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Question Number 59631 Answers: 2 Comments: 3

1) calculate ∫_0 ^(2π) (dx/(acosx +bsinx)) with a , b reals 2)find also ∫_0 ^(2π) ((cosx dx)/((acosx +bsinx)^2 )) and ∫_0 ^(2π) ((sinx dx)/((acosx +bsinx)^2 )) 3) find the value of ∫_0 ^(2π) (dx/(2cosx +(√3)sinx))

$$\left.\mathrm{1}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{dx}}{{acosx}\:+{bsinx}} \\ $$$${with}\:{a}\:,\:{b}\:{reals} \\ $$$$\left.\mathrm{2}\right){find}\:{also}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{cosx}\:{dx}}{\left({acosx}\:+{bsinx}\right)^{\mathrm{2}} }\:\:{and} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sinx}\:{dx}}{\left({acosx}\:+{bsinx}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{dx}}{\mathrm{2}{cosx}\:+\sqrt{\mathrm{3}}{sinx}} \\ $$

Question Number 59627 Answers: 1 Comments: 0

Question Number 59626 Answers: 1 Comments: 0

Rationalize the denominator of (2/(1 − (√(2 + (4)^(1/3) ))))

$${Rationalize}\:\:{the}\:\:{denominator}\:\:{of} \\ $$$$\:\:\:\:\:\:\:\:\frac{\mathrm{2}}{\mathrm{1}\:−\:\sqrt{\mathrm{2}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{4}}}} \\ $$

Question Number 59625 Answers: 0 Comments: 0

Sum the series: ((( ^n C_1 )/( ^n C_0 )))^2 + (2 × (( ^n C_2 )/( ^n C_1 ))) + (3 × (( ^n C_3 )/( ^n C_2 )))^2 + .... n terms

$$\mathrm{Sum}\:\mathrm{the}\:\mathrm{series}:\:\:\:\:\:\:\:\left(\frac{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{1}} }{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{0}} }\right)^{\mathrm{2}} \:+\:\left(\mathrm{2}\:×\:\frac{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{2}} }{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{1}} }\right)\:+\:\left(\mathrm{3}\:×\:\frac{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{3}} }{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{2}} }\right)^{\mathrm{2}} \:+\:....\:\:\boldsymbol{\mathrm{n}}\:\mathrm{terms} \\ $$

Question Number 59624 Answers: 1 Comments: 0

Rationalize the denominator of (2/((√(x+2)) + (√(x+1)) + (√x)))

$${Rationalize}\:\:\:{the}\:\:{denominator}\:\:{of} \\ $$$$\:\:\:\:\:\:\frac{\mathrm{2}}{\sqrt{{x}+\mathrm{2}}\:\:+\:\:\sqrt{{x}+\mathrm{1}}\:\:+\:\:\sqrt{{x}}} \\ $$

Question Number 59620 Answers: 1 Comments: 2

Question Number 59615 Answers: 1 Comments: 0

6+((1/5)×7)

$$\mathrm{6}+\left(\frac{\mathrm{1}}{\mathrm{5}}×\mathrm{7}\right) \\ $$

Question Number 59614 Answers: 1 Comments: 0

1(1/7)+1(1/(14))

$$\mathrm{1}\frac{\mathrm{1}}{\mathrm{7}}+\mathrm{1}\frac{\mathrm{1}}{\mathrm{14}} \\ $$

Question Number 59608 Answers: 0 Comments: 0

For your development solve this (d^2 r/dt^2 )=(A/(r^2 (t))) where r(t)=αt^β

$${For}\:{your}\:{development}\:{solve}\:{this} \\ $$$$\frac{{d}^{\mathrm{2}} {r}}{{dt}^{\mathrm{2}} }=\frac{{A}}{{r}^{\mathrm{2}} \left({t}\right)}\:\:{where}\:{r}\left({t}\right)=\alpha{t}^{\beta} \\ $$

Question Number 59600 Answers: 1 Comments: 0

Question Number 59599 Answers: 1 Comments: 0

Question Number 59595 Answers: 1 Comments: 1

Question Number 59588 Answers: 1 Comments: 1

find x,y in R (x+yi)^3 =((1+(√(15)) i)/((√5) − (√3) i))

$${find}\:{x},{y}\:{in}\:{R} \\ $$$$\left({x}+{yi}\right)^{\mathrm{3}} =\frac{\mathrm{1}+\sqrt{\mathrm{15}}\:{i}}{\sqrt{\mathrm{5}}\:−\:\sqrt{\mathrm{3}}\:{i}} \\ $$

