" %,"(4x+2)sqrt(x^(2)+x+1)

sqrt(x^(2)+x+4)+sqrt(x^(2)+x+1)=sqrt(2x^(2)+2x+4)

int(2x+1)/(sqrt(x^(2)+2x+4))dx=2sqrt(x^(2)+2x+4)-log[(x+1)+sqrt(x^(2)+2x+4)]

If f(x)=tan^(-1)sqrt(x^(2)+4x) +sin^(-1)sqrt(x^(2)+4x+1)

If f(x)=tan^(-1)sqrt(x^(2)+4x) +sin^(-1)sqrt(x^(2)+4x+1)

Integrate the following with respect to x : (i) (2x+1)/(sqrt(9+4x-x^2)) (ii) (x+2)/(sqrt(x^2-1)) (iii) (2x+3)/(sqrt(x^2+4x+1))

lim_(xto oo)(sqrt(4x^(2)+2x+1)-sqrt(4x^(2)+1)) is

If Delta (x) =|{:(4x-4,(x-2)^(2),x^(3)),(8x-4sqrt(2),(x-2sqrt(2)^(2)),(x+1)^(3)),(12x-4sqrt(3),(x-2sqrt(3))^(2),(x-1)^(3)):}| then

If Delta (x) =|{:(4x-4,(x-2)^(2),x^(3)),(8x-4sqrt(2),(x-2sqrt(2)^(2)),(x+1)^(3)),(12x-4sqrt(3),(x-2sqrt(3))^(2),(x-1)^(3)):}| then

int(x^4-1)/(x^2sqrt(x^4+x^2+1))dx= sqrt(x^2+1/(x^2)+1)+C (sqrt(x^4+x^2+1))/(x^2)+C (sqrt(x^4+x^2+1))/x+C (d) none of these

int(x^(4)-1)/(x^(2))sqrt(x^(4)+x^(2)+1)dx equal to (A) sqrt((x^(4)+x^(2)+1)/(x)+c(B)sqrt(x^(4)+2-(1)/(x^(2)))+c)sqrt((x^(4)-x^(2)+1)/(x))+c