`int (dx)/(sin^3 x xos^3 x)=A In |(sqrt2+t)/(sqrt2-t)+B tan^-1 (t)`

Find (dx)/(dt) when x = sin^-1(t.sqrt(1-t) +sqrt(t) sqrt(1-t^2)) .

If x and y are connected parametrically by the equations given, without eliminating the parameter, Find (dy)/(dx) . x=(sin^3t)/(sqrt(cos2t)), y=(cos^3t)/(sqrt(cos2t))

If x=(sin^(3)t)/(sqrt(cos2t)) and y=(cos^(3)t)/(sqrt(cos2t)) , then find (dy)/(dx) .

Find (dy)/(dx) , if x=(sin^3t)/(sqrt(cos2t)) , y=(cos^3t)/(sqrt(cos2t))

int frac{ t^2 + 1}{ t^4 + 1} dt=...........a) frac{1}{sqrt2}[tan^(-1)(sqrt 2t-1)+tan^(-1)(sqrt 2t+1)]+c b) sqrt2[tan^(-1)(sqrt 2t-1)+tan^(-1)(sqrt 2t+1)]+c c) frac{1}{2sqrt2}[tan^(-1)(sqrt 2t-1)+tan^(-1)(sqrt 2t+1)]+c d) 2sqrt2[tan^(-1)(sqrt 2t-1)+tan^(-1)(sqrt 2t+1)]+c

x= sin^3t/sqrt x cos2t , y= cos^3t/ sqrt x cos2t .

If x=int_c^(sint)sin^(-1)z dz ,y =int_k^(sqrt(t))(sinz^2)/zdz, then (dy)/(dx) is equal to (a) (tant)/(2t) (b) (tant)/(t^2) (c) t/(2t^2) (d) (tan t)/(2t^2)

int sqrt(2+ sin 3t) cos 3t dt

If x and y are connected parametrically by the equations given,without eliminating the parameter,Find (dy)/(dx)x=(sin^(3)t)/(sqrt(cos2t)),y=(cos^(3)t)/(sqrt(cos2t))