Evalutate the following:
1.) Integrate sech ^2x/ (2+ tanh x) dx
2.) Integrate from 0 to (Pi/2) sinx/(1+cos^2 x) dx
3.) Find (f^-1)' (a) of f(x)=x^5 - x^3+ 2x, a=2
4.) Find the limit x approaches (2-) e^(3/(2-x))
Integrals are found. The solution is detailed and well presented.