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Question Number 92421    Answers: 1   Comments: 0

∫((cscx)/(cos(2x)+2cos^2 x))dx pleas sir help me

$$\int\frac{{cscx}}{{cos}\left(\mathrm{2}{x}\right)+\mathrm{2}{cos}^{\mathrm{2}} {x}}{dx} \\ $$$${pleas}\:{sir}\:{help}\:{me} \\ $$

Question Number 92420    Answers: 2   Comments: 2

Question Number 92447    Answers: 0   Comments: 1

find ∫_(1/6) ^(1/5) (dx/((√(1−3x))+(√(1+3x))))

$${find}\:\int_{\frac{\mathrm{1}}{\mathrm{6}}} ^{\frac{\mathrm{1}}{\mathrm{5}}} \:\:\frac{{dx}}{\sqrt{\mathrm{1}−\mathrm{3}{x}}+\sqrt{\mathrm{1}+\mathrm{3}{x}}} \\ $$

Question Number 92410    Answers: 0   Comments: 3

find ∫_1 ^(√2) (dx/((√(1+3x))−(√(1−3x))))

$${find}\:\int_{\mathrm{1}} ^{\sqrt{\mathrm{2}}} \:\:\:\:\frac{{dx}}{\sqrt{\mathrm{1}+\mathrm{3}{x}}−\sqrt{\mathrm{1}−\mathrm{3}{x}}} \\ $$

Question Number 92407    Answers: 0   Comments: 0

let f(a) =∫_0 ^1 ln((√(1+x))+a(√(1−x)))dx with a>0 1)explicite f(a) 2)find g(a) =∫_0 ^1 ((√(1−x))/((√(1+x))+a(√(1−x)))) dx 3) find the value of ∫_0 ^1 ln((√(1+x))+2(√(1−x)))dx and ∫_0 ^1 ln((√(1+x))+(1/3)(√(1−x)))dx 4) calculate A(θ) =∫_0 ^1 ln((√(1+x))+sinθ (√(1−x)))dx 0<θ<(π/2)

$${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\sqrt{\mathrm{1}+{x}}+{a}\sqrt{\mathrm{1}−{x}}\right){dx}\:\:\:{with}\:\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right){explicite}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{g}\left({a}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\sqrt{\mathrm{1}−{x}}}{\sqrt{\mathrm{1}+{x}}+{a}\sqrt{\mathrm{1}−{x}}}\:{dx} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\sqrt{\mathrm{1}+{x}}+\mathrm{2}\sqrt{\mathrm{1}−{x}}\right){dx} \\ $$$${and}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\sqrt{\mathrm{1}+{x}}+\frac{\mathrm{1}}{\mathrm{3}}\sqrt{\mathrm{1}−{x}}\right){dx} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:{A}\left(\theta\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\sqrt{\mathrm{1}+{x}}+{sin}\theta\:\sqrt{\mathrm{1}−{x}}\right){dx}\: \\ $$$$\mathrm{0}<\theta<\frac{\pi}{\mathrm{2}} \\ $$

Question Number 92399    Answers: 0   Comments: 1

sin^3 (x)+cos^4 (x) = 0

$$\mathrm{sin}\:^{\mathrm{3}} \left(\mathrm{x}\right)+\mathrm{cos}\:^{\mathrm{4}} \left(\mathrm{x}\right)\:=\:\mathrm{0} \\ $$

Question Number 92398    Answers: 1   Comments: 0

x^3 ((d^2 y/dx^2 )) +x^2 ((dy/dx))^2 = ln (x)

$$\mathrm{x}^{\mathrm{3}} \:\left(\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\right)\:+\mathrm{x}^{\mathrm{2}} \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{\mathrm{2}} \:=\:\mathrm{ln}\:\left(\mathrm{x}\right)\: \\ $$

Question Number 92397    Answers: 0   Comments: 2

∫ (1/(x−(√(1−x^2 )))) dx [ x = sin w ] ∫ ((cos w dw)/(sin w−cos w)) = ∫ (dw/(tan w−1)) = ∫ ((sec^2 w dw)/((tan w−1)sec^2 w)) = ∫ (du/((u−1)(u^2 +1))) ; [ u = tan w ] = ∫ (du/(2(u−1)))−∫ ((u du )/(2(u^2 +1))) = (1/2)ln ∣u−1∣ −(1/4)ln∣u^2 +1∣ −(1/2)tan^(−1) (u) +c = (1/2)ln∣tan w−1∣−(1/4)ln∣tan^2 w+1∣− (1/2) tan^(−1) (tan w) +c = (1/2)ln∣(x/(√(1−x^2 )))−1∣+(1/4)ln∣1−x^2 ∣− (1/2)sin^(−1) (x) + c

