathrm{a}\right)=\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\frac{\mathrm{x}^{\mathrm{4}} }{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)\left(\mathrm{1}+\mathrm{a}^{\mathrm{4}} \mathrm{x}^{\mathrm{4}} \right)}\:\mathrm{dx} \\ $$ Answered by mathmax by abdo…

Calcular-8-2-8-2-8-

Question Number 150029 by mathdanisur last updated on 08/Aug/21 $$\mathrm{Calcular}: \\ $$$$\sqrt{\mathrm{8}\:+\:\mathrm{2}\sqrt{\mathrm{8}\:+\:\mathrm{2}\sqrt{\mathrm{8}\:+\:…}}}\:=\:? \\ $$ Answered by nimnim last updated on 08/Aug/21 $$\mathrm{Let}\:\sqrt{\mathrm{8}+\mathrm{2}\sqrt{\mathrm{8}+\mathrm{2}\sqrt{\mathrm{8}+……}}}=\mathrm{x} \\ $$$$\Rightarrow\sqrt{\mathrm{8}+\mathrm{2x}}=\mathrm{x} \\…

lim-x-pi-3-sin-x-pi-3-1-2cos-x-

Question Number 84492 by john santu last updated on 13/Mar/20 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{3}}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left({x}−\frac{\pi}{\mathrm{3}}\right)}{\mathrm{1}−\mathrm{2cos}\:\left({x}\right)}\:=\: \\ $$ Commented by john santu last updated on 13/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left({x}\right)}{\mathrm{1}−\mathrm{2cos}\:\left({x}+\frac{\pi}{\mathrm{3}}\right)}\:= \\…

Roll-a-fair-die-twice-and-define-A-to-be-event-that-the-sum-of-the-scores-showing-up-is-greater-than-7-B-be-the-event-that-the-sum-of-the-scores-showing-up-is-a-multiple-of-3-and-C-be-the-event-that-

Question Number 150030 by jlewis last updated on 08/Aug/21 $$\mathrm{Roll}\:\mathrm{a}\:\mathrm{fair}\:\mathrm{die}\:\mathrm{twice}\:\mathrm{and}\:\mathrm{define}\:\mathrm{A}\:\mathrm{to}\:\mathrm{be} \\ $$$$\mathrm{event}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{scores}\:\mathrm{showing} \\ $$$$\mathrm{up}\:\mathrm{is}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{7},\:\mathrm{B}\:\mathrm{be}\:\mathrm{the}\:\mathrm{event}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{scores}\:\mathrm{showing}\:\mathrm{up}\:\mathrm{is}\:\mathrm{a} \\ $$$$\mathrm{multiple}\:\mathrm{of}\:\mathrm{3}\:\mathrm{and}\:\mathrm{C}\:\mathrm{be}\:\mathrm{the}\:\mathrm{event}\:\mathrm{that} \\ $$$$\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{scores}\:\mathrm{showing}\:\mathrm{up}\:\mathrm{is}\:\mathrm{a} \\ $$$$\mathrm{prime}\:\mathrm{number}.\:\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{events}\: \\ $$$$\mathrm{A},\mathrm{B}\:\mathrm{and}\:\mathrm{C}\:\mathrm{are}\:\mathrm{independent}\:\mathrm{event}? \\…

Find-the-number-of-numbers-10-8-which-are-neither-perfect-squares-nor-perfect-cubes-nor-perfect-fifth-powers-

Question Number 18949 by Tinkutara last updated on 01/Aug/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{numbers}\:\leqslant\:\mathrm{10}^{\mathrm{8}} \\ $$$$\mathrm{which}\:\mathrm{are}\:\mathrm{neither}\:\mathrm{perfect}\:\mathrm{squares},\:\mathrm{nor} \\ $$$$\mathrm{perfect}\:\mathrm{cubes},\:\mathrm{nor}\:\mathrm{perfect}\:\mathrm{fifth}\:\mathrm{powers}. \\ $$ Commented by prakash jain last updated on 03/Aug/17 $$\mathrm{i}\:\mathrm{retyped}\:\mathrm{the}\:\mathrm{answer}.…