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Question Number 101378 Answers: 2 Comments: 1

∫_(1/e) ^(tanx) (t/(1+t^2 ))dt + ∫_(1/e) ^(cotx) (1/(t(1+t^2 )))dt

$$\int_{\frac{\mathrm{1}}{{e}}} ^{{tanx}} \frac{{t}}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:+\:\int_{\frac{\mathrm{1}}{{e}}} ^{{cotx}} \frac{\mathrm{1}}{{t}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}{dt} \\ $$

Question Number 101375 Answers: 1 Comments: 4

Question Number 101373 Answers: 0 Comments: 1

lim_(n→∞ ) Σ_(r=1) ^(4n) ((√n)/((√r)(3(√r)+4(√n))^2 ))

$$\underset{{n}\rightarrow\infty\:} {\mathrm{lim}}\underset{{r}=\mathrm{1}} {\overset{\mathrm{4}{n}} {\sum}}\frac{\sqrt{{n}}}{\sqrt{{r}}\left(\mathrm{3}\sqrt{{r}}+\mathrm{4}\sqrt{{n}}\right)^{\mathrm{2}} } \\ $$

Question Number 101366 Answers: 1 Comments: 2

lim_(x→0) ((x^3 −sin^3 x)/x^5 ) =?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}^{\mathrm{3}} −\mathrm{sin}\:^{\mathrm{3}} {x}}{{x}^{\mathrm{5}} }\:=? \\ $$

Question Number 101363 Answers: 1 Comments: 0

The solution set of inequality (((√((3x−7)^2 ))−2)/(x−3)) ≤ ((3−(√x^2 ))/(x−3)) is __ (A) (−∞, (1/2)] (D) [(1/2), ∞) (B) [(1/2),1 ] (E) (−∞,(2/3)] (C) (−∞,1 ]

$$\mathrm{The}\:\mathrm{solution}\:\mathrm{set}\:\mathrm{of}\:\mathrm{inequality} \\ $$$$\frac{\sqrt{\left(\mathrm{3x}−\mathrm{7}\right)^{\mathrm{2}} }−\mathrm{2}}{\mathrm{x}−\mathrm{3}}\:\leqslant\:\frac{\mathrm{3}−\sqrt{\mathrm{x}^{\mathrm{2}} }}{\mathrm{x}−\mathrm{3}}\:\mathrm{is}\:\_\_ \\ $$$$\left(\mathrm{A}\right)\:\left(−\infty,\:\frac{\mathrm{1}}{\mathrm{2}}\right]\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\left[\frac{\mathrm{1}}{\mathrm{2}},\:\infty\right) \\ $$$$\left(\mathrm{B}\right)\:\left[\frac{\mathrm{1}}{\mathrm{2}},\mathrm{1}\:\right]\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{E}\right)\:\left(−\infty,\frac{\mathrm{2}}{\mathrm{3}}\right] \\ $$$$\left(\mathrm{C}\right)\:\left(−\infty,\mathrm{1}\:\right]\: \\ $$

Question Number 101362 Answers: 0 Comments: 1

Question Number 101360 Answers: 0 Comments: 0

xy′=y(ylnx+1)

$${xy}'={y}\left({ylnx}+\mathrm{1}\right) \\ $$

Question Number 101350 Answers: 1 Comments: 0

Question Number 101345 Answers: 0 Comments: 3

(1)∫ ((sec^4 x tan x)/(sec^4 x+4)) dx= (2) ∫x^(2x) (2lnx +2) dx = (3) ∫_0 ^1 (√(1−x^2 )) dx =

$$\left(\mathrm{1}\right)\int\:\frac{\mathrm{sec}\:^{\mathrm{4}} {x}\:\mathrm{tan}\:{x}}{\mathrm{sec}\:^{\mathrm{4}} {x}+\mathrm{4}}\:{dx}= \\ $$$$\left(\mathrm{2}\right)\:\int{x}^{\mathrm{2}{x}} \left(\mathrm{2ln}{x}\:+\mathrm{2}\right)\:{dx}\:= \\ $$$$\left(\mathrm{3}\right)\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\:{dx}\:=\: \\ $$

