# Finding the power series expansion of this ln

1. Jul 16, 2012

### tamtam402

1. The problem statement, all variables and given/known data

Find the series expansion of ln(x + sqrt(1+x2))

2. Relevant equations

ln(1+x) = x - x2 /2 + x3/3 - x4/4 + ...

3. The attempt at a solution

I don't know how to solve this. If it was ln(1+f(x) ) I know I could substitute the x's for f(x) in the ln(1+x) series expansion, but I don't know what to do since the ln isn't in the correct form. Am I supposed to rederive the series from scratch?

2. Jul 16, 2012

### tamtam402

Well I solved the whole problem by using the definition of Maclaurin series to find the expansion "from scratch". I used Wolfram Alpha to solve the multiple derivatives necessary, but I'm not satisfied with my answer. I feel like there was a way to solve this by using some kind of substitution, since I managed to solve all the other problems in Mary L Boas book without having to rederive the whole series.

I'm trying to learn the math tools necessary to self-study undergraduate E&M. I'm an electrical engineering student that would like to know the fundations of my engineering branch :D I feel bad for "cheating" on this problem.

3. Jul 16, 2012

### micromass

Staff Emeritus
Hint:

$$ln(x+\sqrt{1+x^2})=ln(x)+ln(1+\frac{\sqrt{1+x^2}}{x})$$

4. Jul 16, 2012

### tamtam402

Wow, I wouldn't have found that by myself. That's a very clever trick, thank you!