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Run Example
(%i1)f(x):=exp(-x^2);
                                              2
(%o1)                          f(x) := exp(- x )
(%i2) tex( expand( integrate( (x-y-l)*f(x), x, l+y, inf) ));
$${{\sqrt{\pi}\,y\,\mathrm{erf}\left(y+l\right)}\over{2}}+{{\sqrt{\pi
 }\,l\,\mathrm{erf}\left(y+l\right)}\over{2}}+{{e^{-y^2-2\,l\,y-l^2}
 }\over{2}}-{{\sqrt{\pi}\,y}\over{2}}-{{\sqrt{\pi}\,l}\over{2}}$$
(%o2)                                false
(%i3) tex(integrate( expand( integrate( (x-y-l)*f(x), x, l+y, inf) * f(y)),y, -inf,inf));
$$\int_{-\infty }^{\infty }{{{\sqrt{\pi}\,y\,e^ {- y^2 }\,
 \mathrm{erf}\left(y+l\right)}\over{2}}+{{\sqrt{\pi}\,l\,e^ {- y^2 }
 \,\mathrm{erf}\left(y+l\right)}\over{2}}-{{\sqrt{\pi}\,y\,e^ {- y^2
  }}\over{2}}-{{\sqrt{\pi}\,l\,e^ {- y^2 }}\over{2}}+{{e^{-2\,y^2-2\,
 l\,y-l^2}}\over{2}}\;dy}$$
(%o3)                                false
(%i4) integrate( expand( integrate( (x-y-l)*f(x), x, l+y, inf) * f(y)),y, -inf,inf);
       inf                     2                               2
      /                     - y                             - y
      [       sqrt(%pi) y %e     erf(y + l)   sqrt(%pi) l %e     erf(y + l)
(%o4) I      (----------------------------- + -----------------------------
      ]                     2                               2
      /
       - inf
                             2                    2          2            2
                          - y                  - y      - 2 y  - 2 l y - l
            sqrt(%pi) y %e       sqrt(%pi) l %e       %e
          - ------------------ - ------------------ + ---------------------) dy
                    2                    2                      2
(%i5) integrate( y*exp(-y^2), y, -inf,inf);
(%o5)                                  0
(%i6) integrate( exp(-y^2)*erf(y+l),y,-inf,inf );
                           inf
                          /           2
                          [        - y
(%o6)                     I      %e     erf(y + l) dy
                          ]
                          /
                           - inf
(%i7) integrate( y*exp(-y^2),y,-inf,inf);
(%o7)                                  0
(%i8) integrate( exp(-y^2),y,-inf,inf);
(%o8)                              sqrt(%pi)
(%i9) integrate( exp(-(y+l)^2),y,-inf,inf);
(%o9)                              sqrt(%pi)
(%i10) romberg(exp(-y^2)*erf(y+l),y,-inf,inf);
                              2
                           - y
(%o10)           romberg(%e     erf(y + l), y, - 1.0 inf, inf)
(%i11) 
Run Example
a:2;
(%o1)                                  2
(%i2) b:1;
(%o2)                                  1
(%i3) x(t):= (a+b/sqrt((b*cos(t))^2+(a*sin(t))^2))*cos(t);
                                         b
(%o3)        x(t) := (a + -------------------------------) cos(t)
                                         2             2
                          sqrt((b cos(t))  + (a sin(t)) )
(%i4) y(t):= (b+a/sqrt((b*cos(t))^2+(a*sin(t))^2))*sin(t);
                                         a
(%o4)        y(t) := (b + -------------------------------) sin(t)
                                         2             2
                          sqrt((b cos(t))  + (a sin(t)) )
(%i5) romberg(2*%pi*x(t)^2*diff(y(t), t), t, 0, %pi/2)-(a^2*b)*4*%pi/3;
                                              16 %pi
(%o5)                     77.10985457200239 - ------
                                                3
(%i6) 
Run Example
assume(x>
0);
(%o1)                               [x > 0]
(%i2) romberg(1/sqrt(-1+exp(x)*erfc(sqrt(x)) + 2*sqrt(x/%pi)),x,0,0.01);
                                   1
(%o2)   romberg(---------------------------------------, x, 0.0, 0.01)
                                     x   2 sqrt(x)
                sqrt(erfc(sqrt(x)) %e  + --------- - 1)
                                         sqrt(%pi)
(%i3) 
[abs,assume,exp,integrate,load,numer,radcan,romberg] [abs,assume,integrate,load,numer,radcan,romberg] [addcol,addrow,diff,do,ev,genmatrix,invert,kill,load,matrix,plot2d,romberg,sqrt,submatrix] [addcol,addrow,diff,ev,genmatrix,invert,kill,length,linsolve,lmax,lmin,load,matrix,plot2d,romberg,sqrt,submatrix] [addcol,addrow,diff,ev,genmatrix,invert,kill,length,lmax,lmin,load,matrix,plot2d,print,romberg,sqrt,submatrix] [addcol,addrow,diff,ev,genmatrix,invert,kill,length,lmax,lmin,load,matrix,plot2d,romberg,sqrt,submatrix] [addcol,addrow,diff,ev,genmatrix,invert,kill,length,load,matrix,plot2d,romberg,sqrt,submatrix] [assume,cos,diff,integrate,numer,pi,romberg,sin,sqrt,trigsimp] [assume,diff,integrate,numer,pi,romberg,sqrt] [bfloat,cos,diff,romberg,sin,sqrt] [cos,csc,factor,float,inf,limit,minf,niceindices,plot3d,powerdisp,powerseries,romberg,sec,sin,solve,trigexpand,trigsimp,true] [cos,diff,romberg,sin,sqrt] [cos,elliptic_f,elliptic_kc,float,load,plot2d,romberg,sqrt] [cos,elliptic_f,elliptic_kc,float,load,romberg,sin,sqrt] [cos,load,pi,romberg,sqrt] [cos,load,romberg] [cos,romberg] [diff,integrate,numer,pi,romberg,sqrt] [diff,load,matrix,plot2d,romberg,sqrt] [diff,romberg,sqrt] [diff,romberg] [erf,ev,exp,romberg] [erf,exp,expand,inf,integrate,load,romberg,tex] [erf,exp,expand,inf,integrate,pi,romberg,sqrt,tex] [erf,exp,expand,inf,integrate,romberg,taylor,tex] [erf,exp,expand,inf,integrate,romberg,tex] [erf,exp,romberg,sqrt] [erf,exp,romberg] [ev,numer,romberg,sin,sum,true] [ev,numer,romberg,sum,true] [float,load,pi,romberg,sin,sqrt] [integrate,romberg] [load,phi,pi,romberg,sin,spherical_harmonic] [load,pi,romberg,sin,spherical_harmonic] [load,pi,romberg,sin,sqrt] [load,pi,romberg,sin] [load,romberg,sin,sqrt] [load,romberg] [pi,romberg,sin] [romberg,sin] [romberg,sqrt,tan] [romberg,sqrt] [romberg]

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