Stokes theorem for non-compact case

Question

Let $X$ be a compact Kähler manifold and $D$ be a snc divisor on it. Then on $X\setminus D$ Stokes theorem holds true

$$\int_{X\setminus D}\Delta\alpha=0 ?$$

In this case $X\setminus D$ is non-compact, but we know of course $\int_{X }\Delta\alpha=0$