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Question Number 82971 Answers: 1 Comments: 2

1)find ∫ (dx/((x^2 +x+1)^6 )) 2)calculate ∫_(−∞) ^(+∞) (dx/((x^2 +x+1)^6 ))

$$\left.\mathrm{1}\right){find}\:\int\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{6}} } \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{−\infty} ^{+\infty} \:\frac{{dx}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{6}} } \\ $$

Question Number 82970 Answers: 0 Comments: 2

1)find ∫ (dx/((x^2 −1)^9 )) 2) calculate ∫_2 ^(+∞) (dx/((x^2 −1)^9 ))

$$\left.\mathrm{1}\right){find}\:\int\:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{9}} } \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{2}} ^{+\infty} \:\frac{{dx}}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{9}} } \\ $$

Question Number 82954 Answers: 1 Comments: 3

∫ ((cos 4x−cos 2x)/(sin 4x−cos 2x)) dx

$$\int\:\frac{\mathrm{cos}\:\mathrm{4x}−\mathrm{cos}\:\mathrm{2x}}{\mathrm{sin}\:\mathrm{4x}−\mathrm{cos}\:\mathrm{2x}}\:\mathrm{dx}\: \\ $$

Question Number 82953 Answers: 0 Comments: 3

verify that: cosh.cosh^(−1) (y) = y, if y ∈ (1, + ∞)

$$\mathrm{verify}\:\mathrm{that}:\:\:\:\:\:\:\mathrm{cosh}.\mathrm{cosh}^{−\mathrm{1}} \left(\mathrm{y}\right)\:\:\:=\:\:\:\mathrm{y},\:\:\:\:\:\mathrm{if}\:\:\:\:\:\mathrm{y}\:\:\in\:\:\left(\mathrm{1},\:\:\:+\:\infty\right) \\ $$

Question Number 82952 Answers: 1 Comments: 0

Show that: y + (√(y^2 − 1)) ≥ 1 and 0 < y − (√(y^2 − 1)) ≤ 1 if y ≥ 1

$$\mathrm{Show}\:\mathrm{that}:\:\:\:\:\:\:\mathrm{y}\:\:+\:\:\sqrt{\mathrm{y}^{\mathrm{2}} \:−\:\mathrm{1}}\:\:\:\geqslant\:\:\mathrm{1}\:\:\:\:\:\mathrm{and}\:\:\:\:\mathrm{0}\:\:<\:\:\mathrm{y}\:\:−\:\:\sqrt{\mathrm{y}^{\mathrm{2}} \:−\:\mathrm{1}}\:\:\leqslant\:\:\mathrm{1} \\ $$$$\mathrm{if}\:\:\mathrm{y}\:\:\geqslant\:\mathrm{1} \\ $$

Question Number 82944 Answers: 1 Comments: 2

sin^2 (27^o )+sin^2 (87^o )+sin^2 (33^o ) =

$$ \\ $$$$\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{27}^{\mathrm{o}} \right)+\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{87}^{\mathrm{o}} \right)+\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{33}^{\mathrm{o}} \right)\:= \\ $$

Question Number 82937 Answers: 0 Comments: 2

Find the area between the curves y= log x and y= (log x)^2 .

$$\:\: \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{between}\:\mathrm{the}\:\mathrm{curves} \\ $$$$\:\mathrm{y}=\:\mathrm{log}\:\mathrm{x}\:\:\mathrm{and}\:\mathrm{y}=\:\left(\mathrm{log}\:\mathrm{x}\right)^{\mathrm{2}} . \\ $$

Question Number 82950 Answers: 1 Comments: 1

lim_(x→0) ((((1+tan x))^(1/(3 )) −((1+sin x))^(1/(3 )) )/x^3 ) =

$$ \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{3}\:}]{\mathrm{1}+\mathrm{tan}\:\mathrm{x}}\:−\sqrt[{\mathrm{3}\:}]{\mathrm{1}+\mathrm{sin}\:\mathrm{x}}}{\mathrm{x}^{\mathrm{3}} }\:=\: \\ $$

Question Number 82929 Answers: 2 Comments: 0

if 2B+A=45° show that; tan B= ((1−2tanA−tan^2 A)/(1+2tanA−tan^2 A))

$${if}\:\mathrm{2}{B}+{A}=\mathrm{45}° \\ $$$${show}\:{that}; \\ $$$${tan}\:{B}=\:\frac{\mathrm{1}−\mathrm{2}{tanA}−{tan}^{\mathrm{2}} {A}}{\mathrm{1}+\mathrm{2}{tanA}−{tan}^{\mathrm{2}} {A}} \\ $$

Question Number 82924 Answers: 1 Comments: 2

lim_(x→0) (((√(tan x))−(√(sin x)))/(x^2 (√x)))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{tan}\:\mathrm{x}}−\sqrt{\mathrm{sin}\:\mathrm{x}}}{\mathrm{x}^{\mathrm{2}} \sqrt{\mathrm{x}}} \\ $$

Question Number 82901 Answers: 1 Comments: 0

Question Number 82897 Answers: 1 Comments: 2

Question Number 82891 Answers: 2 Comments: 0

∫ (1/(√(1−x^4 ))) dx = ?

$$\int\:\frac{\mathrm{1}}{\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{4}} }}\:\mathrm{dx}\:=\:? \\ $$

