" 16."(4x+1)/(sqrt(2x^(2)+x-3))

Evaluate: (i) int(4x+2)sqrt(x^(2)+x+1)dx (ii) int(4x+3)/(sqrt(2x^(2)+3x+1))dx

Evaluate : (i) int((x-1))/(sqrt(x+4))dx (ii) intxsqrt(x+2)dx (iii) f(4x-2)sqrt(x^(2)+x++1)dx (iv) int((4x+3))/(sqrt(2x^(2)+3x+1))dx

Integrate the following with respect to x. (1)/((2x+1)^(3))+(3)/(5-2x)+(1)/(sqrt(1-4x^(2)))

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)

Evaluate underset( x rarr oo )("lim") ( sqrt( 3x^(2) - 1) - sqrt( 2x ^(2) - 1))/( 4x + 3)

Evaluate: (i) int(4x+2)sqrt(x^2+x+1)\ dx (ii) int(4x+3)/(sqrt(2x^2+3x+1))\ dx

Lt_(x to oo) (sqrt(3+9x^(2))+sqrt(4x^(2)-1))/(sqrt(1+16x^(2))-sqrt(9x^(2)+2))=

Using properties of proportion, solve for x : (i) (sqrt(x + 5) + sqrt(x - 16))/ (sqrt(x + 5) - sqrt(x - 16)) = (7)/(3) (ii) (sqrt(x + 1) + sqrt(x - 1))/ (sqrt(x + 1) - sqrt(x - 1)) = (4x -1)/(2) . (iii) (3x + sqrt(9x^(2) -5))/(3x - sqrt(9x^(2) -5)) = 5 .