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ldefint

Run Example
(%i1)ldefint(1/e^(2*x),x,0,inf);
                                                1
                                      limit    ----
                                      x -> inf  2 x
                              1                e
(%o1)                      -------- - -------------
                           2 log(e)     2 log(e)
(%i2) integrate(sin(x)*sin(x-%pi/4)/(e^(2*x-sin(x)^2)),x,0,inf);
                   inf
                  /        2
                  [     sin (x) - 2 x                %pi
(%o2)             I    e              sin(x) sin(x - ---) dx
                  ]                                   4
                  /
                   0
(%i3) 
Run Example
assume (t>
0);
(%o1)                               [t > 0]
(%i2) assume (T>
0);
(%o2)                               [T > 0]
(%i3) ldefint ((2*j+1)*exp(-(t/T)*j*(j+1)), j, 0, inf);
                           2                                  2
                          j  t   j t                         j  t   j t
                  /     - ---- - ---                 /     - ---- - ---
                  [        T      T                  [        T      T
(%o3) 2 (limit    I j %e             dj) - 2 (limit  I j %e             dj)
         j -> inf ]                           j -> 0 ]
                  /                                  /
                                                   t
                                                  ---                        t
                              sqrt(t)             4 T                       ---
               sqrt(%pi) erf(---------) sqrt(T) %e                          4 T
                             2 sqrt(T)                  sqrt(%pi) sqrt(T) %e
             - -------------------------------------- + -----------------------
                             2 sqrt(t)                         2 sqrt(t)
(%i4) 
Run Example
ldefint(1/exp(2*x),x,0,minf);
                                             - 2 x
                                 limit     %e
                             1   x -> minf
(%o1)                        - - -----------------
                             2           2
(%i2) integrate(sin(x)*sin(x-%pi/4)/(exp(2*x-sin(x)^2)),x,0,inf);
                   inf
                  /         2
                  [      sin (x) - 2 x                %pi
(%o2)             I    %e              sin(x) sin(x - ---) dx
                  ]                                    4
                  /
                   0
(%i3) 1/exp(2*x);
                                      - 2 x
(%o3)                               %e
(%i4) 

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