$I_n = \int \frac{t^n}{1+t^2} dt, (n = 1, 2, 3, \ldots) \Rightarrow I_6 + I_4 =$

$\int \frac{d x}{\left(2 a x+x^2\right)^{\frac{3}{2}}} = $

If $\int {\frac{{dx}}{{{x^3}{{\left( {1 + {x^6}} \right)}^{2/3}}}} = xf\left( x \right){{\left( {1 + {x^6}} \right)}^{\frac{1}{3}}} + C} $ where $C$ is a constant of integration,then the function $f(x)$ is equal to

$\int \frac{\sin (x-a)}{\sin (x-b)} d x = A x + B \log |\sin (x-b)| + C \Rightarrow (A, B) = $

$\int \frac{x^4-1}{x^2 \sqrt{x^4+x^2+1}} \, dx =$

$\int \frac{d x}{(x-1) \sqrt{x^2-1}}$ is equal to