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Question Number 59049 Answers: 0 Comments: 1

∫_( 0) ^∞ ((x log x)/((1+x^2 )^2 )) dx =

$$\:\underset{\:\mathrm{0}} {\overset{\infty} {\int}}\:\frac{{x}\:\mathrm{log}\:{x}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dx}\:= \\ $$

Question Number 59040 Answers: 3 Comments: 0

1) ∫_0 ^( (π/4)) ((sin x+cos x)/(cos^2 x+sin^4 x))dx = ?

$$\left.\mathrm{1}\right)\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \:\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\mathrm{cos}\:^{\mathrm{2}} {x}+\mathrm{sin}\:^{\mathrm{4}} {x}}{dx}\:=\:? \\ $$

Question Number 59023 Answers: 0 Comments: 0

please solve my quens

$${please}\:{solve}\:{my}\:{quens} \\ $$

Question Number 59021 Answers: 2 Comments: 10

[Q58885 reposted] How many 4−digit numbers abcd exist which are divisible by 3 and satisfy a≤b≤c≤d?

$$\left[{Q}\mathrm{58885}\:{reposted}\right] \\ $$$${How}\:{many}\:\mathrm{4}−{digit}\:{numbers}\:{abcd}\:{exist} \\ $$$${which}\:{are}\:{divisible}\:{by}\:\mathrm{3}\:{and}\:{satisfy} \\ $$$${a}\leqslant{b}\leqslant{c}\leqslant{d}? \\ $$

Question Number 59018 Answers: 0 Comments: 1

Question Number 59012 Answers: 3 Comments: 0

Question Number 59006 Answers: 0 Comments: 1

probar con h≠0 ((sin(x+h)−sin(x))/h)=((sin(h/2))/(h/2))cos(x+(h/2))

$${probar}\:{con}\:{h}\neq\mathrm{0} \\ $$$$\frac{{sin}\left({x}+{h}\right)−{sin}\left({x}\right)}{{h}}=\frac{{sin}\left({h}/\mathrm{2}\right)}{{h}/\mathrm{2}}{cos}\left({x}+\frac{{h}}{\mathrm{2}}\right) \\ $$$$ \\ $$

Question Number 59003 Answers: 0 Comments: 0

Question Number 59002 Answers: 0 Comments: 0

Question Number 59000 Answers: 1 Comments: 0

Question Number 58986 Answers: 1 Comments: 3

Question Number 58984 Answers: 1 Comments: 0

ABCD is a square, AC is a diagonal. If the coordinate of A, C are (− 5, 8) and (7, − 4) . Find the coordinate of B and D.

$$\mathrm{ABCD}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{square},\:\mathrm{AC}\:\mathrm{is}\:\mathrm{a}\:\mathrm{diagonal}.\:\mathrm{If}\:\:\mathrm{the}\:\mathrm{coordinate}\:\mathrm{of}\:\:\mathrm{A},\:\mathrm{C} \\ $$$$\mathrm{are}\:\:\left(−\:\mathrm{5},\:\mathrm{8}\right)\:\mathrm{and}\:\left(\mathrm{7},\:−\:\mathrm{4}\right)\:.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{coordinate}\:\mathrm{of}\:\:\mathrm{B}\:\mathrm{and}\:\mathrm{D}. \\ $$

Question Number 58979 Answers: 1 Comments: 1

Question Number 58974 Answers: 1 Comments: 0

Question Number 58972 Answers: 0 Comments: 0

Question Number 58971 Answers: 1 Comments: 1

Question Number 58965 Answers: 0 Comments: 0

if a,b ∈C ∣ ∣a∣<1,∣b∣<1 ⇒∣((a−b)/(1−a^ b))∣<1^

$$\mathrm{if}\:{a},{b}\:\in\mathbb{C}\:\mid\:\mid{a}\mid<\mathrm{1},\mid{b}\mid<\mathrm{1} \\ $$$$\Rightarrow\mid\frac{{a}−{b}}{\mathrm{1}−\bar {{a}b}}\mid<\overset{} {\mathrm{1}} \\ $$

Question Number 58964 Answers: 1 Comments: 0

a + b + c = 1 a, b, c ≤ 1 Prove that (1/(a^2 + 1)) + (1/(b^2 + 1)) + (1/(c^2 + 1)) ≤ ((27)/(10))

$${a}\:+\:{b}\:+\:{c}\:\:=\:\:\mathrm{1} \\ $$$${a},\:{b},\:{c}\:\:\leqslant\:\:\mathrm{1} \\ $$$${Prove}\:\:{that} \\ $$$$\:\:\:\:\:\:\frac{\mathrm{1}}{{a}^{\mathrm{2}} \:+\:\mathrm{1}}\:\:+\:\:\frac{\mathrm{1}}{{b}^{\mathrm{2}} \:+\:\mathrm{1}}\:\:+\:\:\frac{\mathrm{1}}{{c}^{\mathrm{2}} \:+\:\mathrm{1}}\:\:\leqslant\:\:\frac{\mathrm{27}}{\mathrm{10}} \\ $$

Question Number 58963 Answers: 1 Comments: 0

solve x^2 −2(1+i)x−5+14i=0

$${solve}\:{x}^{\mathrm{2}} −\mathrm{2}\left(\mathrm{1}+{i}\right){x}−\mathrm{5}+\mathrm{14}{i}=\mathrm{0} \\ $$

Question Number 58962 Answers: 0 Comments: 0

you are welcome sir.

$${you}\:{are}\:{welcome}\:{sir}. \\ $$

Question Number 59037 Answers: 0 Comments: 1

solve (dy/dt)=t^2 +y^2

$${solve}\:\:\frac{{dy}}{{dt}}={t}^{\mathrm{2}} +{y}^{\mathrm{2}} \\ $$

Question Number 58948 Answers: 0 Comments: 3

lim_(x→+∞) ((√x)/(√(x+(√(x+(√x))))))

$$\underset{{x}\rightarrow+\infty} {{lim}}\:\frac{\sqrt{{x}}}{\sqrt{{x}+\sqrt{{x}+\sqrt{{x}}}}} \\ $$

Question Number 58943 Answers: 1 Comments: 0

Add 469+143

$$\mathrm{Add}\:\mathrm{469}+\mathrm{143} \\ $$

Question Number 58942 Answers: 1 Comments: 0

4×(1/(10))

$$\mathrm{4}×\frac{\mathrm{1}}{\mathrm{10}} \\ $$

Question Number 58941 Answers: 1 Comments: 0

6h=30

$$\mathrm{6h}=\mathrm{30} \\ $$

Question Number 58940 Answers: 1 Comments: 3

e^(i∫_(−2) ^2 (x^2 sinx+(√(1−(x^2 /4))))dx) +lim_(x→2) ((∫_2 ^x log(x+8)dx)/(x−2))=?

$${e}^{{i}\int_{−\mathrm{2}} ^{\mathrm{2}} \left({x}^{\mathrm{2}} {sinx}+\sqrt{\mathrm{1}−\frac{{x}^{\mathrm{2}} }{\mathrm{4}}}\right){dx}} +\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\frac{\int_{\mathrm{2}} ^{{x}} {log}\left({x}+\mathrm{8}\right){dx}}{{x}−\mathrm{2}}=? \\ $$

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