" 2."(1)/(log x)-(1)/((log x)^(2))

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

int((log x)^(2)-log x+1)/(((log x)^(2)+1)^((3)/(2)))dx

If x^(y)=e^(x-y), then (dy)/(dx) is (1+x)/(1+log x)(b)(1-log x)/(1+log x)(c) not defined (d) (log x)/((1+log x)^(2))

int(log(x+1)-log x)/(x(x+1))dx= (A) log(x-1)log x+(1)/(2)(log x-1)^(2)-(1)/(2)(log x)^(2)+c (B) (1)/(2)(log(x+1))^(2)+(1)/(2)(log x)^(2)-log(x+1)log x+c (C) -(1)/(2)(log(x+1)^(2))-(1)/(2)(log x)^(2)+log x*log(x+1)+c (D) [log(1+(1)/(x))]^(2)+c

The value of x satisfies the equation (1-2(log x^(2)))/(log x-2(log x)^(2))=1

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

Integrate the functions ,(1+x)(x+log x)^(2),((1+x)(x+log x)^(2))/(x)

log x-(1)/(2)log(x-(1)/(2))=log(x+(1)/(2))-(1)/(2)log(x+(1)/(8))