If $\int\dfrac{3x + 7}{x^2 - 3x + 2}\, dx = m\log\left(\dfrac{x - 2}{x - 1}\right) + n\log(x - 2) + c$, where $m, n \in R$ and $c$ is an integration constant, then $m + n =$

If $f(x) = \dfrac{\sin^{-1}x}{\sqrt{1 - x^2}}$ and $g(x) = e^{\sin^{-1}x}$, then the value of $\int f(x)g(x)\, dx = \ldots$

The function $f(x) = \int_0^x\dfrac{dt}{1 + \cos t}$ satisfies which of the following differential equations?

If $\int_a^b(x^2 - x)\, dx = 18, \int_a^b x^3\, dx = 0$, then $a + b$ is equal to