If $\int \sqrt{2}\sqrt{1+\sin x}\, dx = -4\cos(ax+b) + c$, then the value of $a, b$ respectively are...

$\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 = $