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

There exists $\theta$ such that $a > |\sec \theta|$,then $\int \frac{dx}{1+a \cos x} = $

Find $\int \sqrt{x^{2}+2 x+5} \, dx$.

If $\int {\frac{{\tan x}}{{1 + \tan x + {{\tan }^2}x}}dx} = x - \frac{K}{{\sqrt A }}{\tan ^{ - 1}}\left( {\frac{{K\tan x + 1}}{{\sqrt A }}} \right) + C,$ ($C$ is a constant of integration),then the ordered pair $(K, A)$ is equal to

If $I_n = \int_{\pi / 2}^{\infty} e^{-x} \cos^n x \, dx$, then $\frac{I_{2018}}{I_{2016}} = $

The value of $\int {\frac{{{e^x} + 9\cos x - 2\sin x + 7}}{{{e^x} + 7\sin x + 11\cos x + 14}}\,dx} $ is (where $C$ is the constant of integration).