Chebshev polynomial approximation

[sbashrawi]

Homework Statement

Hi every body

I am triyng to find a polynolial approximation to the function: f(x)= (x+2)ln(x+2)
using the chebyshev polynomials,
the idea is to use MATLAB to find the coeefficients of the approximation poly.
using the comand double(int(...))
but this command doesn't give me any numerical value
what I got was:
>> int((x+2)*log(x+2)*(1-x^2)^-0.5,-1,1)
Warning: Explicit integral could not be found.
ans =
int((log(x + 2)*(x + 2))/(1 - x^2)^(1/2), x = -1..1)
>>
and if I use double(int(...)) an error message shows up
Any help pls

Homework Equations

The Attempt at a Solution

 

[TheoMcCloskey]

Consider the substitution x=\cos(\theta) and note that T_k(x) = \cos(k \,\theta). This should remove the singularity.