` "int(tan^(-1)u)/((1+u)^(2))du`

If y=tan^(-1)((u)/(sqrt(1-u^(2)))) and x=sec^(-1)((1)/(2u^(2)-1))u in(0,(1)/(sqrt(2)))uu((1)/(sqrt(2)),1), prove that 2(dy)/(dx)+1=0

If f(a)= int_(0)^(a)(du)/((1+u^(2))^(1/2)), then value of the expression 3sqrt(2)f(2sqrt(2)) is equal to "

If f(a)=int_(0)^(a)(du)/((1+u^(2))^(3/2)) , then value of the expression 3sqrt(2)f(2sqrt(2)) is equal to

If y=tan[(1)/(2)cos^-1((1-u^(2))/(1+u^(2)))+(1)/(2)sin^(-1)((2u)/(1+u^(2)))]" and "x=(2u)/(1-u^(2))," then: "(dy)/(dx)=

Let U=sin^(-1)((2x)/(1+x^(2))) and V=tan^(-1)((2x)/(1-x^(2))), then (dU)/(dV)=1/2(b)x(c)(1-x^(2))/(1+x^(2))(d)1

int(1)/(sqrt(u))du

If variables x and y are related by the equation x=int_(0)^(y)(1)/(sqrt(1+9u^(2))) du, then (dy)/(dx) is equal to

If quad tan((1)/(2)(cos^(-1))(1-u^(2))/(1+u^(2))+(1)/(2)(sin^(-1))(2u)/(1+u^(2))) and x=(2u)/(1-u^(2)) then (dy)/(dx)

if int x tan^(-1)xdx=u tan^(-1)x-(x)/(2)+c then u=