$$\int\:\frac{\mathrm{1}}{{x}−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:{dx}\: \\ $$$$\left[\:{x}\:=\:\mathrm{sin}\:{w}\:\right]\: \\ $$$$\int\:\frac{\mathrm{cos}\:\mathrm{w}\:\mathrm{dw}}{\mathrm{sin}\:\mathrm{w}−\mathrm{cos}\:\mathrm{w}}\:=\:\int\:\frac{\mathrm{dw}}{\mathrm{tan}\:\mathrm{w}−\mathrm{1}} \\ $$$$=\:\int\:\frac{\mathrm{sec}^{\mathrm{2}} \:\mathrm{w}\:\mathrm{dw}}{\left(\mathrm{tan}\:\mathrm{w}−\mathrm{1}\right)\mathrm{sec}^{\mathrm{2}} \:\mathrm{w}} \\ $$$$=\:\int\:\frac{\mathrm{du}}{\left(\mathrm{u}−\mathrm{1}\right)\left(\mathrm{u}^{\mathrm{2}} +\mathrm{1}\right)}\:;\:\left[\:\mathrm{u}\:=\:\mathrm{tan}\:\mathrm{w}\:\right]\: \\ $$$$=\:\int\:\frac{\mathrm{du}}{\mathrm{2}\left(\mathrm{u}−\mathrm{1}\right)}−\int\:\frac{\mathrm{u}\:\mathrm{du}\:}{\mathrm{2}\left(\mathrm{u}^{\mathrm{2}} +\mathrm{1}\right)} \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\:\mid\mathrm{u}−\mathrm{1}\mid\:−\frac{\mathrm{1}}{\mathrm{4}}\mathrm{ln}\mid\mathrm{u}^{\mathrm{2}} +\mathrm{1}\mid\:−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{u}\right)\:+\mathrm{c} \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\mid\mathrm{tan}\:\mathrm{w}−\mathrm{1}\mid−\frac{\mathrm{1}}{\mathrm{4}}\mathrm{ln}\mid\mathrm{tan}\:^{\mathrm{2}} \mathrm{w}+\mathrm{1}\mid− \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{tan}\:\mathrm{w}\right)\:+\mathrm{c} \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\mid\frac{{x}}{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}−\mathrm{1}\mid+\frac{\mathrm{1}}{\mathrm{4}}\mathrm{ln}\mid\mathrm{1}−{x}^{\mathrm{2}} \mid− \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}^{−\mathrm{1}} \left({x}\right)\:+\:{c} \\ $$

Question Number 92394    Answers: 0   Comments: 2

∫ ln ((√(1−x)) + (√(1+x)) ) dx

$$\int\:\mathrm{ln}\:\left(\sqrt{\mathrm{1}−{x}}\:+\:\sqrt{\mathrm{1}+{x}}\:\right)\:{dx}\: \\ $$

Question Number 92390    Answers: 0   Comments: 2

What is the meaning of this symbol (ε) in limit please. or as used in convergent/divergent series

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{meaning}\:\mathrm{of}\:\mathrm{this}\:\mathrm{symbol}\:\:\left(\varepsilon\right)\:\mathrm{in}\:\mathrm{limit}\:\mathrm{please}. \\ $$$$\mathrm{or}\:\mathrm{as}\:\mathrm{used}\:\mathrm{in}\:\mathrm{convergent}/\mathrm{divergent}\:\mathrm{series} \\ $$

Question Number 92366    Answers: 0   Comments: 3

Question Number 92356    Answers: 0   Comments: 7

Question Number 92379    Answers: 1   Comments: 5

f(x) and g(x) are functions with no constants. if f ′(x)=g ′(x) is that mean f(x)=g(x) ??

$${f}\left({x}\right)\:{and}\:{g}\left({x}\right)\:{are}\:{functions}\:{with}\:{no} \\ $$$${constants}. \\ $$$${if}\:{f}\:'\left({x}\right)={g}\:'\left({x}\right)\:{is}\:{that}\:{mean}\:{f}\left({x}\right)={g}\left({x}\right) \\ $$$$?? \\ $$

Question Number 92347    Answers: 1   Comments: 3

Question Number 92346    Answers: 3   Comments: 3

solve ((1+(√x)))^(1/3) +((1−(√x)))^(1/3) =(5)^(1/3)

$${solve} \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{1}+\sqrt{{x}}}+\sqrt[{\mathrm{3}}]{\mathrm{1}−\sqrt{{x}}}=\sqrt[{\mathrm{3}}]{\mathrm{5}} \\ $$

Question Number 92344    Answers: 0   Comments: 3

∫_0 ^1 (dx/((√(1+3x))−(√(1−3x))))

