$\int_{3\pi/8}^{\pi/8} \frac{ \tan^{2025} x}{ \tan^{2025} x + \cot^{2025} x} dx$ is equal to

$\int \frac{x^2 - 4}{(x+2)(x-1)(x-3)} dx =$

The value of integral $\int_{-\pi/2}^{\pi/2} \frac{1}{1+e^{\sin x}}dx$ is

$\int \frac{1}{\cos^2 x (1 + \tan x)^3} \, dx =$

$\int \frac{x^2+1}{(x+1)^2} e^x \, dx$ is equal to

$\int \left\{\frac{1}{\log x} - \frac{1}{(\log x)^2}\right\} dx$ is equal to:(where C is an arbitrary constant)

If $f(x)=\int \sqrt{\dfrac{x+8}{x-8}}\,dx; f(8)=24\log_e 2$, then $f(10)$ is equal to: