Solve {ccc}{5/2x_{1}-3/2x_{3}}&{2}&{3}{4}&{-3/2x_{2}+13/2x_{3}}&{6}{7}&{8}&{frac{5}{2}x_{1}+frac{13}{2}x_{3}}

$$\left| \begin{array} { c c c } { \frac { 5 } { 2 } x _ { 1 } - \frac { 3 } { 2 } x _ { 3 } } & { 2 } & { 3 } \\ { 4 } & { - \frac { 3 } { 2 } x _ { 2 } + \frac { 13 } { 2 } x _ { 3 } } & { 6 } \\ { 7 } & { 8 } & { \frac { 5 } { 2 } x _ { 1 } + \frac { 13 } { 2 } x _ { 3 } } \end{array} \right|$$

Evaluate

$$\frac{\left(5x_{1}-3x_{3}\right)\left(13x_{3}-3x_{2}\right)\left(5x_{1}+13x_{3}\right)+252x_{2}-932x_{3}-1120x_{1}+1440}{8}$$

Integrate w.r.t. x_1

$$\frac{x_{1}\left(13x_{3}-3x_{2}\right)\left(25x_{1}^{2}+75x_{1}x_{3}-117x_{3}^{2}\right)}{24}+\frac{63x_{1}x_{2}}{2}-\frac{233x_{1}x_{3}}{2}-70x_{1}^{2}+180x_{1}+С$$