$\int \csc^2 x \, dx$ is equal to

The value of $\int \frac{x^{2}+1}{x^{2}-1} d x$ is

$\int \frac{1 - \tan x}{1 + \tan x} \, dx = $

The solution of the equation $\frac{d^2y}{dx^2} = e^{-2x}$ is

If $\int \frac{\sqrt{x}}{\sqrt{x}-\sqrt[3]{x}} d x=x+E x^{5 / 6}+D x^{2 / 3}+C x^{1 / 2}+B x^{1 / 3}+A x^{1 / 6}+\log (\sqrt[6]{x}-1)^6+K$, then $A+B+C+D+E=$

The value of $\int \frac{d x}{7+6 x-x^2}$ is equal to