(2x+1)/(sqrt(2x^(2)+x-3))

(2x+1)/(sqrt(x^(2)+2x+3))

sqrt(x^(2)+2x-3)<1

int(dx)/((x^(3)+3x^(2)+3x+1)sqrt(x^(2)+2x-3))

int(dx)/((x^(3)+3x^(2)+3x+1)sqrt(x^(2)+2x-3))

int(2x+1)/(sqrt(x^2+2x+3))dx=

lim_(x to oo ) (sqrt(3x^(2)-1)-sqrt(2x^(2)-3))/(4x+3)

lim_(x to oo ) (sqrt(3x^(2)-1)-sqrt(2x^(2)-3))/(4x+3)

Prove that the function f(x) = a sqrt(x - 1) + b sqrt(2x - 1)-sqrt(2x^(2) - 3x + 1) , where a + 2b = 2 and a, b in R always has a root in (1, 5) AA b in R

Prove that the function f(x) = a sqrt(x - 1) + b sqrt(2x - 1)-sqrt(2x^(2) - 3x + 1) , where a + 2b = 2 and a, b in R always has a root in (1, 5) AA b in R