If $\int f(x)\, dx = g(x)$ then $\int x^3 f(x^2)\, dx$ is equal to

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 value of $\int \dfrac{\sin^3 x}{(\cos^4 x + 3\cos^2 x + 1)\tan^{-1}(\sec x + \cos x)}\,dx$ is