`int_1^e 1/x dx`= (a)e (b)0 (c)1 (d)log(1+e)

If y=tan^(-1){((log)_e(e//x^2))/((log)_e(e x^2))}+tan^(-1)((3+2\ (log)_e x)/(1-6\ (log)_e x)) , then (d^2y)/(dx^2)= (a) 2 (b) 1 (c) 0 (d) -1

int (1+log_e x)/x dx

If f(x)=(log)_x(log x),t h e nf^(prime)(x) at x=e is equal to (a) 1/e (b) e (c) 1 (d) zero

If f(x)=(log)_(x^2)(logx) , then f^(prime)(x) at x=e is (a) 0 (b) 1 (c) 1/e (d) 1/2e

int_1^elogx\ dx= a. 1 b. e-1 c. e+1 d. 0

lim_(x->0^+)((sinx)/(x-sinx))^(sinx) is (a)0 (b) 1 (c) ln e (d) e^1

The minimum value of x\ (log)_e x is equal to e (b) 1//e (c) -1//e (d) 2e (e) e

The value of int_0^1e^(x^2-x) dx is (a) 1 (c) > e^(-1/4) (d) < e^(-1/4)

The minimum value of x/((log)_e x) is e (b) 1//e (c) 1 (d) none of these

int_0^1(e^x dx)/(1+e^x)