y= lnx/ 1+lnx find the derivative

integrate from 0 to pie over 2 tan (x/2) dx

integrate from pie over 2 to pie 2 cot x/3 dx

integrate dx/(2 sqaure root of x)(2x)

i have the answers in the back of the book but i have no idea how to solve! I really need to understand this.

also, suppose f(x) is positive, continuous, and increasing over the interval [a,b] by interpreting the graph of f show that:

integrate from a to b f(x)dx + integrate f(a) to f(b) f inverse(y) dy = bf(b)-af(a)