Obtaining one taylor series from another taylor series?

Question

I computed the taylor series for

$$ \frac{2}{(3+x)} $$

which is

$$ (-1)^n \times \frac{2}{(3^n+1)} \times x^n $$

Now I need to compute the infinite series for

$$ 2 \ln(3+x) $$ using what I found for the taylor series in the first part.I'm really not seeing the linke here??Please help

Answer 1

Note that $$\int_a^x \frac{2}{3+t}dt=2\ln(x+3)-2\ln(3+a)$$ So you integrate the series that you get for first part.