Find a power series which converges to the given function and state the interval on which it converges.

$($a$)f(x)=ln(1+x^3)$

$($b$)g(x)=\frac{1+x}{3-6x}$

$($d$)k(x)=\frac{x^2}{(1+x{)}^4}$

$($c$)h(x)=\frac{3x^2}{(1+x^3{)}^2}$

$($e$)l(x)=arctan(\frac{2x-1}{\sqrt[\phantom{2}]{3}})$

$($f$)M(x)=\frac{2}{3+x}$

Find the Taylor series for the function centered at the given value of $a.$

$($a$)f(x)=x^3{e}^{-x},a=0$

$($b$)g(x)=lnx,a=1$

$($c$)h(x)=\frac{sinx}{x},a=0$

$($d$)k(x)=\frac{1}{1-x},a=2$