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Question Number 101269    Answers: 1   Comments: 0

calculate ∫_4 ^(+∞) (dx/((x−2)^5 (x+3)^7 ))

$$\mathrm{calculate}\:\int_{\mathrm{4}} ^{+\infty} \:\:\:\:\:\frac{\mathrm{dx}}{\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{5}} \left(\mathrm{x}+\mathrm{3}\right)^{\mathrm{7}} } \\ $$

Question Number 101268    Answers: 1   Comments: 0

calculate ∫_(−∞) ^∞ ((cos(arctan(2x+1)))/(x^2 +2x+2))dx

$$\mathrm{calculate}\:\int_{−\infty} ^{\infty} \:\frac{\mathrm{cos}\left(\mathrm{arctan}\left(\mathrm{2x}+\mathrm{1}\right)\right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{2x}+\mathrm{2}}\mathrm{dx} \\ $$

Question Number 101266    Answers: 0   Comments: 0

calculate ∫_1 ^(+∞) (dx/(x^2 (x+1)^3 (x+2)^4 ))

$$\mathrm{calculate}\:\:\int_{\mathrm{1}} ^{+\infty} \:\:\:\:\:\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2}} \left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{3}} \left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{4}} } \\ $$

Question Number 101286    Answers: 0   Comments: 3

∫(((x^m −x^n )^2 )/(√x))dx=?

$$\int\frac{\left(\mathrm{x}^{\mathrm{m}} −\mathrm{x}^{\mathrm{n}} \right)^{\mathrm{2}} }{\sqrt{\mathrm{x}}}\mathrm{dx}=? \\ $$

Question Number 101258    Answers: 2   Comments: 2

minimum value f(x,y)=x^2 +y^2 with constrain g(x,y)= x^2 y−16

$$\mathrm{minimum}\:\mathrm{value}\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \\ $$$$\mathrm{with}\:\mathrm{constrain}\:\mathrm{g}\left(\mathrm{x},\mathrm{y}\right)=\:\mathrm{x}^{\mathrm{2}} \mathrm{y}−\mathrm{16} \\ $$

Question Number 101252    Answers: 0   Comments: 1

(√(1+2(√(1+4(√(1+5(√(1+6(√(1+7(√(1+8..))))))))))))∞=?

$$\sqrt{\mathrm{1}+\mathrm{2}\sqrt{\mathrm{1}+\mathrm{4}\sqrt{\mathrm{1}+\mathrm{5}\sqrt{\mathrm{1}+\mathrm{6}\sqrt{\mathrm{1}+\mathrm{7}\sqrt{\mathrm{1}+\mathrm{8}..}}}}}}\infty=? \\ $$

Question Number 101250    Answers: 0   Comments: 0

Question Number 101249    Answers: 0   Comments: 8

As request by many users earlier, ability to convert written equations to plain text is now available. Plain text may be useful when you need to enter question content on internet sites. Standard convention for limits and power are used during processing and sites so one liner integral, summation, limits derviates should be directly usable. You might need do some small editing depending upon app used. Parser is implemented on server.

$$\mathrm{As}\:\mathrm{request}\:\mathrm{by}\:\mathrm{many}\:\mathrm{users}\:\mathrm{earlier}, \\ $$$$\mathrm{ability}\:\mathrm{to}\:\mathrm{convert}\:\mathrm{written}\:\mathrm{equations} \\ $$$$\mathrm{to}\:\mathrm{plain}\:\mathrm{text}\:\mathrm{is}\:\mathrm{now}\:\mathrm{available}. \\ $$$$\mathrm{Plain}\:\mathrm{text}\:\mathrm{may}\:\mathrm{be}\:\mathrm{useful}\:\mathrm{when}\:\mathrm{you} \\ $$$$\mathrm{need}\:\mathrm{to}\:\mathrm{enter}\:\mathrm{question}\:\mathrm{content} \\ $$$$\mathrm{on}\:\mathrm{internet}\:\mathrm{sites}. \\ $$$$\mathrm{Standard}\:\mathrm{convention}\:\mathrm{for}\:\mathrm{limits} \\ $$$$\mathrm{and}\:\mathrm{power}\:\mathrm{are}\:\mathrm{used}\:\mathrm{during}\:\mathrm{processing} \\ $$$$\mathrm{and}\:\mathrm{sites}\:\mathrm{so}\:\mathrm{one}\:\mathrm{liner}\:\mathrm{integral}, \\ $$$$\mathrm{summation},\:\mathrm{limits}\:\mathrm{derviates}\:\mathrm{should} \\ $$$$\mathrm{be}\:\mathrm{directly}\:\mathrm{usable}.\:\mathrm{You}\:\mathrm{might} \\ $$$$\mathrm{need}\:\mathrm{do}\:\mathrm{some}\:\mathrm{small}\:\mathrm{editing} \\ $$$$\mathrm{depending}\:\mathrm{upon}\:\mathrm{app}\:\mathrm{used}. \\ $$$$\boldsymbol{\mathrm{Parser}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{implemented}}\:\boldsymbol{\mathrm{on}}\:\boldsymbol{\mathrm{server}}. \\ $$

