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defint-laplace-sin

eq1:sin(w*x);

eq2:defint(eq1,x,a-b,a);

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defint(x^2,x,a,b);

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defint

Run Example
(%i1)defint(x,x,a-b,a);
                              2    2            2
                             a    b  - 2 a b + a
(%o1)                        -- - ---------------
                             2           2
(%i2) eq1:sin(w*x);
(%o2)                              sin(w x)
(%i3) eq2:defint(eq1,x,a-b,a);
                           cos((a - b) w)   cos(a w)
(%o3)                      -------------- - --------
                                 w             w
(%i4) laplace(eq2,a,s);
                     w sin(b w) + s cos(b w)        s
(%o4)                ----------------------- - -----------
                               2    2              2    2
                           w (w  + s )         w (w  + s )
(%i5) 
Run Example
assume (x*y>
0);
(%o1)                              [x y > 0]
(%i2) f(x,y):=defint(%e^(-t^2),t,0,(x*y));
                                            2
                                         - t
(%o2)                f(x, y) := defint(%e    , t, 0, x y)
(%i3) sol:solve(rhs(%o1));

solve: variable list is empty, continuing anyway.
(%o3)                                 all
(%i4) 
Run Example
defint((sqrt(7)*sin(%pi*7*f)/(%pi*7*f))^2,f, -inf,inf);
(%o1)                                  1
(%i2) 

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