If the primitive of `1/(e^x-1)^2` is `f(x)-log g(x)+c` then

If the primitive of (1)/(f(x)) is equal to log{f(x)}^(2)+C , then f(x) is

If primitive of sin (log x) is f(x)*{sin g(x)- cos h(x)}+c, (c being constant of integration), then which of the following is correct (i) lim_(x->2)f(x)=1 (ii) lim_(x->1)g(x)/(h(x))=1 (iii) g(e^3)=3 (iv) h(e^5)=5

The primitive of the function f(x)=(1-1/(x^2))a^(x+1/x)\ ,\ a >0 is (a) (a^(x+1/x))/((log)_e a) (b) (log)_e adota^(x+1/x) (c) (a^(x+1/x))/x(log)_e a (d) x(a^(x+1/x))/((log)_e a)

The derivative of (log x) ^(x) w.r.t x is (log x)^(x-1) [1+ log x log (log x)] R : (d)/(dx) {f (x) ^(g(x))[g (x) (f'(x))/(f (x)) + g'(x) log (f(x) ]

The primitive of the function f(x)=(1-(1)/(x^(2)))a^(x+(1)/(x)),a>0 is (a^(x+(1)/(x)))/((log)_(e)a) (b) (log_(e)adot a^(x+(1)/(x))(c)(a^(x+(1)/(x)))/(x)(log)_(e)a(d)x(a^(x+(1)/(x)))/((log)_(e)a)