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Question Number 82440 Answers: 0 Comments: 1

find ∫ ((x+1)/(x+2))(√((1−x)/(1+x)))dx

$${find}\:\int\:\frac{{x}+\mathrm{1}}{{x}+\mathrm{2}}\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}{dx} \\ $$

Question Number 82439 Answers: 0 Comments: 1

calculate I_n =∫_0 ^1 x^n (√(1+x+x^2 ))dx

$${calculate}\:{I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{{n}} \sqrt{\mathrm{1}+{x}+{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 82442 Answers: 0 Comments: 1

1)find ∫ ((√(x^2 −x+1))/(x^2 +3))dx 2)calculate ∫_0 ^1 ((√(x^2 −x+1))/(x^2 +3))dx

$$\left.\mathrm{1}\right){find}\:\int\:\frac{\sqrt{{x}^{\mathrm{2}} −{x}+\mathrm{1}}}{{x}^{\mathrm{2}} \:+\mathrm{3}}{dx} \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\sqrt{{x}^{\mathrm{2}} −{x}+\mathrm{1}}}{{x}^{\mathrm{2}} \:+\mathrm{3}}{dx} \\ $$

Question Number 82435 Answers: 0 Comments: 1

calculate ∫_4 ^(+∞) (x^3 /((2x+1)^3 (x−3)^5 ))dx

$${calculate}\:\int_{\mathrm{4}} ^{+\infty} \:\:\:\:\:\frac{{x}^{\mathrm{3}} }{\left(\mathrm{2}{x}+\mathrm{1}\right)^{\mathrm{3}} \left({x}−\mathrm{3}\right)^{\mathrm{5}} }{dx} \\ $$

Question Number 82434 Answers: 0 Comments: 0

1)decompose inside C(x)and R(x) the fraction F(x)=((2x+1)/((x^2 +1)^3 (x−1)^2 )) 2) find the value of ∫_3 ^(+∞) F(x)dx

$$\left.\mathrm{1}\right){decompose}\:{inside}\:{C}\left({x}\right){and}\:{R}\left({x}\right)\:{the}\:{fraction} \\ $$$${F}\left({x}\right)=\frac{\mathrm{2}{x}+\mathrm{1}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{3}} \left({x}−\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{3}} ^{+\infty} {F}\left({x}\right){dx} \\ $$

Question Number 82433 Answers: 0 Comments: 1

1)decompose inside C(x)and R(x) F=(1/((x^2 +x+1)^2 )) 2)calculate ∫_0 ^∞ (dx/((x^2 +x+1)^2 ))

$$\left.\mathrm{1}\right){decompose}\:{inside}\:{C}\left({x}\right){and}\:{R}\left({x}\right)\:{F}=\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 82431 Answers: 1 Comments: 5

Question Number 82426 Answers: 0 Comments: 2

Lim ((e^x −1−x^2 )/(x^4 +x^3 +x^2 )) = ... x→0

$$\mathrm{Lim}\:\frac{\mathrm{e}^{\mathrm{x}} −\mathrm{1}−\mathrm{x}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{4}} +\mathrm{x}^{\mathrm{3}} +\mathrm{x}^{\mathrm{2}} }\:=\:... \\ $$$$\mathrm{x}\rightarrow\mathrm{0} \\ $$

Question Number 82425 Answers: 0 Comments: 4

Lim ((1/(ex)))^(6x) =..... x→0

$$\mathrm{Lim}\:\left(\frac{\mathrm{1}}{\mathrm{ex}}\right)^{\mathrm{6x}} =..... \\ $$$$\mathrm{x}\rightarrow\mathrm{0} \\ $$

Question Number 82421 Answers: 1 Comments: 0

Question Number 82416 Answers: 0 Comments: 1

Question Number 82415 Answers: 0 Comments: 1

Question Number 82410 Answers: 1 Comments: 1

Question Number 82402 Answers: 0 Comments: 0

Question Number 82404 Answers: 1 Comments: 7

Question Number 82398 Answers: 0 Comments: 0

Question Number 82397 Answers: 0 Comments: 2

Question Number 82392 Answers: 0 Comments: 2

Question Number 82391 Answers: 0 Comments: 1

∫ sin x cos (sin x) dx ?

$$\int\:\mathrm{sin}\:{x}\:\mathrm{cos}\:\left(\mathrm{sin}\:{x}\right)\:{dx}\:? \\ $$

Question Number 82387 Answers: 0 Comments: 0

Question Number 82386 Answers: 0 Comments: 0

Question Number 82378 Answers: 1 Comments: 1

Question Number 82375 Answers: 2 Comments: 0

if x+y=8 ,,x,y∈R^+ prove that (x+(1/y))^2 +(y+(1/x))^2 ≥((289)/8)

$${if}\:\:{x}+{y}=\mathrm{8}\:\:\:\:\:,,{x},{y}\in\mathbb{R}^{+} \\ $$$${prove}\:{that}\: \\ $$$$\left({x}+\frac{\mathrm{1}}{{y}}\right)^{\mathrm{2}} +\left({y}+\frac{\mathrm{1}}{{x}}\right)^{\mathrm{2}} \geqslant\frac{\mathrm{289}}{\mathrm{8}} \\ $$

Question Number 82365 Answers: 0 Comments: 3

Question Number 82358 Answers: 0 Comments: 3

Show that: a_n = − rω^2 , show clearly how you arrive at your result.

$$\mathrm{Show}\:\mathrm{that}:\:\:\:\:\:\:\:\mathrm{a}_{\mathrm{n}} \:\:=\:\:−\:\mathrm{r}\omega^{\mathrm{2}} \:,\:\:\:\mathrm{show}\:\mathrm{clearly}\:\mathrm{how}\:\mathrm{you}\:\mathrm{arrive} \\ $$$$\mathrm{at}\:\mathrm{your}\:\mathrm{result}. \\ $$

Question Number 82356 Answers: 0 Comments: 1

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