Question Number 59581 Answers: 2 Comments: 0

Determine a , b , c in terms of α , β , γ. ab+c=γ bc+a=α ca+b=β

$$\mathcal{D}{etermine}\:{a}\:,\:{b}\:,\:{c}\:{in}\:{terms}\:{of}\:\alpha\:,\:\beta\:,\:\gamma. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{ab}+{c}=\gamma\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{bc}+{a}=\alpha \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{ca}+{b}=\beta \\ $$

Question Number 59580 Answers: 1 Comments: 1

decompose at simple element the fraction F(x) =(1/(x^7 (x^2 −1)^2 ))

$${decompose}\:{at}\:{simple}\:{element}\:{the}\:{fraction}\: \\ $$$${F}\left({x}\right)\:=\frac{\mathrm{1}}{{x}^{\mathrm{7}} \left({x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 59576 Answers: 0 Comments: 4

let f(x) =∫ (dt/((x+t)(√(t^2 −x^2 )))) 1) determine a explicit form of f(x) 2) determine ∫ (dt/((x+2)(√(t^2 −4)))) and ∫ (dt/((x+1)(√(t^2 −1))))

$${let}\:{f}\left({x}\right)\:=\int\:\:\:\:\:\:\:\frac{{dt}}{\left({x}+{t}\right)\sqrt{{t}^{\mathrm{2}} −{x}^{\mathrm{2}} }} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{determine}\:\int\:\:\:\:\:\frac{{dt}}{\left({x}+\mathrm{2}\right)\sqrt{{t}^{\mathrm{2}} −\mathrm{4}}}\:\:{and}\:\:\int\:\:\:\:\:\:\frac{{dt}}{\left({x}+\mathrm{1}\right)\sqrt{{t}^{\mathrm{2}} −\mathrm{1}}} \\ $$

Question Number 59575 Answers: 1 Comments: 0

find ∫ ((sin(2x))/(1+cos^2 x))dx

$${find}\:\int\:\:\frac{{sin}\left(\mathrm{2}{x}\right)}{\mathrm{1}+{cos}^{\mathrm{2}} {x}}{dx} \\ $$

Question Number 59562 Answers: 1 Comments: 0

Derive the equations of motion 1)Vu+at

$$\left.\mathrm{Derive}\:\:\mathrm{the}\:\mathrm{equations}\:\mathrm{of}\:\mathrm{motion}\:\mathrm{1}\right)\mathrm{Vu}+\mathrm{at} \\ $$

Question Number 59552 Answers: 1 Comments: 0

(1/4)+((1/4)+(1/8))

$$\frac{\mathrm{1}}{\mathrm{4}}+\left(\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{8}}\right) \\ $$

Question Number 59551 Answers: 1 Comments: 0

1.8×1.6

$$\mathrm{1}.\mathrm{8}×\mathrm{1}.\mathrm{6} \\ $$

Question Number 59550 Answers: 1 Comments: 0

9+(5×4+5^3 )

$$\mathrm{9}+\left(\mathrm{5}×\mathrm{4}+\mathrm{5}^{\mathrm{3}} \right) \\ $$

Question Number 59549 Answers: 2 Comments: 0

(1/5)×i i=7

$$\frac{\mathrm{1}}{\mathrm{5}}×\mathrm{i}\:\:\mathrm{i}=\mathrm{7} \\ $$

Question Number 59547 Answers: 1 Comments: 0

4+t×c t=3 c=6

$$\mathrm{4}+\mathrm{t}×\mathrm{c}\:\mathrm{t}=\mathrm{3}\:\mathrm{c}=\mathrm{6} \\ $$

Question Number 59542 Answers: 0 Comments: 4

lim_(x→0) ((ln(cosx))/x^2 ) I have a doubt

$$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:\frac{\mathrm{ln}\left(\mathrm{cosx}\right)}{\mathrm{x}^{\mathrm{2}} } \\ $$$${I}\:{have}\:{a}\:{doubt} \\ $$

Question Number 59563 Answers: 2 Comments: 1

Question Number 59528 Answers: 0 Comments: 5

let f(x) =∫_0 ^1 (dt/(1+xch(t))) with x real 1) determine a explicit form of f(x) 2)find also g(x)=∫_0 ^1 (dt/((1+xch(t))^2 )) 3) calculate ∫_0 ^1 (dt/(1+3ch(t))) and ∫_0 ^1 (dt/((1+3ch(t))^2 ))

$${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\mathrm{1}+{xch}\left({t}\right)}\:{with}\:{x}\:{real} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{also}\:{g}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{dt}}{\left(\mathrm{1}+{xch}\left({t}\right)\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dt}}{\mathrm{1}+\mathrm{3}{ch}\left({t}\right)}\:{and}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{dt}}{\left(\mathrm{1}+\mathrm{3}{ch}\left({t}\right)\right)^{\mathrm{2}} } \\ $$

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