Question Number 101248    Answers: 0   Comments: 0

Π_(p∈P/(2..3)) ((1/p))^2 =? p is prime number Any help ?

$$\:\:\:\underset{\boldsymbol{{p}}\in\boldsymbol{{P}}/\left(\mathrm{2}..\mathrm{3}\right)} {\prod}\left(\frac{\mathrm{1}}{\boldsymbol{{p}}}\right)^{\mathrm{2}} =?\:\:\:\:\:\boldsymbol{{p}}\:{is}\:{prime}\:{number} \\ $$$${Any}\:{help}\:? \\ $$

Question Number 101247    Answers: 1   Comments: 0

Question Number 101243    Answers: 0   Comments: 3

Find the solution xa^(1/x) +(1/x)a^x =2a a∈{−1,0,1} and also find when a is not given

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{solution}\: \\ $$$$\:\:\mathrm{xa}^{\frac{\mathrm{1}}{\mathrm{x}}} +\frac{\mathrm{1}}{\mathrm{x}}\mathrm{a}^{\mathrm{x}} =\mathrm{2a}\:\:\:\mathrm{a}\in\left\{−\mathrm{1},\mathrm{0},\mathrm{1}\right\}\:\:\:{and}\:{also}\:{find}\:{when}\:{a}\:\:{is}\:{not}\:{given} \\ $$

Question Number 101307    Answers: 0   Comments: 5

Some comments with inapproriate language were deleted. Kindly refrain from posting abusive comments. Forum has been around for a long time without these occurrences. Every new user, please scroll through the previous posts and abide by the established conventions followed by everyone else.

$$\mathrm{Some}\:\mathrm{comments}\:\mathrm{with}\:\mathrm{inapproriate} \\ $$$$\mathrm{language}\:\mathrm{were}\:\mathrm{deleted}. \\ $$$$\mathrm{Kindly}\:\mathrm{refrain}\:\mathrm{from}\:\mathrm{posting}\:\mathrm{abusive} \\ $$$$\mathrm{comments}.\:\mathrm{Forum}\:\mathrm{has}\:\mathrm{been}\:\mathrm{around} \\ $$$$\mathrm{for}\:\mathrm{a}\:\mathrm{long}\:\mathrm{time}\:\mathrm{without}\:\mathrm{these} \\ $$$$\mathrm{occurrences}. \\ $$$$\mathrm{Every}\:\mathrm{new}\:\mathrm{user},\:\mathrm{please}\:\mathrm{scroll}\:\mathrm{through} \\ $$$$\mathrm{the}\:\mathrm{previous}\:\mathrm{posts}\:\mathrm{and}\:\mathrm{abide}\:\mathrm{by}\:\mathrm{the}\: \\ $$$$\mathrm{established}\:\mathrm{conventions}\:\mathrm{followed}\:\mathrm{by}\: \\ $$$$\mathrm{everyone}\:\mathrm{else}. \\ $$

Question Number 101239    Answers: 1   Comments: 0

lim_(x→∞) (((1+(1/2)+(1/3)+......+(1/n))/(1+(1/3)+(1/5)......+(1/(2n+1)))))

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+......+\frac{\mathrm{1}}{{n}}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{5}}......+\frac{\mathrm{1}}{\mathrm{2}{n}+\mathrm{1}}}\right) \\ $$

Question Number 101234    Answers: 0   Comments: 0

Show that the greatest integer function is Riemann integrable within all segments of R

$$\mathcal{S}\mathrm{how}\:\mathrm{that}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{integer}\:\mathrm{function}\:\mathrm{is}\:\mathrm{Riemann} \\ $$$$\mathrm{integrable}\:\mathrm{within}\:\mathrm{all}\:\mathrm{segments}\:\mathrm{of}\:\mathbb{R} \\ $$

