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Question Number 162015 Answers: 2 Comments: 0

find ∫_(−∞) ^(+∞) (dx/((x^2 −x+1)^4 ))

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

Question Number 162003 Answers: 2 Comments: 0

((27((27((27.... ))^(1/4) ))^(1/4) ))^(1/4) =x (√(5(√(5(√(5(√(5.....))))))))=y y^2 −x^2 =?

$$\sqrt[{\mathrm{4}}]{\mathrm{27}\sqrt[{\mathrm{4}}]{\mathrm{27}\sqrt[{\mathrm{4}}]{\mathrm{27}....\:}}}={x} \\ $$$$\sqrt{\mathrm{5}\sqrt{\mathrm{5}\sqrt{\mathrm{5}\sqrt{\mathrm{5}.....}}}}={y} \\ $$$${y}^{\mathrm{2}} −{x}^{\mathrm{2}} =? \\ $$

Question Number 162002 Answers: 1 Comments: 0

calculate Ω = ∫_0 ^( 1) Li_( 2) (1 − x^( 4) )dx = ? −−−−−

$$ \\ $$$$\:\:\:\:\:\:\:\:{calculate} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \mathrm{Li}_{\:\mathrm{2}} \:\left(\mathrm{1}\:−\:{x}^{\:\mathrm{4}} \right){dx}\:=\:? \\ $$$$\:\:\:\:−−−−− \\ $$

Question Number 162001 Answers: 1 Comments: 0

nature of: ∫_0 ^(+oo) ((sint)/(e^t −1))dt

$${nature}\:{of}: \\ $$$$\int_{\mathrm{0}} ^{+{oo}} \frac{{sint}}{{e}^{{t}} −\mathrm{1}}{dt} \\ $$

Question Number 161999 Answers: 1 Comments: 0

∫(dx/( (√(x^3 −4x))))

$$\int\frac{{dx}}{\:\sqrt{{x}^{\mathrm{3}} −\mathrm{4}{x}}} \\ $$

Question Number 161994 Answers: 0 Comments: 0

∫_0 ^1 ((ln∣x∣ln∣((1+x)/(1−x))∣)/(1−x^2 ))dx=???

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{ln}}\mid\boldsymbol{{x}}\mid\boldsymbol{\mathrm{ln}}\mid\frac{\mathrm{1}+\boldsymbol{\mathrm{x}}}{\mathrm{1}−\boldsymbol{\mathrm{x}}}\mid}{\mathrm{1}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\boldsymbol{\mathrm{dx}}=??? \\ $$

Question Number 161991 Answers: 1 Comments: 1

Question Number 161968 Answers: 1 Comments: 0

Find coefficient of x^(29) in expansion of (1+x^5 +x^7 +x^9 )^(1000) .

$${Find}\:\:{coefficient}\:\:{of}\:\:{x}^{\mathrm{29}} \:\:{in}\:\:{expansion}\:\:{of}\:\:\:\left(\mathrm{1}+{x}^{\mathrm{5}} +{x}^{\mathrm{7}} +{x}^{\mathrm{9}} \right)^{\mathrm{1000}} \:. \\ $$

Question Number 161967 Answers: 3 Comments: 0

∫_0 ^1 ((ln^2 (x))/((1−x^2 )))dx=?

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{ln}}^{\mathrm{2}} \left(\boldsymbol{\mathrm{x}}\right)}{\left(\mathrm{1}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} \right)}\boldsymbol{\mathrm{dx}}=? \\ $$

Question Number 161966 Answers: 1 Comments: 0

∫x^2 7^x^2 dx=?

$$\int\boldsymbol{\mathrm{x}}^{\mathrm{2}} \mathrm{7}^{\boldsymbol{\mathrm{x}}^{\mathrm{2}} } \boldsymbol{\mathrm{dx}}=? \\ $$

Question Number 161964 Answers: 2 Comments: 0

Prove that: (a series inspired Knopp Konrad) (√e^𝛑 ) = Σ_(k=0) ^∞ ((sin(((kπ)/4)))/((k!) (√2^k ))) π^k

$$\mathrm{Prove}\:\mathrm{that}:\:\left(\mathrm{a}\:\mathrm{series}\:\mathrm{inspired}\:\mathrm{Knopp}\:\mathrm{Konrad}\right) \\ $$$$\sqrt{\mathrm{e}^{\boldsymbol{\pi}} }\:\:=\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{sin}\left(\frac{{k}\pi}{\mathrm{4}}\right)}{\left(\mathrm{k}!\right)\:\sqrt{\mathrm{2}^{\boldsymbol{\mathrm{k}}} }}\:\:\pi^{\boldsymbol{\mathrm{k}}} \\ $$

Question Number 161952 Answers: 0 Comments: 5

!!8=?

$$!!\mathrm{8}=? \\ $$

Question Number 161951 Answers: 2 Comments: 0

x^x =2^(2048) x=?

$${x}^{{x}} =\mathrm{2}^{\mathrm{2048}} \\ $$$${x}=? \\ $$

Question Number 161947 Answers: 2 Comments: 0

abc=8 a+b+c=7 a^3 +b^3 +c^3 =73 then faind the vole of (1/a)+(1/b)+(1/c)=?

