Answer
$x+x^2+\dfrac{x^3}{3}-\dfrac{x^5}{30}-...$
Work Step by Step
Find $e^x \sin x$
$e^x \sin x=(1+x+\dfrac{x^2}{2!}+\dfrac{x^3}{3!}+....)(x-\dfrac{x^3}{3!}+\dfrac{x^5}{5!}+..)$
$\implies e^x \sin x=x+x^2+\dfrac{x^3}{3}-\dfrac{x^5}{30}-...$