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Question Number 156779 Answers: 2 Comments: 0

∫((ln(1+x^2 ))/(1+x^2 ))

$$\int\frac{{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$

Question Number 156761 Answers: 2 Comments: 0

prove that ∫((a + b sin x)/((b + a sin x)^2 ))dx=((−cos x)/(b + a sin x))

$${prove}\:{that} \\ $$$$\int\frac{{a}\:+\:{b}\:\mathrm{sin}\:{x}}{\left({b}\:+\:{a}\:\mathrm{sin}\:{x}\right)^{\mathrm{2}} }{dx}=\frac{−\mathrm{cos}\:{x}}{{b}\:+\:{a}\:\mathrm{sin}\:{x}} \\ $$

Question Number 156807 Answers: 1 Comments: 3

f(x)=arctg(1/(x^2 +x+1)) and α=f(1)+f(2)+…+f(21) find tg(α)=?

$${f}\left({x}\right)={arctg}\frac{\mathrm{1}}{{x}^{\mathrm{2}} +{x}+\mathrm{1}}\:\:{and}\:\alpha={f}\left(\mathrm{1}\right)+{f}\left(\mathrm{2}\right)+\ldots+{f}\left(\mathrm{21}\right) \\ $$$${find}\:\:{tg}\left(\alpha\right)=? \\ $$

Question Number 156806 Answers: 1 Comments: 0

Question Number 156754 Answers: 1 Comments: 0

Question Number 156744 Answers: 2 Comments: 0

y“+y′=e^x +3x

$$\mathrm{y}``+\mathrm{y}'=\mathrm{e}^{\mathrm{x}} +\mathrm{3x} \\ $$$$ \\ $$

Question Number 156743 Answers: 2 Comments: 0

Question Number 156739 Answers: 0 Comments: 1

Question Number 156734 Answers: 1 Comments: 1

Question Number 156729 Answers: 1 Comments: 0

Question Number 156727 Answers: 1 Comments: 0

Question Number 156710 Answers: 1 Comments: 4

Question Number 156709 Answers: 1 Comments: 0

solve (x^3 )^(1/(1/x)) = 27

$$\boldsymbol{{solve}}\:\sqrt[{\frac{\mathrm{1}}{\boldsymbol{{x}}}}]{\boldsymbol{{x}}^{\mathrm{3}} }\:=\:\mathrm{27} \\ $$

Question Number 156695 Answers: 1 Comments: 0

∫sin(ln(x))dx=?

$$\int{sin}\left({ln}\left({x}\right)\right){dx}=? \\ $$

Question Number 156691 Answers: 1 Comments: 0

Show that (Σ_(k=1) ^n x_k y_k )^2 ≤(Σ_(k=1) ^n x_k ^2 )×(Σ_(k=1) ^n y_k ^2 )t

$${Show}\:{that} \\ $$$$\left(\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{x}_{{k}} {y}_{{k}} \right)^{\mathrm{2}} \leqslant\left(\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{x}_{{k}} ^{\mathrm{2}} \right)×\left(\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{y}_{{k}} ^{\mathrm{2}} \right){t} \\ $$

Question Number 156689 Answers: 0 Comments: 0

Question Number 156684 Answers: 2 Comments: 0

solve the D.E [1+e^(x/y) ]dx+e^(x/y) [1−(x/y)]dy=0 any one can help pls

$${solve}\:{the}\:{D}.{E}\: \\ $$$$\left[\mathrm{1}+{e}^{\frac{{x}}{{y}}} \right]{dx}+{e}^{\frac{{x}}{{y}}} \left[\mathrm{1}−\frac{{x}}{{y}}\right]{dy}=\mathrm{0} \\ $$$${any}\:{one}\:{can}\:{help}\:{pls} \\ $$

