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)
Since you did try something, it would have been better to show what you had tried than just saying " i have no idea how to solve".
To differentiate , use, as you say, the quotient rule: .
Now (ln(x))'= and (1+ ln(x))' is also since the derivative of "1" is 0. So the quotient rule gives
So I guess the question is where did you get the in the denominator?