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

$\int \frac{dx}{x(x^2+1)^3} = ?$

If $\int \frac{2x^2+3}{(x^2-1)(x^2-4)} dx = \log \left[\left(\frac{x-2}{x+2}\right)^a \cdot \left(\frac{x+1}{x-1}\right)^b\right] + c$,(where $c$ is the constant of integration),then the value of $a+b$ is equal to

Let $I(x) = \int \frac{(x+1)}{x(1+x e^x)^2} dx, x > 0$. If $\lim_{x \rightarrow \infty} I(x) = 0$,then $I(1)$ is equal to

$\int \frac{dx}{x(x^3+1)} = $

$\int \frac{dx}{x(x^5 + 1)} = $