" 7.(i) "e^(x)((1+x log x))/(x)

A: int e^(x)((1+x log x)/(x))=e^(x)log x+c R: int e^(x)[f(x)+f'(x)]dx=e^(x)f(x)+c

" (i) "int e^(x)[e^(log x)+1]dx

" (i) "int e^(x)[e^(log x)+2]dx

I=int e^(x log x)(1+log x)

(7) Find the value of lim_(x->0) ((e^(x)-1) log(1+x))/(x^(2))

The differential coefficient of f(log_(e)x)w*r.t.x, where f(x)=log_(e)x, is (i) (x)/(ln x)( ii) (ln x)/(x)( iii) (1)/(x ln x)( iv )x ln x

The differentiation of log _(e)x,x>0is(1)/(x)* i.e.(d)/(dx)(log_(e)x)=(1)/(x)

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 differentiation of (log)_a x (a >0) with respect to x i.e. d/(dx)((log)_a x)= 1/(x(log)_e a)

The differentiation of log_(a)x(a>0,a)*!=1 with respect to x is (1)/(x log_(a)a) i.e.(d)/(dx)(log_(a)x)=(1)/(x log_(a)a)