If $$A=\left[\begin{array}{cc}2 a & -3 b \\ 3 & 2\end{array}\right]$$ and $$A \cdot \operatorname{adj} A=A A^T$$, then $$2 a+3 b$$ is

$$\int\left(\frac{\tan \left(\frac{1}{x}\right)}{x}\right)^2 d x=$$

$$\int \frac{1}{(x+2)(1+x)^2} d x$$ has the value

If two angles of $$\triangle \mathrm{ABC}$$ are $$\frac{\pi}{4}$$ and $$\frac{\pi}{3}$$, then the ratio of the smallest and greatest sides are