$${abc}=\mathrm{8} \\ $$$${a}+{b}+{c}=\mathrm{7} \\ $$$${a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} =\mathrm{73} \\ $$$${then}\:{faind}\:\:{the}\:{vole}\:{of} \\ $$$$\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}+\frac{\mathrm{1}}{{c}}=? \\ $$

Question Number 161946 Answers: 2 Comments: 0

Question Number 161945 Answers: 1 Comments: 0

Prove that ∫_0 ^∞ (((xcos(x)−sin(x))^2 )/x^6 )dx =(𝛑/(15))

$$\:\:\boldsymbol{{P}\mathrm{rove}}\:\boldsymbol{\mathrm{that}}\:\int_{\mathrm{0}} ^{\infty} \frac{\left(\boldsymbol{{xcos}}\left(\boldsymbol{{x}}\right)−\boldsymbol{{sin}}\left(\boldsymbol{{x}}\right)\right)^{\mathrm{2}} }{\boldsymbol{{x}}^{\mathrm{6}} }\boldsymbol{{dx}}\:=\frac{\boldsymbol{\pi}}{\mathrm{15}} \\ $$

Question Number 161939 Answers: 0 Comments: 0

Σ_(n=1) ^(1010) tg^2 (((πn)/(2022)))=?

$$\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\mathrm{1010}} {\sum}}\boldsymbol{\mathrm{tg}}^{\mathrm{2}} \left(\frac{\pi\boldsymbol{\mathrm{n}}}{\mathrm{2022}}\right)=? \\ $$

Question Number 161931 Answers: 0 Comments: 4

If (( 1−sin(x)−cos(x))/(1+sin(x)−cos(x))) = (1/4) then find the value of: tan(x) + (1/(cos(x))) =?

$$ \\ $$$$\:\:\:\:\:\:\mathrm{I}{f}\:\:\:\:\frac{\:\mathrm{1}−{sin}\left({x}\right)−{cos}\left({x}\right)}{\mathrm{1}+{sin}\left({x}\right)−{cos}\left({x}\right)}\:=\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\:\:\:\:\:\:\:{then}\:\:{find}\:{the}\:{value}\:{of}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{tan}\left({x}\right)\:+\:\frac{\mathrm{1}}{{cos}\left({x}\right)}\:=? \\ $$$$\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 161930 Answers: 1 Comments: 0

{ ((a_0 =−2 )),((a_n =a_(n−1) +2n)) :} ; a_n =?

$$\begin{cases}{{a}_{\mathrm{0}} =−\mathrm{2}\:}\\{{a}_{{n}} ={a}_{{n}−\mathrm{1}} +\mathrm{2}{n}}\end{cases}\:\:\:\:\:;\:{a}_{{n}} =? \\ $$

Question Number 161926 Answers: 0 Comments: 0

Question Number 161919 Answers: 1 Comments: 0

∫_(−∞) ^( ∞) sin(x^2 +x+1)dx

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

Question Number 161917 Answers: 0 Comments: 0

∫_(−∞) ^( ∞) (1/( (√(x^4 +x+1)) )) dx

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{−\infty} ^{\:\infty} \:\frac{\mathrm{1}}{\:\sqrt{{x}^{\mathrm{4}} +{x}+\mathrm{1}}\:}\:{dx} \\ $$$$\: \\ $$

Question Number 161914 Answers: 1 Comments: 0

If , x^( 2) + 9y^( 2) + 4x +18y −23=0 then find the value of , M_ ax ( 3x+2y ) . −−−−−−−−−

$$\:\mathrm{If}\:, \\ $$$$\:\:\:{x}^{\:\mathrm{2}} \:+\:\mathrm{9}{y}^{\:\mathrm{2}} \:+\:\mathrm{4}{x}\:+\mathrm{18}{y}\:−\mathrm{23}=\mathrm{0} \\ $$$$ \\ $$$$\:{then}\:\:{find}\:{the}\:{value}\:\:{of}\:\:,\:\:\mathrm{M}_{\:} {ax}\:\left(\:\mathrm{3}{x}+\mathrm{2}{y}\:\right)\:. \\ $$$$\:−−−−−−−−− \\ $$$$ \\ $$

Question Number 161912 Answers: 1 Comments: 6

Question Number 162027 Answers: 1 Comments: 0

Question Number 161907 Answers: 0 Comments: 1

(1)((1/2)+cos (π/(20)))((1/2)+cos ((3π)/(20)))((1/2)+cos ((9π)/(20)))((1/2)+cos ((27π)/(20)))=? (2) tan (π/(30)) tan ((7π)/(30)) tan ((11π)/(30)) =?

$$\left(\mathrm{1}\right)\left(\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{cos}\:\frac{\pi}{\mathrm{20}}\right)\left(\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{cos}\:\frac{\mathrm{3}\pi}{\mathrm{20}}\right)\left(\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{cos}\:\frac{\mathrm{9}\pi}{\mathrm{20}}\right)\left(\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{cos}\:\frac{\mathrm{27}\pi}{\mathrm{20}}\right)=? \\ $$$$\left(\mathrm{2}\right)\:\mathrm{tan}\:\frac{\pi}{\mathrm{30}}\:\mathrm{tan}\:\frac{\mathrm{7}\pi}{\mathrm{30}}\:\mathrm{tan}\:\frac{\mathrm{11}\pi}{\mathrm{30}}\:=? \\ $$

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