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

The integral $\int \frac{2 x^3-1}{x^4+x} \mathrm{~d} x$ is equal to

If $\int \frac{\log \left(t+\sqrt{1+t^2}\right)}{\sqrt{1+t^2}} d t=\frac{1}{2}(g(t))^2+c$ where c is a constant of integration, then $\mathrm{g}(2)$ is equal to