Question Number 101231    Answers: 1   Comments: 1

Question Number 101225    Answers: 0   Comments: 4

Question Number 101220    Answers: 1   Comments: 0

∫∫_D (√(x^2 +y^2 ))dxdy D= { (((x,y)∈R, x^2 +y^2 ≥2y, x^2 +y^2 ≤1)),((x≥0 , y≥0)) :}

$$\int\int_{\mathrm{D}} \sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }\mathrm{dxdy}\:\:\:\mathcal{D}=\begin{cases}{\left(\mathrm{x},\mathrm{y}\right)\in\mathbb{R},\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \geqslant\mathrm{2y},\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \leqslant\mathrm{1}}\\{\mathrm{x}\geqslant\mathrm{0}\:,\:\mathrm{y}\geqslant\mathrm{0}}\end{cases} \\ $$

Question Number 101303    Answers: 1   Comments: 1

i^i^(i.∞) =?

$${i}^{{i}^{{i}.\infty} } =? \\ $$

Question Number 101293    Answers: 1   Comments: 8

Question Number 101291    Answers: 1   Comments: 0

Question Number 101285    Answers: 0   Comments: 1

∫(((x^m −x^n ))/(√x))dx=?

$$\int\frac{\left(\mathrm{x}^{\mathrm{m}} −\mathrm{x}^{\mathrm{n}} \right)}{\sqrt{\mathrm{x}}}\mathrm{dx}=? \\ $$

Question Number 101278    Answers: 0   Comments: 2

Did I miss some updates? Do we get a prize or at least an award for the fastest answer? Or for the “best”, or for the most sophisticated answer? Or for using the largest font size and the brightest colour? Annoying developments...

$$\mathrm{Did}\:\mathrm{I}\:\mathrm{miss}\:\mathrm{some}\:\mathrm{updates}? \\ $$$$\mathrm{Do}\:\mathrm{we}\:\mathrm{get}\:\mathrm{a}\:\mathrm{prize}\:\mathrm{or}\:\mathrm{at}\:\mathrm{least}\:\mathrm{an}\:\mathrm{award}\:\mathrm{for}\:\mathrm{the} \\ $$$$\mathrm{fastest}\:\mathrm{answer}?\:\mathrm{Or}\:\mathrm{for}\:\mathrm{the}\:``\mathrm{best}'',\:\mathrm{or}\:\mathrm{for}\:\mathrm{the} \\ $$$$\mathrm{most}\:\mathrm{sophisticated}\:\mathrm{answer}?\:\mathrm{Or}\:\mathrm{for}\:\mathrm{using}\:\mathrm{the} \\ $$$$\mathrm{largest}\:\mathrm{font}\:\mathrm{size}\:\mathrm{and}\:\mathrm{the}\:\mathrm{brightest}\:\mathrm{colour}? \\ $$$$\mathrm{Annoying}\:\mathrm{developments}... \\ $$

Question Number 101277    Answers: 2   Comments: 0

∫_0 ^1 (((x−1) dx )/((x+1)ln (x)))

$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\left({x}−\mathrm{1}\right)\:{dx}\:}{\left({x}+\mathrm{1}\right)\mathrm{ln}\:\left({x}\right)} \\ $$$$ \\ $$

Question Number 101156    Answers: 1   Comments: 0

Find the range of the function: h : x = 2 − x^2 sin(x), x ≥ 0

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}: \\ $$$$\:\:\:\:\:\mathrm{h}\::\:\mathrm{x}\:\:\:=\:\:\mathrm{2}\:\:−\:\:\mathrm{x}^{\mathrm{2}} \:\mathrm{sin}\left(\mathrm{x}\right),\:\:\:\:\:\:\mathrm{x}\:\:\geqslant\:\:\mathrm{0} \\ $$

Question Number 101212    Answers: 2   Comments: 1

∫e^x sin x dx = −e^x cos x + e^x sin x − ∫ e^x sin x dx

$$\int{e}^{{x}} \mathrm{sin}\:{x}\:{dx}\:=\:−{e}^{{x}} {cos}\:{x}\:+\:{e}^{{x}} \:{sin}\:{x}\:−\:\int\:{e}^{{x}} \:\mathrm{sin}\:\:{x}\:{dx} \\ $$

Question Number 101148    Answers: 0   Comments: 2

lim_(x→0) ((sin (ln (1+x))−ln(1+sin x))/(sin^4 ((x/2)))) =?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:\left(\mathrm{ln}\:\left(\mathrm{1}+\mathrm{x}\right)\right)−\mathrm{ln}\left(\mathrm{1}+\mathrm{sin}\:\mathrm{x}\right)}{\mathrm{sin}\:^{\mathrm{4}} \left(\frac{\mathrm{x}}{\mathrm{2}}\right)}\:=?\: \\ $$

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