our goal is to find a power series for - 1 / (6 - x) and then integrate it. or -1 from the numerator and 6…

our goal is to find a power series for - 1 / (6 - x) and then integrate it. or -1 from the numerator and 6 from the denominator. this will give us - 1 / (6 - x) = - 1 / 6 (1 / (1 - ( ))) .

our goal is to find a power series for - 1 / (6 - x) and then integrate it. or -1 from the numerator and 6 from the denominator. this will give us - 1 / (6 - x) = - 1 / 6 (1 / (1 - ( ))) .

Answer

Explanation:

Step1: Rewrite the denominator

We want to rewrite $-\frac{1}{6 - x}$ in the form of $-\frac{1}{6}\frac{1}{1 - u}$. Given $-\frac{1}{6 - x}=-\frac{1}{6}\frac{1}{1-\frac{x}{6}}$, so $u = \frac{x}{6}$.

Answer:

$\frac{x}{6}$