Power Series Representation of xln(1+x^2)

[PCSL]

Write a power series representation of xln(1+x²)

My first instinct was to attempt to take the second derivative and then find the summation and then integrate but that approach seemed to be a dead end. Basically, the x thrown in there confuses me and you can't split the function into two separate summations since one would not converge. Any hints..?

 

[PCSL]

Help, anyone?

 

[Dick]

I assume you are expanding around x=0. The power series expansion of x is x. What's the power series expansion of ln(1+u) around u=0? Hence what's the power series expansion of ln(1+x^2). There is no double summation to worry about.

 

[PCSL]

I assume you are expanding around x=0. The power series expansion of x is x. What's the power series expansion of ln(1+u) around u=0? Hence what's the power series expansion of ln(1+x^2). There is no double summation to worry about.

I really need to put more thought into problems before posting here. Thanks, and I figured it out.