$\int \dfrac{\sqrt{x-2}}{x}dx = $

If $f(x)$ and $g(x)$ are integrable functions then $\left[\int f(x)dx\right]\left[\int g(x)dx\right] = $

If an antiderivative of $f(x)$ is $e^x$ and an antiderivative of $g(x)$ is $\cos x$, then $\int f(x)\cos x\, dx + \int g(x)e^x\, dx = $

$\int_0^{\log 10}\left[\dfrac{e^x \sqrt{e^x - 1}}{e^x + 8}\right]dx = $