Time to Evaluate

$\int_{2}^{5} xh''(x)dx$ , we can solve this integral by integration by parts.

let $u=x \implies du= dx\ and \ dv=h''(x) \implies v= h'(x)$ ;

Using this property: $\int udv = uv-\int vdu$ (integration by parts property)

$\implies \int_{2}^{5} xh''(x)dx = xh'(x)|_{2}^{5} - \int_{2}^{5} h'(x)dx$ ;

$\implies \int_{2}^{5} xh''(x)dx = xh'(x)-h(x)|_{2}^{5}$ =

$\implies$ $(5h'(5)-h(5)) - (2h'(2) - h(2))= 40 -9 -8 +3 = \boxed {26}$ .