The value of $\int_{-100}^{100} \frac{x+x^3+x^5}{1+x^2+x^4+x^6} dx$ is

If $I_{n}=\int_0^{\frac{\pi}{4}} \tan ^n x \, dx$,then $I_{13}+I_{11}=$

$\int_{0}^{1} \sin \left( 2 \tan^{-1} \sqrt{\frac{1+x}{1-x}} \right) \, dx = $

The value of $\int_{-1}^{1} x^{2} e^{[x^{3}]} dx$,where $[t]$ denotes the greatest integer $\leq t$,is

If the value of $\int_{0}^{\pi/2} \sin^{4}(x) \cdot \cos^{2}(x) dx = \frac{\pi}{32}$,then the value of $\int_{0}^{\pi/2} \cos^{4}(x) \cdot \sin^{2}(x) dx$ is:

$\int_{0}^{\pi} \frac{x \tan x}{\sec x + \tan x} dx =$