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Question Number 62195 Answers: 0 Comments: 0

calculate A_n =∫_(−∞) ^(+∞) (dx/((x^2 +x+1)^n )) with n integr natural(n≥1)

$${calculate}\:\:{A}_{{n}} =\int_{−\infty} ^{+\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+{x}+\mathrm{1}\right)^{{n}} }\:\:\:{with}\:{n}\:{integr}\:{natural}\left({n}\geqslant\mathrm{1}\right) \\ $$

Question Number 62192 Answers: 1 Comments: 0

Question Number 62186 Answers: 0 Comments: 0

∫(e^(3x^2 ) /((1−x^4 ))^(1/8) ) dx

$$\int\frac{{e}^{\mathrm{3}{x}^{\mathrm{2}} } }{\sqrt[{\mathrm{8}}]{\mathrm{1}−{x}^{\mathrm{4}} }}\:{dx} \\ $$

Question Number 62185 Answers: 1 Comments: 0

∫(dx/(sin3x+sin4x))

$$\int\frac{{dx}}{{sin}\mathrm{3}{x}+{sin}\mathrm{4}{x}} \\ $$

Question Number 62184 Answers: 0 Comments: 1

((2x−1))^(1/3) + (√(3x+1)) = 3(x)^(1/4)

$$\sqrt[{\mathrm{3}}]{\mathrm{2}{x}−\mathrm{1}}\:+\:\sqrt{\mathrm{3}{x}+\mathrm{1}}\:=\:\mathrm{3}\sqrt[{\mathrm{4}}]{{x}} \\ $$

Question Number 62180 Answers: 0 Comments: 5

lim_(x→∞) ((senx)/x)

$$\underset{{x}\rightarrow\infty} {{lim}}\:\frac{{senx}}{{x}} \\ $$

Question Number 62179 Answers: 0 Comments: 1

∫_( 0) ^( 2 (√(ln 3))) ∫_( (y/2)) ^( (√(ln 3))) e^x^2 dx dy

$$\int_{\:\:\mathrm{0}} ^{\:\mathrm{2}\:\sqrt{\mathrm{ln}\:\mathrm{3}}} \:\int_{\:\:\frac{\mathrm{y}}{\mathrm{2}}} ^{\:\sqrt{\mathrm{ln}\:\mathrm{3}}} \:\:\:\mathrm{e}^{\mathrm{x}^{\mathrm{2}} } \:\:\mathrm{dx}\:\mathrm{dy} \\ $$

Question Number 62176 Answers: 2 Comments: 0

Question Number 62169 Answers: 1 Comments: 0

Prove without induction that: (1 + (√2))^(2n) + (1 − (√2))^(2n) is even for every natural number n.

$$\mathrm{Prove}\:\mathrm{without}\:\mathrm{induction}\:\mathrm{that}:\:\:\left(\mathrm{1}\:+\:\sqrt{\mathrm{2}}\right)^{\mathrm{2n}} \:+\:\left(\mathrm{1}\:−\:\sqrt{\mathrm{2}}\right)^{\mathrm{2n}} \:\:\mathrm{is}\:\mathrm{even}\:\mathrm{for}\:\mathrm{every} \\ $$$$\mathrm{natural}\:\mathrm{number}\:\mathrm{n}.\:\:\: \\ $$

Question Number 62147 Answers: 0 Comments: 0

Question Number 62146 Answers: 0 Comments: 0

calculate ∫ (√((x−1)/(x^2 +3)))dx .

$${calculate}\:\int\:\sqrt{\frac{{x}−\mathrm{1}}{{x}^{\mathrm{2}} \:+\mathrm{3}}}{dx}\:. \\ $$

Question Number 62145 Answers: 1 Comments: 1

calculate ∫_0 ^π ln(x^2 −2xsinθ +1)dθ

$${calculate}\:\:\int_{\mathrm{0}} ^{\pi} {ln}\left({x}^{\mathrm{2}} −\mathrm{2}{xsin}\theta\:+\mathrm{1}\right){d}\theta \\ $$

