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Question Number 66739 Answers: 1 Comments: 0

find∫(√(dx ))

$${find}\int\sqrt{{dx}\:} \\ $$

Question Number 66734 Answers: 0 Comments: 0

Question Number 66731 Answers: 0 Comments: 1

y=x^2 −3x y=2x find area

$${y}={x}^{\mathrm{2}} −\mathrm{3}{x}\:\:\:\:\:{y}=\mathrm{2}{x}\:{find}\:{area} \\ $$

Question Number 66728 Answers: 2 Comments: 2

∫_1 ^∞ (1/(x(√(x^2 +1))))=?

$$\int_{\mathrm{1}} ^{\infty} \frac{\mathrm{1}}{{x}\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}=? \\ $$

Question Number 66727 Answers: 0 Comments: 0

let U_n =Σ_(k=0) ^n (1/(3k+1)) and H_n =Σ_(k=1) ^n (1/k) calculate U_n interms of H_n

$${let}\:\:{U}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\frac{\mathrm{1}}{\mathrm{3}{k}+\mathrm{1}}\:\:\:{and}\:{H}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}} \\ $$$${calculate}\:{U}_{{n}} \:{interms}\:{of}\:{H}_{{n}} \\ $$

Question Number 66718 Answers: 0 Comments: 3

Question Number 66715 Answers: 0 Comments: 4

if f(x)=((ln (x+(√(1+x^2 ))))/(√(1+x^2 ))) f^(−1) (x)=?

$${if}\:{f}\left({x}\right)=\frac{\mathrm{ln}\:\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)}{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }} \\ $$$${f}^{−\mathrm{1}} \left({x}\right)=? \\ $$

Question Number 66697 Answers: 1 Comments: 1

Question Number 66696 Answers: 2 Comments: 3

calculate lim_(x→0) ((arctan(1+x^3 )−(π/4))/(xsin(x^2 )))

$${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\:\:\frac{{arctan}\left(\mathrm{1}+{x}^{\mathrm{3}} \right)−\frac{\pi}{\mathrm{4}}}{{xsin}\left({x}^{\mathrm{2}} \right)} \\ $$

Question Number 66695 Answers: 1 Comments: 3

calculate ∫_0 ^∞ ((cos(arctanx))/(4+x^2 ))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({arctanx}\right)}{\mathrm{4}+{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 66694 Answers: 0 Comments: 3

let f(a) =∫_(−∞) ^(+∞) (dx/((x^4 +x^2 +a))) with a∈](1/4),+∞[ 1) calculate f(a) 2)find also g(a) =∫_(−∞) ^(+∞) (dx/((x^4 +x^2 +a)^2 )) 3) find the value of integrals ∫_0 ^∞ (dx/((x^4 +x^2 +3))) and ∫_0 ^∞ (dx/((x^4 +x^2 +1)^2 )) 4) developp f at integrserie.

$$\left.{let}\:{f}\left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{4}} +{x}^{\mathrm{2}} \:+{a}\right)}\:{with}\:{a}\in\right]\frac{\mathrm{1}}{\mathrm{4}},+\infty\left[\right. \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{also}\:{g}\left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\frac{{dx}}{\left({x}^{\mathrm{4}} \:+{x}^{\mathrm{2}} +{a}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:{integrals}\:\:\int_{\mathrm{0}} ^{\infty} \:\frac{{dx}}{\left({x}^{\mathrm{4}} \:+{x}^{\mathrm{2}} \:+\mathrm{3}\right)}\:{and} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{4}} \:+{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{4}\right)\:{developp}\:{f}\:{at}\:{integrserie}. \\ $$

Question Number 66693 Answers: 1 Comments: 1

calculate ∫_(−∞) ^(+∞) (dx/((x^2 −x+1)^3 ))

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

Question Number 66684 Answers: 1 Comments: 0