2. Using partial integration $\int_0^1x^2\cosh(2x)dx=\left.\frac{1}{2}\sinh(2x)x ^2\right|^1_0-\int_0^1x\sinh(2x)dx$ $=\frac{\sinh 2}{2}-\left\{\left.\frac{1}{2}\cosh (2x)x\right|^1_0-\frac{1}{2}\int_0^1\cosh(2x)dx\right\}=\frac{\sinh 2}{2}-\frac{\cosh 2}{2}+\frac{\sinh 2}{4}$ $=\frac{3\sinh 2}{4}-\frac{\cosh 2}{2}$.