`int(e^y)/(2+e^y)dy=int1/(x+1)dx+c^(prime)log|2+e^y|=log|x+1|!=logc`

int_(e^(-1))^(e^(2))|(ln x)/(x)|dx

int_((1)/(e))^(e)|log x|dx=

int_(0)^(log 2)(e^(x))/(1+e^(x))dx=

int_(0)^(log 2)(e^(x))/(1+e^(x))dx=

int_(1)^(e^(2))(dx)/(x(1+log x)^(2))=

int_(1//e)^(e) (dx)/(x(log x)^(1//3))

int_(1//e)^(e) (dx)/(x(log x)^(1//3))

If y(x) is solution of differential equation satisfying (dy)/(dx)+((2x+1)/x)y=e^(-2x), y(1)=1/2e^(-2) then (A) y(log_e2)=log_e2 (B) y(log_e2)=(log_e2)/4 (C) y(x) is decreasing is (0,1) (D) y(x) is decreasing is (1/2,1)