x(1)/(6)|" 17."(log x)^(x)+x^(log x)

(log x)^(log x),x gt1

(log x)^(log x),x gt1

int_(1)^(e )(1)/(6x(log x)^(2)+7x log x + 2x)dx=

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

int (1+log x)/(1+x log x)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))

The differential coefficient of f(log x) with respect to x, where f(x)=log x is (x)/(log x) (b) (log x)/(x)(c)(x log x)^(-1)(d) none of these

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

(1)/(x log x log (log x ))