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

int(dx)/(sin^(3)x xos^(3)x)=AIn|(sqrt(2)+t)/(sqrt(2)-t)+B tan^(-1)(t)

If int (dx )/(cos ^(3) x-sin ^(3))=A tan ^(-1) (f (x)) +bln |(sqrt2+f (x))/(sqrt2-f (x))|+C where f (x) = sin x + cos x find the value of (12A+9sqrt2V)-3.

x=sqrt(sin 2t),y=sqrt(cos 2 t)

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

int(dx)/(3+sin2x)=(1)/(sqrt(k))Tan^(-1)((3Tan x+1)/(sqrt(8)))+C where k is

Find (dy)/(dx), when x=cos^(-1)(1)/(sqrt(1+t^(2))) and y=sin^(-1)(t)/(sqrt(1+t^(2))),t in R

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

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))

If int(dx)/(cos^(3)x sqrt(sin2x))=a(tan^(2)x+b)sqrt(tan x)+c

Find the derivative (dy)/(dx) of the following implicit functions : (a) int_(0)^(y) e^(-t^(2)) dt + int_(0)^(x^(3)) sin ^(2) t dt = 0 (b) int_(0)^(y) e^(t) dt + int _(0)^(x) sin t dt = 0 (c) int _(pi//2)^(x) sqrt(3 - 2 sin^(2)z ) dz + int_(0)^(y) cos t dt = 0