" 12."(1)/(x cos^(2)(1+log x))

int(1)/(x cos^(2)(1+log x))dx

int(d(1+log x))/(cos^(2)(1+log x))

The solution of the differential equation log x (dy)/(dx) + (y)/(x) = sin 2x is a) y log | x | = C - (1)/(2) cos x b) y log |x| = C + (1)/(2) cos 2x c) y log | x| = C - (1)/(2) cos 2x d) xy log | x | = C - (1)/(2) cos 2x

Suppose 3 sin^(-1) ( log _(2) x) + cos^(-1) ( log _(2) y) =pi //2 and sin^(-1) ( log _(2) x ) + 2 cos^(-1) ( log_(2) y) = 11 pi //6 . then the value of 1/x^(2) + 1/y^(2) equals .

Suppose 3 sin^(-1) ( log _(2) x) + cos^(-1) ( log _(2) y) =pi //2 and sin^(-1) ( log _(2) x ) + 2 cos^(-1) ( log_(2) y) = 11 pi //6 . then the value of 1/x^(-2) + 1/y^(-2) equals .

If f(x) = cos^(-1) [(1-(log x)^(2))/(1+(log x)^(2))] , then f^(')(e) =

int sin2x.log cos xdx is equal to 1) cos^(2)x((1)/(2)+log cos x)+k 2) cos^(2)x*log cos x+k 3) cos^(2)x((1)/(2)-log cos x)+k 4) cos^(2)x+log cos x+k

int(1)/((cos^(2)(ln((1+x)/(1-x)))(1-x^(2))))dx

If y=cos ^(-1) ((log x^(2))/( 1+(log x)^(2))) ,then (dy)/(dx)=