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Question Number 85637 Answers: 1 Comments: 2

∫ (dx/(x+(√(x^2 +1))))

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

Question Number 85630 Answers: 0 Comments: 1

∫_0 ^(2Π) (dx/((√2)−cosx))

$$\int_{\mathrm{0}} ^{\mathrm{2}\Pi} \:\:\:\frac{{dx}}{\sqrt{\mathrm{2}}−{cosx}}\:\: \\ $$

Question Number 85625 Answers: 1 Comments: 0

lim_(x→0) ((x^n −(sin x)^n )/((sin x)^(n+2) ))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{x}^{\mathrm{n}} −\left(\mathrm{sin}\:\mathrm{x}\right)^{\mathrm{n}} }{\left(\mathrm{sin}\:\mathrm{x}\right)^{\mathrm{n}+\mathrm{2}} } \\ $$

Question Number 85624 Answers: 0 Comments: 0

Question Number 85623 Answers: 1 Comments: 0

prove that sin x cos 2x = (1/(4sin 4x sec x))

$$\mathrm{prove}\:\mathrm{that}\: \\ $$$$\mathrm{sin}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{2x}\:=\:\frac{\mathrm{1}}{\mathrm{4sin}\:\mathrm{4x}\:\mathrm{sec}\:\mathrm{x}} \\ $$

Question Number 85620 Answers: 1 Comments: 0

prove that cosh (x−y)=cosh xcosh y−sinh xsinh y

$${prove}\:{that} \\ $$$$ \\ $$$$\mathrm{cosh}\:\left({x}−{y}\right)=\mathrm{cosh}\:{x}\mathrm{cosh}\:{y}−\mathrm{sinh}\:{x}\mathrm{sinh}\:{y} \\ $$

Question Number 85606 Answers: 0 Comments: 7

Question Number 85603 Answers: 0 Comments: 0

prove the relation ∫_0 ^1 ((li_5 ((x)^(1/5) ))/(x)^(1/5) )dx=(5/4)(((25)/(3072))−((ζ(2))/2^6 )+((ζ(3))/2^4 )−((ζ(4))/2^2 )+ζ(5))

$${prove}\:{the}\:{relation} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{li}_{\mathrm{5}} \left(\sqrt[{\mathrm{5}}]{{x}}\right)}{\sqrt[{\mathrm{5}}]{{x}}}{dx}=\frac{\mathrm{5}}{\mathrm{4}}\left(\frac{\mathrm{25}}{\mathrm{3072}}−\frac{\zeta\left(\mathrm{2}\right)}{\mathrm{2}^{\mathrm{6}} }+\frac{\zeta\left(\mathrm{3}\right)}{\mathrm{2}^{\mathrm{4}} }−\frac{\zeta\left(\mathrm{4}\right)}{\mathrm{2}^{\mathrm{2}} }+\zeta\left(\mathrm{5}\right)\right) \\ $$

Question Number 85592 Answers: 1 Comments: 0

∫(((u+1)^2 )/(u^3 +u))du

$$\int\frac{\left(\mathrm{u}+\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{u}^{\mathrm{3}} +\mathrm{u}}\mathrm{du} \\ $$

Question Number 85591 Answers: 1 Comments: 0

∫((1+4u)/(−4u^2 +2u+2))du

$$\int\frac{\mathrm{1}+\mathrm{4u}}{−\mathrm{4u}^{\mathrm{2}} +\mathrm{2u}+\mathrm{2}}\mathrm{du} \\ $$$$ \\ $$

Question Number 85590 Answers: 0 Comments: 0

∫((1+4u)/(−4u^2 +2u+2))du

$$\int\frac{\mathrm{1}+\mathrm{4u}}{−\mathrm{4u}^{\mathrm{2}} +\mathrm{2u}+\mathrm{2}}\mathrm{du} \\ $$$$ \\ $$

Question Number 85588 Answers: 0 Comments: 6

Question Number 85601 Answers: 0 Comments: 2

∫((4u)/(4u^2 −4u+1))du

$$\int\frac{\mathrm{4u}}{\mathrm{4u}^{\mathrm{2}} −\mathrm{4u}+\mathrm{1}}\mathrm{du} \\ $$

Question Number 85600 Answers: 1 Comments: 3

∫(x^2 /(√(1+x^2 ))) dx

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

Question Number 85596 Answers: 1 Comments: 1

∫(((√(x+1))−1)/((√(x−1))+1)) dx

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

Question Number 85583 Answers: 0 Comments: 0

Question Number 85580 Answers: 0 Comments: 0

Solve: (D^2 +2D+1)y= x cos x

$$\boldsymbol{\mathrm{Solve}}: \\ $$$$\:\left(\mathrm{D}^{\mathrm{2}} +\mathrm{2D}+\mathrm{1}\right)\mathrm{y}=\:\mathrm{x}\:\mathrm{cos}\:\mathrm{x} \\ $$$$ \\ $$

Question Number 85582 Answers: 0 Comments: 1

cos ((π/9))+cos (((2π)/9))+cos (((4π)/9))=

$$\mathrm{cos}\:\left(\frac{\pi}{\mathrm{9}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{2}\pi}{\mathrm{9}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{4}\pi}{\mathrm{9}}\right)= \\ $$

Question Number 85568 Answers: 4 Comments: 2

∫ _0 ^(2π) (dx/((√2)−cos x))

$$\int\underset{\mathrm{0}} {\overset{\mathrm{2}\pi} {\:}}\:\frac{\mathrm{dx}}{\sqrt{\mathrm{2}}−\mathrm{cos}\:\mathrm{x}} \\ $$

Question Number 85557 Answers: 0 Comments: 3

x = (√(1+ (√(5+ (√(11+ (√(19+...)))))))) x = ?

$${x}\:\:=\:\:\sqrt{\mathrm{1}+\:\sqrt{\mathrm{5}+\:\sqrt{\mathrm{11}+\:\sqrt{\mathrm{19}+...}}}} \\ $$$${x}\:\:=\:\:\:? \\ $$

Question Number 85555 Answers: 1 Comments: 0

2x^2 +5x+7=0

$$\mathrm{2}{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{7}=\mathrm{0} \\ $$

Question Number 85554 Answers: 0 Comments: 1

2x^2 +5x+7=0

$$\mathrm{2}{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{7}=\mathrm{0} \\ $$

Question Number 85551 Answers: 0 Comments: 1

∫ (dx/(x^2 (x^4 +1)^(3/4) ))

$$\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{4}} +\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{4}}} } \\ $$

Question Number 85546 Answers: 0 Comments: 1

Question Number 85542 Answers: 1 Comments: 4

Question Number 85540 Answers: 1 Comments: 0

find the range y=((x+[x])/(1−[x]+x))

$${find}\:{the}\:{range} \\ $$$${y}=\frac{{x}+\left[{x}\right]}{\mathrm{1}−\left[{x}\right]+{x}} \\ $$

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