Chọn phương án A.

Đặt $\begin{cases}
u=x\\ v'=\mathrm{e}^{30x}
\end{cases}\Rightarrow\begin{cases}
u'=1\\ v=\dfrac{1}{30}\mathrm{e}^{30x}
\end{cases}$. Ta có $$\begin{aligned}\displaystyle\int\limits_{0}^{10}x\mathrm{e}^{30x}\mathrm{\,d}x&=\dfrac{x}{30}\mathrm{e}^{30x}\bigg|_0^{10}-\displaystyle\int\limits_{0}^{10}\dfrac{1}{30}\mathrm{e}^{30x}\mathrm{\,d}x\\ &=\dfrac{1}{3}\mathrm{e}^{300}-\dfrac{1}{900}\mathrm{e}^{30x}\bigg|_0^{10}=\dfrac{1}{900}\left(299\mathrm{e}^{300}+1\right).\end{aligned}$$