$$\int[1+2 \tan x(\tan x+\sec x)]^{\frac{1}{2}} d x= $$

If $$\int \frac{x^3}{\sqrt{1+x^2}} d x=a\left(1+x^2\right)^{\frac{3}{2}}+b \sqrt{1+x^2}+c$$, then $$a+b=$$, (where $$c$$ is constant of integration)

$$\int e^{\tan x}\left(\sec ^2 x+\sec ^3 x \sin x\right) d x=$$

$$\int \sec ^4 x \cdot \tan ^4 x d x=\frac{\tan ^m x}{m}+\frac{\tan ^n x}{n}+c$$ (where c is constant of integration), then m + n =