In the integral , use the power-series

[Jamin2112]

Homework Statement

I wrote it on Word for increased clarity.

Homework Equations

This is in the chapter where we learned about integrals of the "second" type, ones that have a problem as x approaches the upper or lower limit.

The Attempt at a Solution

I know that the power series expansion for log(1+x) is 1 - x²/2 + x³/3 - x⁴/4 + ... .

But raising that to the q power ... How is that done?

 

[Dick]

Correct that to log(1+x)=x-x^2/2+x^3/3+... And the only problem is at the lower limit, right? So you can take x to be very close to zero. I'd just say log(1+x)~x. Raising that to the q power should be easy.