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Question Number 175669 Answers: 0 Comments: 0

∫(([cos^(−1) x{(√((1−x^2 )))}]^(−1) )/(log_e {1+(((sin[2x(√((1−x^2 ))) ])/π) }))dx

$\int \frac{{[\cos^{- 1} x {\sqrt{(1 - x^{2})}}]}^{- 1}}{\log_{e} {1 + (\frac{\sin [2 x \sqrt{(1 - x^{2})}]}{π}}} d x$

Question Number 175670 Answers: 1 Comments: 0

Solve the differential equation (1+y^2 )dx−(1+x^2 )xydy=0

$S o l v e t h e d i f f e r e n t i a l e q u a t i o n$ $(1 + y^{2}) d x - (1 + x^{2}) x y d y = 0$

Question Number 181509 Answers: 1 Comments: 0

Solve: (dy/dx)=((y^2 −3xy−5x^2 )/x^2 ) y(1)=−1 M.m

$Solve :$ $\frac{dy}{dx} = \frac{y^{2} - 3 xy - {5 x}^{2}}{x^{2}} y (1) = - 1$ $M . m$

Question Number 175655 Answers: 1 Comments: 0

Question Number 175653 Answers: 2 Comments: 0

Q: prove that the following equation has no solution. (√(x +⌊ x ⌋)) + (√(x −(√x) )) = 1

$Q : p r o v e t h a t t h e f o l l o w i n g$ $e q u a t i o n h a s n o s o l u t i o n .$ $\sqrt{x + ⌊ x ⌋} + \sqrt{x - \sqrt{x}} = 1$

Question Number 175650 Answers: 0 Comments: 0

cos(5x)= a.cos^( 5) (x)+b.cos^( 4) (x)+c.cos^3 (x)+ d.cos^( 2) (x)+e.cos(x)+f a , b , c , d , e , f =?

$c o s (5 x) = a . {c o s}^{5} (x) + b . {c o s}^{4} (x) + c . {c o s}^{3} (x) + d . {c o s}^{2} (x) + e . c o s (x) + f$ $a, b, c, d, e, f = ?$

Question Number 175652 Answers: 0 Comments: 0

Question Number 175644 Answers: 0 Comments: 0

Question Number 175639 Answers: 1 Comments: 0

x^(99) +y^(99) = x^(100) Interger solutions?

$x^{99} + y^{99} = x^{100}$ $I n t e r g e r s o l u t i o n s ?$

Question Number 175638 Answers: 0 Comments: 0

Ω = ∫_0 ^( (π/2)) (( sin( 3x ))/( (√( 1− sin(x).cos(x))))) dx = 2((√( a)) .ln( 1 + (√(b )) ) + c ) find the value of : a + b + c = ? ■ m.n

$Ω = \int_{0}^{\frac{π}{2}} \frac{s i n (3 x)}{\sqrt{1 - s i n (x) . c o s (x)}} d x = 2 (\sqrt{a} . l n (1 + \sqrt{b}) + c)$ $f i n d t h e v a l u e o f : a + b + c = ? ◼ m . n$

Question Number 175637 Answers: 1 Comments: 0

Question Number 175620 Answers: 0 Comments: 1

the domain of f(x) = (√(log_x {x})) ; {.} denote the fractional part is

$t h e d o m a i n o f f (x) = \sqrt{\log_{x} {x}};$ ${.} d e n o t e t h e f r a c t i o n a l p a r t i s$

Question Number 175618 Answers: 1 Comments: 2

Question Number 175614 Answers: 1 Comments: 0

∫(1/(4t^3 +3t^2 +4t+1))dt

$\int \frac{1}{4 t^{3} + 3 t^{2} + 4 t + 1} d t$

Question Number 175608 Answers: 1 Comments: 3

Question Number 175602 Answers: 1 Comments: 2

∫ (dx/(csc x+ cos x)) =?

$\int \frac{dx}{\csc x + \cos x} = ?$

Question Number 175601 Answers: 2 Comments: 0

Question Number 175623 Answers: 1 Comments: 0

min f(x)=(√(x^2 −2x+5)) +(√(4x^2 −4x+10))

$\min f (x) = \sqrt{x^{2} - 2 x + 5} + \sqrt{{4 x}^{2} - 4 x + 10}$

Question Number 175624 Answers: 3 Comments: 0

let p(x) = x^6 +ax^5 +bx^4 +cx^3 +dx^2 +ex+f be a polynomial function such that p(1) = 1 ; p(2) = 2 ; p(3) = 3 p(4) = 4 ; p(5) = 5 ; p(6) = 6 then find p(7) = ?

$let p (x) = x^{6} + {ax}^{5} + {bx}^{4} + {cx}^{3} + {dx}^{2} + ex + f$ $be a polynomial function such$ $that p (1) = 1; p (2) = 2; p (3) = 3$ $p (4) = 4; p (5) = 5; p (6) = 6 then$ $find p (7) = ?$

Question Number 175595 Answers: 0 Comments: 0

Question Number 175593 Answers: 0 Comments: 3

If 0<a≤b then prove that: determinant ((1,a,(log(a^a ))),(1,((√((a^2 +b^2 )/2)) (√((a^2 +b^2 )/8)) ∙ log(((a^2 +b^2 )/2))),),(1,b,(log(b^b ))))≥ 0

$If 0 < a ⩽ b then prove that :$ $| \begin{matrix} 1 & a & \log (a^{a}) \\ 1 & \sqrt{\frac{a^{2} + b^{2}}{2}} \sqrt{\frac{a^{2} + b^{2}}{8}} \cdot \log (\frac{a^{2} + b^{2}}{2}) \\ 1 & b & \log (b^{b}) \end{matrix} | ⩾ 0$

Question Number 175588 Answers: 2 Comments: 1

Question Number 175585 Answers: 1 Comments: 6

in AB^Δ C prove that: sin ((( A)/2) ) ≤ (( a)/( b + c)) ■

$i n A \overset{Δ}{B C} p r o v e t h a t :$ $s i n (\frac{A}{2}) ⩽ \frac{a}{b + c} ◼$

Question Number 175583 Answers: 0 Comments: 1

∫_0 ^2 x^t dt=3 solve for x

$\int_{0}^{2} x^{t} d t = 3$ $s o l v e f o r x$

Question Number 175579 Answers: 0 Comments: 0

lim_(x→∞) ((x^(1−sin ((1/x))) .(x^(sin ((1/x))) −1))/(ln x))

$\lim_{x \to \infty} \frac{x^{1 - \sin (\frac{1}{x})} . (x^{\sin (\frac{1}{x})} - 1)}{\ln x}$

Question Number 175573 Answers: 0 Comments: 0

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