Question Number 62142 Answers: 0 Comments: 0

6.38÷0.2

$$\mathrm{6}.\mathrm{38}\boldsymbol{\div}\mathrm{0}.\mathrm{2} \\ $$

Question Number 62141 Answers: 0 Comments: 1

let A =∫_0 ^(+∞) (dx/((x^2 −i)^2 )) ( i^2 =−1) 1) calculate A 2) let R =Re(A) and I =Im(A) find the value of R and I .

$${let}\:{A}\:=\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:−{i}\right)^{\mathrm{2}} }\:\:\:\:\:\left(\:{i}^{\mathrm{2}} =−\mathrm{1}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A} \\ $$$$\left.\mathrm{2}\right)\:{let}\:{R}\:={Re}\left({A}\right)\:{and}\:{I}\:={Im}\left({A}\right) \\ $$$${find}\:\:{the}\:{value}\:{of}\:{R}\:{and}\:{I}\:. \\ $$

Question Number 62140 Answers: 1 Comments: 0

2÷(1/3)

$$\mathrm{2}\boldsymbol{\div}\frac{\mathrm{1}}{\mathrm{3}} \\ $$

Question Number 62139 Answers: 0 Comments: 0

6+5>3×5 true or false

$$\mathrm{6}+\mathrm{5}>\mathrm{3}×\mathrm{5}\:\mathrm{true}\:\mathrm{or}\:\mathrm{false} \\ $$

Question Number 62138 Answers: 0 Comments: 0

5^1

$$\mathrm{5}^{\mathrm{1}} \\ $$

Question Number 62137 Answers: 0 Comments: 0

((1/4))^3

$$\left(\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{3}} \\ $$

Question Number 62136 Answers: 0 Comments: 0

3 of (1/6)

$$\mathrm{3}\:\mathrm{of}\:\frac{\mathrm{1}}{\mathrm{6}} \\ $$

Question Number 62135 Answers: 0 Comments: 0

(√(100))

$$\sqrt{\mathrm{100}} \\ $$

Question Number 62134 Answers: 0 Comments: 0

8^4 ×8^2

$$\mathrm{8}^{\mathrm{4}} ×\mathrm{8}^{\mathrm{2}} \\ $$

Question Number 62133 Answers: 0 Comments: 0

5(2+3+1)

$$\mathrm{5}\left(\mathrm{2}+\mathrm{3}+\mathrm{1}\right) \\ $$

Question Number 62132 Answers: 0 Comments: 0

(3×2)^2

$$\left(\mathrm{3}×\mathrm{2}\right)^{\mathrm{2}} \\ $$

Question Number 62131 Answers: 0 Comments: 0

(1/3)+3(1/4)

$$\frac{\mathrm{1}}{\mathrm{3}}+\mathrm{3}\frac{\mathrm{1}}{\mathrm{4}} \\ $$

Question Number 62130 Answers: 1 Comments: 0

(√(α^2 −β^2 )) simplify

$$\sqrt{\alpha^{\mathrm{2}} −\beta^{\mathrm{2}} } \\ $$$${simplify}\: \\ $$$$ \\ $$

Question Number 62129 Answers: 0 Comments: 4

let f(x)=ln(x+1−2(√x)) 1) find D_f 2) determine f^(−1) 3) calculate ∫f (x)dx and ∫ f^(−1) (x)dx

$${let}\:{f}\left({x}\right)={ln}\left({x}+\mathrm{1}−\mathrm{2}\sqrt{{x}}\right) \\ $$$$\left.\mathrm{1}\right)\:{find}\:{D}_{{f}} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{f}^{−\mathrm{1}} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\:\int{f}\:\left({x}\right){dx}\:{and}\:\:\int\:{f}^{−\mathrm{1}} \left({x}\right){dx} \\ $$

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