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Question Number 116669 Answers: 1 Comments: 1

Question Number 116667 Answers: 1 Comments: 0

... nice calculus... very nice integral:: demonstrate::: Ω = ∫_0 ^( 1) ((1−x)/((1+x+x^2 +x^3 )log(x))) dx=^(???) log((√(1/2))) .m.n.1970.

$$\:\:\:\:\:\:\:\:\:\:\:\:...\:\:\:{nice}\:\:{calculus}... \\ $$$$ \\ $$$$\:\:\:\:\:\:{very}\:{nice}\:\:{integral}:: \\ $$$$\:\:\:\:\:\:\:{demonstrate}::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{1}−{x}}{\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} +{x}^{\mathrm{3}} \right){log}\left({x}\right)}\:{dx}\overset{???} {=}{log}\left(\sqrt{\frac{\mathrm{1}}{\mathrm{2}}}\right) \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.{m}.{n}.\mathrm{1970}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\: \\ $$

Question Number 116666 Answers: 1 Comments: 0

Question Number 116763 Answers: 0 Comments: 1

∫(dx/( ((1+x^3 ))^(1/3) ))=?

$$ \\ $$$$\:\:\:\:\:\int\frac{{dx}}{\:\sqrt[{\mathrm{3}}]{\mathrm{1}+{x}^{\mathrm{3}} }}=? \\ $$

Question Number 116759 Answers: 2 Comments: 0

Question Number 116658 Answers: 2 Comments: 2

Question Number 116717 Answers: 2 Comments: 0

∫xdx

$$\int{xdx} \\ $$

Question Number 116725 Answers: 4 Comments: 3

what the value of log _(10) (−1) in complex number

$$\mathrm{what}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{log}\:_{\mathrm{10}} \left(−\mathrm{1}\right)\:\mathrm{in}\: \\ $$$$\mathrm{complex}\:\mathrm{number} \\ $$

Question Number 116722 Answers: 1 Comments: 0

find the range of values of k for which the equation e^x −5=k has no solution

$${find}\:{the}\:{range}\:{of}\:{values}\:{of}\:{k}\:{for} \\ $$$${which}\:{the}\:{equation}\:{e}^{{x}} −\mathrm{5}={k}\:{has}\:{no} \\ $$$${solution} \\ $$

Question Number 116641 Answers: 1 Comments: 0

Question Number 116633 Answers: 1 Comments: 0

Question Number 116630 Answers: 3 Comments: 0

Given cosec x + cot x = p , find the value of cosec x =?

$$\mathrm{Given}\:\mathrm{cosec}\:\mathrm{x}\:+\:\mathrm{cot}\:\mathrm{x}\:=\:\mathrm{p}\:,\:\mathrm{find}\:\mathrm{the}\: \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{cosec}\:\mathrm{x}\:=? \\ $$

Question Number 116627 Answers: 2 Comments: 0

... nice calculus... please evaluate :: Φ = (((∫_0 ^( (π/2)) ((e^x +e^(−x) )/(sin(x)+cos(x)))dx)^2 )/((∫_0 ^( (π/2)) (e^x /(sin(x)+cos(x)))dx)(∫_0 ^( (π/2)) (e^(−x) /(sin(x)+cos(x)))dx))) =??? m.n.1970

$$\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:...\:\:{nice}\:\:\:{calculus}... \\ $$$$ \\ $$$$\:\:\:\:\:\:{please}\:\:\:{evaluate}\::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Phi\:=\:\frac{\left(\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{e}^{{x}} +{e}^{−{x}} }{{sin}\left({x}\right)+{cos}\left({x}\right)}{dx}\right)^{\mathrm{2}} }{\left(\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{e}^{{x}} }{{sin}\left({x}\right)+{cos}\left({x}\right)}{dx}\right)\left(\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{e}^{−{x}} }{{sin}\left({x}\right)+{cos}\left({x}\right)}{dx}\right)}\:=???\:\:\:\: \\ $$$$ \\ $$$$\:\:\:\:{m}.{n}.\mathrm{1970} \\ $$$$ \\ $$

Question Number 116626 Answers: 2 Comments: 0

Π_(n=1) ^∞ (((a^2 n^2 )/((an)^2 −1))))=???

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\frac{{a}^{\mathrm{2}} {n}^{\mathrm{2}} }{\left.\left({an}\right)^{\mathrm{2}} −\mathrm{1}\right)}\right)=??? \\ $$$$ \\ $$

Question Number 116616 Answers: 0 Comments: 1

Question Number 116614 Answers: 2 Comments: 3

(x^2 cos^2 ((x/y))−y)dx + x dy = 0 where y(1)= (π/4)

$$\:\left(\mathrm{x}^{\mathrm{2}} \:\mathrm{cos}\:^{\mathrm{2}} \left(\frac{\mathrm{x}}{\mathrm{y}}\right)−\mathrm{y}\right)\mathrm{dx}\:+\:\mathrm{x}\:\mathrm{dy}\:=\:\mathrm{0} \\ $$$$\mathrm{where}\:\mathrm{y}\left(\mathrm{1}\right)=\:\frac{\pi}{\mathrm{4}} \\ $$

Question Number 116611 Answers: 1 Comments: 1

Question Number 116610 Answers: 1 Comments: 1

solve : ((1/( (√2))))^(2h) + (((√3)/2))^h = 1

$$ \\ $$$$\:\:\:\:\:{solve}\:: \\ $$$$\:\:\:\:\:\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\right)^{\mathrm{2}{h}} \:+\:\left(\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\right)^{{h}} \:=\:\mathrm{1} \\ $$

Question Number 116603 Answers: 1 Comments: 0

When f(x) divided by (x−1)(x+2), the remainder is (x+3) When f(x) divided by (x^2 +2x+5), the remainder is (2x+1) Find the remainder if f(x) is divided by(x−1)(x^2 +2x+5)

$$\mathrm{When}\:{f}\left({x}\right)\:\mathrm{divided}\:\mathrm{by}\:\left({x}−\mathrm{1}\right)\left({x}+\mathrm{2}\right), \\ $$$$\mathrm{the}\:\mathrm{remainder}\:\mathrm{is}\:\left({x}+\mathrm{3}\right) \\ $$$$\mathrm{When}\:{f}\left({x}\right)\:\mathrm{divided}\:\mathrm{by}\:\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{5}\right), \\ $$$$\mathrm{the}\:\mathrm{remainder}\:\mathrm{is}\:\left(\mathrm{2}{x}+\mathrm{1}\right) \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{if}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{divided} \\ $$$$\mathrm{by}\left({x}−\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{5}\right) \\ $$

Question Number 116601 Answers: 2 Comments: 0

If (x,y) satisfies the system of equations { ((∣x∣−x−y+2=0)),((∣y∣+y+5x=1)) :} find the value of x+y.

$$\mathrm{If}\:\left({x},{y}\right)\:\mathrm{satisfies}\:\mathrm{the}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equations} \\ $$$$\begin{cases}{\mid{x}\mid−{x}−{y}+\mathrm{2}=\mathrm{0}}\\{\mid{y}\mid+{y}+\mathrm{5}{x}=\mathrm{1}}\end{cases}\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}+{y}.\: \\ $$

Question Number 116595 Answers: 1 Comments: 0

If (1−2x+3x^2 )^(10) =a_0 +a_1 x+a_2 x^2 +...+a_(20) x^(20) find the value of a_1 +a_2 +...+a_(20)

$$\mathrm{If}\:\left(\mathrm{1}−\mathrm{2}{x}+\mathrm{3}{x}^{\mathrm{2}} \right)^{\mathrm{10}} ={a}_{\mathrm{0}} +{a}_{\mathrm{1}} {x}+{a}_{\mathrm{2}} {x}^{\mathrm{2}} +...+{a}_{\mathrm{20}} {x}^{\mathrm{20}} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{a}_{\mathrm{1}} +{a}_{\mathrm{2}} +...+{a}_{\mathrm{20}} \\ $$

Question Number 116590 Answers: 2 Comments: 0

∫ ((√x)/(1+x^3 )) dx =?

$$\:\int\:\frac{\sqrt{\mathrm{x}}}{\mathrm{1}+\mathrm{x}^{\mathrm{3}} }\:\mathrm{dx}\:=? \\ $$

Question Number 116588 Answers: 2 Comments: 0

lim_(x→0) ((4x)/(2 cosec x (1−(√(cos x))))) =?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{4x}}{\mathrm{2}\:\mathrm{cosec}\:\mathrm{x}\:\left(\mathrm{1}−\sqrt{\mathrm{cos}\:\mathrm{x}}\right)}\:=? \\ $$

Question Number 116586 Answers: 0 Comments: 0

1) explicite ∫_0 ^∞ ((arctan(1+x(2+t^2 )))/(2+t^2 ))dt withx>0 2)determine values of ∫_0 ^∞ ((arctan(3+t^2 ))/(2+t^2 ))dt and ∫_0 ^∞ ((arctan(5+2t^2 ))/(2+t^2 ))dt

$$\left.\mathrm{1}\right)\:{explicite}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{arctan}\left(\mathrm{1}+{x}\left(\mathrm{2}+{t}^{\mathrm{2}} \right)\right)}{\mathrm{2}+{t}^{\mathrm{2}} }{dt} \\ $$$${withx}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right){determine}\:{values}\:{of} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\frac{{arctan}\left(\mathrm{3}+{t}^{\mathrm{2}} \right)}{\mathrm{2}+{t}^{\mathrm{2}} }{dt}\:{and}\: \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\frac{{arctan}\left(\mathrm{5}+\mathrm{2}{t}^{\mathrm{2}} \right)}{\mathrm{2}+{t}^{\mathrm{2}} }{dt} \\ $$

Question Number 116578 Answers: 3 Comments: 0

solve for x determinant (((1 x x^2 x^3 )),((1 2 2^2 2^3 )),((1 3 3^2 3^3 )),((1 4 4^2 4^3 )))= 0

$$\mathrm{solve}\:\mathrm{for}\:\mathrm{x}\: \\ $$$$\:\begin{vmatrix}{\mathrm{1}\:\:\:\mathrm{x}\:\:\:\:\mathrm{x}^{\mathrm{2}} \:\:\:\:\mathrm{x}^{\mathrm{3}} }\\{\mathrm{1}\:\:\:\mathrm{2}\:\:\:\:\mathrm{2}^{\mathrm{2}} \:\:\:\:\mathrm{2}^{\mathrm{3}} }\\{\mathrm{1}\:\:\:\mathrm{3}\:\:\:\:\mathrm{3}^{\mathrm{2}} \:\:\:\:\mathrm{3}^{\mathrm{3}} }\\{\mathrm{1}\:\:\:\mathrm{4}\:\:\:\:\mathrm{4}^{\mathrm{2}} \:\:\:\:\mathrm{4}^{\mathrm{3}} }\end{vmatrix}=\:\mathrm{0} \\ $$

Question Number 116576 Answers: 3 Comments: 1

lim_(x→0) (((sin x)/x))^(1/x^2 ) =?

$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{x}}\right)^{\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }} \:=? \\ $$

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