$\int_{-1/24}^{1/24} \sec x \log \left(\frac{1-x}{1+x}\right) dx =$

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

Let $I_1 = \int\limits_0^{\frac{\pi }{2}} {{e^{ - {x^2}}}\sin (x)dx} $,$I_2 = \int\limits_0^{\frac{\pi }{2}} {{e^{ - {x^2}}}dx} $,and $I_3 = \int\limits_0^{\frac{\pi }{2}} {{e^{ - {x^2}}}(1 + x)\,dx} $. Consider the following statements:
$I: I_1 < I_2$
$II: I_2 < I_3$
$III: I_1 = I_3$
Which of the following is (are) true?

Let $f(x)$ be an even function with period $2$ and $f(x)$ be integrable on every interval. If $g(x) = \int_0^x f(t) dt$,then $g(x+2) =$

Let the function $F$ be defined as $F(x) = \int_{1}^{x} \frac{e^{t}}{t} dt, x > 0$. Then the value of the integral $\int_{1}^{x} \frac{e^{t}}{t+a} dt$,where $a > 0$,is

$\int_{ - 1/2}^{1/2} {\cos x \ln \left( \frac{1 + x}{1 - x} \right) dx}$ is equal to