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

IfI=int(dx)/(x^(3)sqrt(x^(2)-1)), then Iequals a.(1)/(2)((sqrt(x^(2)-1))/(x^(3))+tan^(-1)sqrt(x^(2)-1))+C b.(1)/(2)((sqrt(x^(2)-1))/(x^(2))+x tan^(-1)sqrt(x^(2)-1))+Cc(1)/(2)((sqrt(x^(2)-1))/(x^(2))+tan^(-1)sqrt(x^(2)-1))+Cd(1)/(2)((sqrt(x^(2)-1))/(x^(2))+tan^(-1)sqrt(x^(2)-1))+C

If y=(1)/(3)"log" (x+1)/(sqrt(x^(2)-x+1))+(1)/(sqrt(3))"tan"^(-1)(2x-1)/(sqrt(3)) , show that, (dy)/(dx)=(1)/(x^(3)+1)

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

Evaluate: lim_(x rarr oo)(sqrt(3x^(2)-1)-sqrt(2x^(2)-1))/(4x+3)

Evaluate the following limits : Lim_(x to oo) (sqrt(3x^(2)-1)-sqrt(2x^(2)-1))/(4x+3)

Evaluate the following limits : Lim_(x to oo) (sqrt(3x^(2)-1)-sqrt(2x^(2)-1))/(4x+3)

If f(x)=sin^(-1)((sqrt(3))/(2)x-(1)/(2)sqrt(1-x^(2))),-(1)/(2)<=x<=1, then f(x) is equal to

int(x^(3)dx)/(sqrt(1+x^(2))) is equal to (A) (1)/(3)sqrt(1+x^(2))(2+x^(2))+C(B)(1)/(3)sqrt(1+x^(2))(x^(2)-1)+C(C)(1)/(3)(1+x^(2))^((3)/(2))+C(D)(1)/(3)sqrt(1+x^(2))(x^(2)-2)+C

int(2x-sqrt(sin^(-1)x))/(sqrt(1-x^(2)))dx equals to :(A)-2(1-x^(2))^((1)/(2))-(sin^(-1)x)^((3)/(2))sqrt(1-x^(2))+c