解答

$${I=\int(x+1)\cos xdx}$$

$$\begin{eqnarray*} I&=&\int\underbrace{(x+1)}_{f}\times \underbrace{(\sin x)'}_... ...\ &=& (x+1)\sin x-\int \sin xdx\\ &=& (x+1)\sin x+\cos x+C \end{eqnarray*}$$