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{dx}}{\sqrt{\mathrm{1}+\mathrm{3x}}−\sqrt{\mathrm{1}−\mathrm{3x}}} \\ $$

Question Number 92340    Answers: 0   Comments: 2

Π_(i = 1) ^∞ ((5^(((1/2))^i ) +3^(((1/2))^i ) )/2) =

$$\underset{\mathrm{i}\:=\:\mathrm{1}} {\overset{\infty} {\prod}}\:\frac{\mathrm{5}^{\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{i}} } +\mathrm{3}^{\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{i}} } }{\mathrm{2}}\:=\: \\ $$

Question Number 92337    Answers: 0   Comments: 0

Question Number 92335    Answers: 0   Comments: 0

(√({x})) = 1+ ln(x)

$$\sqrt{\left\{\mathrm{x}\right\}}\:=\:\mathrm{1}+\:\mathrm{ln}\left(\mathrm{x}\right)\: \\ $$

Question Number 92334    Answers: 0   Comments: 0

Question Number 92324    Answers: 1   Comments: 0

Find the value of x for which Σ_(n = 0) ^(n = ∞) 16((3/4)x + 1)^n (a) Is convergent (b) Is equal to 10(2/3)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{x}\:\:\mathrm{for}\:\mathrm{which}\:\:\:\:\underset{\mathrm{n}\:\:=\:\:\mathrm{0}} {\overset{\mathrm{n}\:\:=\:\:\infty} {\sum}}\:\mathrm{16}\left(\frac{\mathrm{3}}{\mathrm{4}}\mathrm{x}\:\:+\:\:\mathrm{1}\right)^{\mathrm{n}} \\ $$$$\left(\mathrm{a}\right)\:\:\:\mathrm{Is}\:\mathrm{convergent} \\ $$$$\left(\mathrm{b}\right)\:\:\:\mathrm{Is}\:\mathrm{equal}\:\mathrm{to}\:\:\mathrm{10}\frac{\mathrm{2}}{\mathrm{3}} \\ $$

Question Number 92323    Answers: 2   Comments: 3

Question Number 92319    Answers: 0   Comments: 3

log _9 (x+(7/2)).log _(3/4) (x^2 ) ≥ log _(3/4) (x+(7/2))

$$\mathrm{log}\:_{\mathrm{9}} \left(\mathrm{x}+\frac{\mathrm{7}}{\mathrm{2}}\right).\mathrm{log}\:_{\mathrm{3}/\mathrm{4}} \left(\mathrm{x}^{\mathrm{2}} \right)\:\geqslant\: \\ $$$$\mathrm{log}\:_{\mathrm{3}/\mathrm{4}} \left(\mathrm{x}+\frac{\mathrm{7}}{\mathrm{2}}\right)\: \\ $$

Question Number 92301    Answers: 1   Comments: 2

given eq of line (1) [ x,y ] = [3,−2] + t [4,−5] (2) [x,y] = [1,1] + s [ 7,k ] find t and s if (1) ∥ (2) if (1) ⊥ (2)

$$\mathrm{given}\:\mathrm{eq}\:\mathrm{of}\:\mathrm{line}\: \\ $$$$\left(\mathrm{1}\right)\:\left[\:\mathrm{x},\mathrm{y}\:\right]\:=\:\left[\mathrm{3},−\mathrm{2}\right]\:+\:\mathrm{t}\:\left[\mathrm{4},−\mathrm{5}\right]\: \\ $$$$\left(\mathrm{2}\right)\:\left[\mathrm{x},\mathrm{y}\right]\:=\:\left[\mathrm{1},\mathrm{1}\right]\:+\:\mathrm{s}\:\left[\:\mathrm{7},\mathrm{k}\:\right]\: \\ $$$$\mathrm{find}\:\mathrm{t}\:\mathrm{and}\:\mathrm{s}\:\mathrm{if}\:\left(\mathrm{1}\right)\:\parallel\:\left(\mathrm{2}\right) \\ $$$$\mathrm{if}\:\left(\mathrm{1}\right)\:\bot\:\left(\mathrm{2}\right) \\ $$

Question Number 92291    Answers: 0   Comments: 1

lim_(x→1^− ) (1−x)^(ln x) =?

$$ \\ $$$$\underset{{x}\rightarrow\mathrm{1}^{−} } {\mathrm{lim}}\:\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{ln}\:\mathrm{x}} \:=?\: \\ $$

Question Number 92289    Answers: 0   Comments: 1

lim_(x→∞) ln((((3+e)^x )/(2x))) ?

$$ \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{ln}\left(\frac{\left(\mathrm{3}+\mathrm{e}\right)^{\mathrm{x}} }{\mathrm{2x}}\right)\:? \\ $$

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