If $f(5-x)=f(x)$ and $\int_2^3 f(x) dx=2$,then $\int_2^3 x f(x) dx=$

The value of the integral $\int_{-1}^{1}\left\{\frac{x^{2015}}{e^{\mid x \mid}\left(x^{2}+\cos x\right)}+\frac{1}{e^{\mid{x} \mid}}\right\} d x$ is equal to

If $f(x) = \frac{e^x}{1+e^x}$, $l_1 = \int_{f(-a)}^{f(a)} x g(x(1-x)) dx$ and $l_2 = \int_{f(-a)}^{f(a)} g(x(1-x)) dx$, then the value of $\frac{l_2}{l_1}$ is

The value of $\int_{0}^{\pi / 2} \frac{\sin^3 x}{\sin x + \cos x} dx$ is

$\int_0^{\pi /2} \frac{\sqrt{\cos x}}{\sqrt{\sin x} + \sqrt{\cos x}} \, dx = $

Let $N$ be the set of natural numbers. For $n \in N$,define $I_n = \int_0^\pi \frac{x \sin^{2n}(x)}{\sin^{2n}(x) + \cos^{2n}(x)} dx$. Then,for $m, n \in N$,which of the following is true?