Prove that the function `f(x)=(log)_e(x^2+1)-e^(-x)+1` is strictly increasing `AAx in Rdot`

Prove that the function f(x)=x^(2)-2x-3 is strictly increasing in (2, infty)

For the function f(x)=x^4(12(log)_e x-7)

Prove that the function f(x)=x^(2)+2 is strictly increasing in the interval (2,7) and strictly decreasing in the interval (-2, 0).

The domain of the function f(x)=(log)_(3+x)(x^2-1) is

The function f (x) = log (x + sqrt(x^2 +1)) is

Prove that the function f given by f(x) = x ^(2) – x + 1 is neither strictly increasing nor decreasing on (– 1, 1).

If the function f(x) = 2cotx+(2a+1) ln|cosec x| + (2-a)x is strictly decreasing in (0, pi/2) then range of a is

Integrate the functions (e^(2x)-1)/(e^(2x)+1)

Find the possible values of a such that f(x)=e^(2x)-(a+1)e^x+2x is monotonically increasing for x in Rdot