Question Number 82887 Answers: 1 Comments: 1

find without using l′hopital lim_(x→0) ((ln(1+cos(x))−ln(2))/x)

$${find}\:{without}\:{using}\:{l}'{hopital} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\frac{{ln}\left(\mathrm{1}+{cos}\left({x}\right)\right)−{ln}\left(\mathrm{2}\right)}{{x}} \\ $$

Question Number 82886 Answers: 0 Comments: 2

prove (tanx+cot^2 x)^2 =sex^2 x+cosec^2 x

$${prove}\: \\ $$$$\left({tanx}+{cot}^{\mathrm{2}} {x}\right)^{\mathrm{2}} ={sex}^{\mathrm{2}} {x}+{cosec}^{\mathrm{2}} {x} \\ $$

Question Number 82883 Answers: 1 Comments: 0

[(e^(−2(√x)) /(√x))−(y/(√x)) ] .(dx/dy) = 1 , x ≠ 0

$$\left[\frac{\mathrm{e}^{−\mathrm{2}\sqrt{\mathrm{x}}} }{\sqrt{\mathrm{x}}}−\frac{\mathrm{y}}{\sqrt{\mathrm{x}}}\:\right]\:.\frac{\mathrm{dx}}{\mathrm{dy}}\:=\:\mathrm{1}\:,\:\mathrm{x}\:\neq\:\mathrm{0} \\ $$

Question Number 82881 Answers: 1 Comments: 2

(√(√(...(√(6561))))) = 3^8^x (60 times) find x

$$ \\ $$$$\sqrt{\sqrt{...\sqrt{\mathrm{6561}}}}\:=\:\mathrm{3}^{\mathrm{8}^{\mathrm{x}} } \:\left(\mathrm{60}\:\mathrm{times}\right) \\ $$$$\mathrm{find}\:\mathrm{x} \\ $$

Question Number 82879 Answers: 0 Comments: 1

prove that ((cos^2 a+sin^2 b)/(sin acos a + sin bcos b)) = cot (a+b)

$$\mathrm{prove}\:\mathrm{that}\: \\ $$$$\frac{\mathrm{cos}\:^{\mathrm{2}} \mathrm{a}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{b}}{\mathrm{sin}\:\mathrm{acos}\:\mathrm{a}\:+\:\mathrm{sin}\:\mathrm{bcos}\:\mathrm{b}}\:=\:\mathrm{cot}\:\left(\mathrm{a}+\mathrm{b}\right) \\ $$

Question Number 82878 Answers: 1 Comments: 3

Question Number 82920 Answers: 1 Comments: 0

calculate lim_(x→0) ((ln(1+ln(1+x)))/x)

$${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{{ln}\left(\mathrm{1}+{ln}\left(\mathrm{1}+{x}\right)\right)}{{x}} \\ $$

Question Number 82919 Answers: 1 Comments: 2

bangun datar

$${bangun}\:{datar} \\ $$

Question Number 82872 Answers: 0 Comments: 1

1)find ∫∫_W ((xdx)/(a^2 +x^2 +y^2 )) with W_a →x^2 +y^2 ≤a^2 and x>0 (a>0) 2)calculate ∫∫_W_1 ((xdx)/(x^2 +y^2 +1))

$$\left.\mathrm{1}\right){find}\:\int\int_{{W}} \:\frac{{xdx}}{{a}^{\mathrm{2}} \:+{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }\:{with} \\ $$$${W}_{{a}} \rightarrow{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:\leqslant{a}^{\mathrm{2}} \:{and}\:{x}>\mathrm{0}\:\:\:\:\:\left({a}>\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:\int\int_{{W}_{\mathrm{1}} } \:\:\:\frac{{xdx}}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:+\mathrm{1}} \\ $$

Question Number 82871 Answers: 0 Comments: 1

find ∫∫_([0,1]^2 ) ∣x^2 −y^2 ∣dxdy

$${find}\:\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{2}} } \:\:\:\mid{x}^{\mathrm{2}} −{y}^{\mathrm{2}} \mid{dxdy} \\ $$

Question Number 82873 Answers: 1 Comments: 2

Question Number 82867 Answers: 0 Comments: 3

hello prove that ∫_0 ^(+∞) sin(x^4 )dx=sin((π/8))∫_0 ^(+∞) e^(−x^4 ) dx? verry nice day Good Bless You

$${hello}\:{prove}\:{that}\:\int_{\mathrm{0}} ^{+\infty} {sin}\left({x}^{\mathrm{4}} \right){dx}={sin}\left(\frac{\pi}{\mathrm{8}}\right)\int_{\mathrm{0}} ^{+\infty} {e}^{−{x}^{\mathrm{4}} } {dx}? \\ $$$${verry}\:{nice}\:{day}\:{Good}\:{Bless}\:{You} \\ $$

Question Number 82843 Answers: 1 Comments: 0

show that (((1+(√3) i)^4 (1+i)^8 )/((cos100°−i sin100)^3 ))=−256

$${show}\:{that} \\ $$$$\frac{\left(\mathrm{1}+\sqrt{\mathrm{3}}\:{i}\right)^{\mathrm{4}} \left(\mathrm{1}+{i}\right)^{\mathrm{8}} }{\left({cos}\mathrm{100}°−{i}\:{sin}\mathrm{100}\right)^{\mathrm{3}} }=−\mathrm{256} \\ $$

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