Question Number 156683 Answers: 1 Comments: 3

Question Number 156677 Answers: 1 Comments: 3

Question Number 156676 Answers: 3 Comments: 1

Question Number 156671 Answers: 2 Comments: 0

Question Number 156663 Answers: 0 Comments: 2

calcul ∫_0 ^(10) e^(x−E(x)) dx (E la partie entiere) besoin d′aide

$${calcul}\:\int_{\mathrm{0}} ^{\mathrm{10}} {e}^{{x}−{E}\left({x}\right)} {dx}\:\left({E}\:{la}\:{partie}\:{entiere}\right) \\ $$$${besoin}\:{d}'{aide} \\ $$

Question Number 156662 Answers: 0 Comments: 0

I =∫_( 0) ^( 1) ((2 ln x - x + (1/2))/((1 + x^2 ) ln^3 x)) dx = ?

$$\boldsymbol{\mathrm{I}}\:=\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\frac{\mathrm{2}\:\mathrm{ln}\:\mathrm{x}\:-\:\mathrm{x}\:+\:\frac{\mathrm{1}}{\mathrm{2}}}{\left(\mathrm{1}\:+\:\mathrm{x}^{\mathrm{2}} \right)\:\mathrm{ln}^{\mathrm{3}} \:\mathrm{x}}\:\mathrm{dx}\:=\:? \\ $$

Question Number 156661 Answers: 0 Comments: 0

if 1≤x ; y≤2 ; 3≤z ; t≤4 prove that: ((x^2 +y^2 +1)/(xz+yt+3)) + ((√6)/3) ≤ ((3+xz+yt)/(9+z^2 +t^2 )) + ((11)/(12))

$$\mathrm{if}\:\:\mathrm{1}\leqslant\mathrm{x}\:\:;\:\:\mathrm{y}\leqslant\mathrm{2}\:\:;\:\:\mathrm{3}\leqslant\mathrm{z}\:\:;\:\:\mathrm{t}\leqslant\mathrm{4}\:\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{1}}{\mathrm{xz}+\mathrm{yt}+\mathrm{3}}\:+\:\frac{\sqrt{\mathrm{6}}}{\mathrm{3}}\:\leqslant\:\frac{\mathrm{3}+\mathrm{xz}+\mathrm{yt}}{\mathrm{9}+\mathrm{z}^{\mathrm{2}} +\mathrm{t}^{\mathrm{2}} }\:+\:\frac{\mathrm{11}}{\mathrm{12}} \\ $$

Question Number 156660 Answers: 0 Comments: 0

Question Number 156652 Answers: 1 Comments: 0

Sirs, please give me the general solutions to a quadratic ineqality. (1) ax^2 + bx + c > 0 (2) ax^2 + bx + c ≥ 0 (3) ax^2 + bx + c < 0 (4) ax^2 + bx + c ≤ 0

$$\mathrm{Sirs},\:\mathrm{please}\:\mathrm{give}\:\mathrm{me}\:\mathrm{the}\:\mathrm{general}\:\mathrm{solutions}\:\mathrm{to}\:\mathrm{a}\:\mathrm{quadratic}\:\mathrm{ineqality}. \\ $$$$\left(\mathrm{1}\right)\:\:\:\:\:\:\mathrm{ax}^{\mathrm{2}} \:\:\:+\:\:\:\mathrm{bx}\:\:\:+\:\:\:\mathrm{c}\:\:\:\:>\:\:\:\:\mathrm{0} \\ $$$$\left(\mathrm{2}\right)\:\:\:\:\:\:\mathrm{ax}^{\mathrm{2}} \:\:\:+\:\:\:\mathrm{bx}\:\:\:+\:\:\:\mathrm{c}\:\:\:\:\geqslant\:\:\:\:\mathrm{0} \\ $$$$\left(\mathrm{3}\right)\:\:\:\:\:\:\mathrm{ax}^{\mathrm{2}} \:\:\:+\:\:\:\mathrm{bx}\:\:\:+\:\:\:\mathrm{c}\:\:\:\:<\:\:\:\:\mathrm{0} \\ $$$$\left(\mathrm{4}\right)\:\:\:\:\:\:\mathrm{ax}^{\mathrm{2}} \:\:\:+\:\:\:\mathrm{bx}\:\:\:+\:\:\:\mathrm{c}\:\:\:\:\leqslant\:\:\:\:\mathrm{0} \\ $$

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