$$\int \frac{\mathrm{e}^{\tan ^{-1} x}}{1+x^2}\left[\left(\sec ^{-1} \sqrt{1+x^2}\right)^2+\cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right)\right] \mathrm{d} x,$$ where $x>0$ is

$$\int \frac{x^3-7 x+6}{x^2+3 x} \mathrm{~d} x=$$

If $f(x)=\frac{\sin ^2 \pi x}{1+\pi^x}$, then $\int(f(x)+f(-x)) d x$ is equal to

If $\int \frac{\mathrm{d} x}{\cos ^3 x \sqrt{2 \sin 2 x}}=(\tan x)^A+C(\tan x)^B+\mathrm{k}$ where k is a constant of integration, then $A+B+C$ equals