Question Number 101342 Answers: 1 Comments: 0

find U_n =∫_0 ^1 ((x^(2n) −1)/(lnx))dx with n integr natural and n≥2 find nature of the serie Σ U_n

$$\mathrm{find}\:\:\mathrm{U}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{x}^{\mathrm{2n}} −\mathrm{1}}{\mathrm{lnx}}\mathrm{dx}\:\:\mathrm{with}\:\mathrm{n}\:\mathrm{integr}\:\mathrm{natural}\:\mathrm{and}\:\mathrm{n}\geqslant\mathrm{2} \\ $$$$\mathrm{find}\:\mathrm{nature}\:\mathrm{of}\:\mathrm{the}\:\mathrm{serie}\:\Sigma\:\mathrm{U}_{\mathrm{n}} \\ $$

Question Number 101402 Answers: 0 Comments: 3

I desire the developmenter of this apps improve adding some other functions like as:choose whole text by tap in text or choose some line at one time has many colours more

$$\mathrm{I}\:\mathrm{desire}\:\mathrm{the}\:\mathrm{developmenter}\:\mathrm{of}\:\mathrm{this}\:\mathrm{apps} \\ $$$$\mathrm{improve}\:\mathrm{adding}\:\mathrm{some}\:\mathrm{other}\:\mathrm{functions} \\ $$$$\mathrm{like}\:\mathrm{as}:\mathrm{choose}\:\mathrm{whole}\:\mathrm{text}\:\mathrm{by}\:\mathrm{tap}\:\mathrm{in} \\ $$$$\mathrm{text}\:\mathrm{or}\:\mathrm{choose}\:\mathrm{some}\:\mathrm{line}\:\mathrm{at}\:\mathrm{one}\:\mathrm{time} \\ $$$$\mathrm{has}\:\mathrm{many}\:\mathrm{colours}\:\mathrm{more} \\ $$

Question Number 101330 Answers: 0 Comments: 5

Evaluate. ∫_(−π) ^π x^9 cos x dx

$${Evaluate}. \\ $$$$\int_{−\pi} ^{\pi} {x}^{\mathrm{9}} \mathrm{cos}\:{x}\:{dx} \\ $$

Question Number 101329 Answers: 1 Comments: 0

Question Number 101328 Answers: 0 Comments: 1

this i a beautifull old question in the forum by sir.Ali Esam i Reposted it trying to find any idea to solve I=∫_(−1) ^1 (((sin(x))/(sinh^(−1) (x))))(((sin^(−1) (x))/(sinh(x))))dx i solved it numerical the value is 2.03383

$${this}\:{i}\:{a}\:{beautifull}\:{old}\:{question}\:{in}\:{the}\:{forum} \\ $$$${by}\:{sir}.{Ali}\:{Esam}\:{i}\:{Reposted}\:{it}\:{trying}\:{to} \\ $$$${find}\:{any}\:{idea}\:{to}\:{solve} \\ $$$$ \\ $$$${I}=\int_{−\mathrm{1}} ^{\mathrm{1}} \left(\frac{{sin}\left({x}\right)}{{sinh}^{−\mathrm{1}} \left({x}\right)}\right)\left(\frac{{sin}^{−\mathrm{1}} \left({x}\right)}{{sinh}\left({x}\right)}\right){dx} \\ $$$$ \\ $$$${i}\:{solved}\:{it}\:{numerical}\: \\ $$$${the}\:{value}\:{is}\:\mathrm{2}.\mathrm{03383} \\ $$

Question Number 101319 Answers: 1 Comments: 4

find the area bounded the parabola y=4x^2 and y=8−4x^2 ? by using intigral? help me

$${find}\:{the}\:{area}\:{bounded}\:{the}\:{parabola}\: \\ $$$${y}=\mathrm{4}{x}^{\mathrm{2}} \:\:\:{and}\:\:{y}=\mathrm{8}−\mathrm{4}{x}^{\mathrm{2}} \:\:?\:\:{by}\:{using}\:{intigral}? \\ $$$${help}\:{me} \\ $$

Question Number 101273 Answers: 0 Comments: 0

caoculate lim_(x→0) ((sh(sin(2x))−sin(sh(2x)))/x^3 )

$$\mathrm{caoculate}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \:\:\:\frac{\mathrm{sh}\left(\mathrm{sin}\left(\mathrm{2x}\right)\right)−\mathrm{sin}\left(\mathrm{sh}\left(\mathrm{2x}\right)\right)}{\mathrm{x}^{\mathrm{3}} } \\ $$

Question Number 101272 Answers: 1 Comments: 2

∫(√(sec x)) dx

$$\int\sqrt{\mathrm{sec}\:{x}}\:{dx}\: \\ $$

Question Number 101271 Answers: 0 Comments: 2

find ∫ ((xdx)/((√(x^2 +x+1))+(√(x^2 −x+1))))