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Question Number 55999 Answers: 0 Comments: 1

Question Number 55998 Answers: 1 Comments: 1

find f(x) =∫_0 ^1 arctan(t^2 +xt +1)dt .

$${find}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} {arctan}\left({t}^{\mathrm{2}} +{xt}\:+\mathrm{1}\right){dt}\:\:. \\ $$

Question Number 55997 Answers: 0 Comments: 0

calculate ∫_(π/3) ^(π/2) (dx/(x+sinx))

$${calculate}\:\int_{\frac{\pi}{\mathrm{3}}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{dx}}{{x}+{sinx}} \\ $$

Question Number 55996 Answers: 0 Comments: 1

find ∫_(π/3) ^(π/2) (x/(cosx))dx

$${find}\:\int_{\frac{\pi}{\mathrm{3}}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{x}}{{cosx}}{dx}\: \\ $$

Question Number 55995 Answers: 1 Comments: 1

find I =∫ arctan(1−x)dx and J =∫ actan(1+x) dx

$${find}\:{I}\:=\int\:\:{arctan}\left(\mathrm{1}−{x}\right){dx}\:\:{and}\:{J}\:=\int\:{actan}\left(\mathrm{1}+{x}\right)\:{dx} \\ $$

Question Number 55994 Answers: 1 Comments: 0

calculate ∫_0 ^1 arctan(x^2 −x)dx

$${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {arctan}\left({x}^{\mathrm{2}} −{x}\right){dx} \\ $$

Question Number 55992 Answers: 0 Comments: 2

1 + x + x^2 + . . . + x^(99) =0 need an explanation.

$$\mathrm{1}\:+\:{x}\:+\:{x}^{\mathrm{2}} \:+\:.\:.\:.\:+\:{x}^{\mathrm{99}} =\mathrm{0} \\ $$$${need}\:{an}\:{explanation}. \\ $$

Question Number 55991 Answers: 0 Comments: 2

Question Number 55987 Answers: 0 Comments: 0

Question Number 55980 Answers: 0 Comments: 1

Does the function f(x) = x^x have an antiderivative ? □ yes □ no How this may be proved ?

$${Does}\:{the}\:{function}\:{f}\left({x}\right)\:=\:{x}^{{x}} \:{have} \\ $$$${an}\:{antiderivative}\:? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Box\:{yes}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Box\:{no} \\ $$$${How}\:{this}\:{may}\:{be}\:{proved}\:? \\ $$

Question Number 55971 Answers: 1 Comments: 2

Question Number 55970 Answers: 1 Comments: 0

Question Number 55969 Answers: 1 Comments: 0

solve for x & y x^(logy) = 4 xy = 40

$$\:\:\:\boldsymbol{\mathrm{solve}}\:\:\:\boldsymbol{\mathrm{for}}\:\:\:\boldsymbol{\mathrm{x}}\:\:\:\&\:\:\boldsymbol{\mathrm{y}} \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{logy}}} \:\:\:=\:\:\mathrm{4} \\ $$$$\:\: \\ $$$$\:\:\:\:\boldsymbol{\mathrm{xy}}\:\:\:\:=\:\:\:\:\mathrm{40}\: \\ $$

Question Number 55967 Answers: 0 Comments: 1

Question Number 55954 Answers: 1 Comments: 0

Question Number 55948 Answers: 1 Comments: 0

Question Number 55942 Answers: 0 Comments: 1

Prove that: (1/(∣A∣)) = A^1

$$\mathrm{Prove}\:\mathrm{that}:\:\:\:\:\:\frac{\mathrm{1}}{\mid\boldsymbol{\mathrm{A}}\mid}\:\:=\:\:\boldsymbol{\mathrm{A}}^{\mathrm{1}} \\ $$

Question Number 55939 Answers: 1 Comments: 0

((y′)/y)=1−cot x y=?

$$\frac{{y}'}{{y}}=\mathrm{1}−\mathrm{cot}\:{x} \\ $$$${y}=? \\ $$

Question Number 55933 Answers: 2 Comments: 1

Question Number 55930 Answers: 2 Comments: 0

∫_0 ^( π) ((xtan x)/(sec x+tan x))dx = (is it (π^2 /2)−π)?

$$\int_{\mathrm{0}} ^{\:\:\pi} \frac{{x}\mathrm{tan}\:{x}}{\mathrm{sec}\:{x}+\mathrm{tan}\:{x}}{dx}\:=\:\left({is}\:{it}\:\frac{\pi^{\mathrm{2}} }{\mathrm{2}}−\pi\right)? \\ $$

Question Number 55926 Answers: 1 Comments: 0

Ancient Roman Number Magic: take 5 matches or picks and form a roman 3 ∣∣∣_(−) ^(−) now subtract 2 so that a little more than 3 is left

$$\mathrm{Ancient}\:\mathrm{Roman}\:\mathrm{Number}\:\mathrm{Magic}: \\ $$$$\mathrm{take}\:\mathrm{5}\:\mathrm{matches}\:\mathrm{or}\:\mathrm{picks}\:\mathrm{and}\:\mathrm{form}\:\mathrm{a}\:\mathrm{roman}\:\mathrm{3} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{−} {\overline {\mid\mid\mid}} \\ $$$$\mathrm{now}\:\mathrm{subtract}\:\mathrm{2}\:\mathrm{so}\:\mathrm{that}\:\mathrm{a}\:\mathrm{little}\:\mathrm{more}\:\mathrm{than}\:\mathrm{3}\:\mathrm{is}\:\mathrm{left} \\ $$

Question Number 55920 Answers: 0 Comments: 1

Calculate. Σ_(a=1) ^∞ Σ_(b=1) ^∞ Σ_(c=1) ^∞ ((ab(3a+c))/(4^(a+b+c) (a+b)(b+c)(c+a))).

$$\boldsymbol{\mathrm{Calculate}}. \\ $$$$\underset{\boldsymbol{{a}}=\mathrm{1}} {\overset{\infty} {\sum}}\underset{\boldsymbol{{b}}=\mathrm{1}} {\overset{\infty} {\sum}}\underset{\boldsymbol{{c}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\boldsymbol{{ab}}\left(\mathrm{3}\boldsymbol{{a}}+\boldsymbol{{c}}\right)}{\mathrm{4}^{\boldsymbol{{a}}+\boldsymbol{{b}}+\boldsymbol{{c}}} \left(\boldsymbol{{a}}+\boldsymbol{{b}}\right)\left(\boldsymbol{{b}}+\boldsymbol{{c}}\right)\left(\boldsymbol{{c}}+\boldsymbol{{a}}\right)}. \\ $$

Question Number 55918 Answers: 1 Comments: 0

Two similar spheres of the same material have masses of 12kg and250kg respectively. find the radius of the smaller sphere if the radius of the bigger shere is 12.5cm

Question Number 55914 Answers: 1 Comments: 0

Question Number 55913 Answers: 1 Comments: 0

Question Number 55909 Answers: 0 Comments: 0

If E={f ∣f : R→R continoues function f(x) ∈Q, ∀x ∈R} then E=...

$$\mathrm{If}\:{E}=\left\{{f}\:\mid{f}\::\:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{continoues}\:\mathrm{function}\right. \\ $$$$\left.{f}\left({x}\right)\:\in\mathrm{Q},\:\forall{x}\:\in\mathbb{R}\right\}\:\mathrm{then}\:{E}=... \\ $$

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