Solve `y=(lnx)^((lnx)^((lnx)^(...^oo)))`

y=e^(x)lnx

f(x)=x^(2)+lnx

Solve x(dy)/(dx)+y=y^2lnx

If I=int((lnx)^(5))/(sqrt(x^(2)+x^(2)(lnx)^(3)))dx=ksqrt((lnx)^(3)+1)((lnx)^(3)-2)+c (where c is the constant of integration), then 9k is equal to

If I=int((lnx)^(5))/(sqrt(x^(2)+x^(2)(lnx)^(3)))dx=ksqrt((lnx)^(3)+1)((lnx)^(3)-2)+c (where c is the constant of integration), then 9k is equal to

intx^(100x).(1+lnx)dx=

If y=x^((lnx)^ln(lnx)) , then (dy)/(dx) is equal to