> Int(x^2*(2*x-3)^2, x=1..2)=int(x^2*(2*x-3)^2,x=1..2);

                        2
                       /
                      |    2          2
                      |   x  (2 x - 3)  dx = 4/5
                      |
                     /
                       1

> Int(x^2*(2*x-3)*(3*x^2-6*x+2),x=1..2)=int(x^2*(2*x-3)*(3*x^2-6*x+2),x=
> 1..2);

                 2
                /
               |    2               2                 13
               |   x  (2 x - 3) (3 x  - 6 x + 2) dx = --
               |                                      10
              /
                1

> Int(x^2*(3*x^2-6*x+2)^2,x=1..2)=int(x^2*(3*x^2-6*x+2)^2,x=1..2);

                     2
                    /
                   |    2     2           2      233
                   |   x  (3 x  - 6 x + 2)  dx = ---
                   |                             105
                  /
                    1

> -6*Int(x^3-3*x^2+2*x,x=1..2)=-6*int(x^3-3*x^2+2*x,x=1..2);

                         2
                        /
                       |    3      2
                   -6  |   x  - 3 x  + 2 x dx = 3/2
                       |
                      /
                        1

> -6*Int(x^4-3*x^3+2*x^2,x=1..2)=-6*int(x^4-3*x^3+2*x^2,x=1..2);

                         2
                        /
                       |    4      3      2      23
                   -6  |   x  - 3 x  + 2 x  dx = --
                       |                         10
                      /
                        1

> with(linalg):
> A:=matrix(2,2,[[4/5,13/10],[13/10,233/105]]);

                               [       13 ]
                               [4/5    -- ]
                               [       10 ]
                          A := [          ]
                               [13     233]
                               [--     ---]
                               [10     105]

> a:=vector([3/2,23/10]);

                                 [     23]
                            a := [3/2, --]
                                 [     10]

> C:=linsolve(A,a);

                                [711  -231]
                           C := [---, ----]
                                [179  179 ]

> C[1]:=711/179=evalf(711/179); C[2]:=-231/179=evalf(-231/179);

                              711
                      C[1] := --- = 3.972067039
                              179


                             -231
                     C[2] := ---- = -1.290502793
                             179

> y[2]:=(x-1)*(x-2)*(C[1]+C[2]*x);

                          /711   231 x\
  y[2] := (x - 1) (x - 2) |--- - -----| =
                          \179    179 /

        (x - 1) (x - 2) (3.972067039 - 1.290502793 x)

> y[1]:=15*(x-1)*(x-2)/8;

                              15 (x - 1) (x - 2)
                      y[1] := ------------------
                                      8

> y[2]:=(x-1)*(x-2)*(711/179-231*x/179);

                                        /711   231 x\
                y[2] := (x - 1) (x - 2) |--- - -----|
                                        \179    179 /

> y[ex]:=-9+3*x+6/x;

                       y[ex] := -9 + 3 x + 6/x

> plot({y[1],y[2],y[ex]},x=1..2);

> 
