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exp-integrate-tan

integrate(exp(x)*tan(...

Calculate

exp

F:exp(3*x^3-x^2+5*x-6);

Calculate

exp-inf-integrate-pi-sqrt-tex

f(x,k):=exp(-(x-k)^2/...

integrate((x-y)*f(x,0...

tex(integrate((x-y)*f...

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exp-integrate

integrate(5*exp(3*x-1...

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exp-linsolve

eq1:x*4+y-2=y;

eq2:x+2=y;

linsolve([eq1,eq2],[x...

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exp-integrate-pi-sqrt

f(x, sigma) := exp(-(...

integrate(f(x, sigma)...

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exp-taylor

l:1;

a:3;

taylor(exp(-(l*t)^a),...

Calculate

exp-numer-pi

exp(pi),numer;

1+2;

Calculate

exp-plot2d-tan
plot2d([f(t),f1(t)],[t,-5,5]);

b:0.5;

f(t):= 1/(1+exp(-b*t));

f1(t):=tan(x);

Calculate

exp-expand

B_1: 1/k*(1-exp(-k*(T...

A_1: (h-v^2/(2*k^2))*...

expand(A_1);

Calculate

exp

Run Example
(%i1)a:exp(%i*2*%pi/3);
                                sqrt(3) %i   1
(%o1)                           ---------- - -
                                    2        2
(%i2) F:1/3*matrix([1,1,1],[1,a,a^2],[1,a^2,a]);
                  [ 1          1                  1         ]
                  [ -          -                  -         ]
                  [ 3          3                  3         ]
                  [                                         ]
                  [     sqrt(3) %i   1     sqrt(3) %i   1 2 ]
                  [     ---------- - -    (---------- - -)  ]
                  [ 1       2        2         2        2   ]
(%o2)             [ -   --------------    ----------------- ]
                  [ 3         3                   3         ]
                  [                                         ]
                  [     sqrt(3) %i   1 2   sqrt(3) %i   1   ]
                  [    (---------- - -)    ---------- - -   ]
                  [ 1       2        2         2        2   ]
                  [ -  -----------------   --------------   ]
                  [ 3          3                 3          ]
(%i3) M:((%i*Xc1*(RL+%i*Xc1))/(%i*Xc+RL+%i*XL));
                             %i Xc1 (RL + %i Xc1)
(%o3)                        --------------------
                              %i XL + RL + %i Xc
(%i4) 
Run Example
hex(psi) := 1.02 * exp(5.66 *psi);
(%o1)                   hex(psi) := 1.02 exp(5.66 psi)
(%i2) hex(-1.0);
(%o2)                         0.0035521672361759
(%i3) dhex(psi) := ''(diff(hex(psi),psi));
                                              5.66 psi
(%o3)                   dhex(psi) := 5.7732 %e
(%i4) dhex(-1.0);
(%o4)                          0.020105266556756
(%i5) f_vanL(ftsw)  := 1- exp(-5* ftsw);
(%o5)                 f_vanL(ftsw) := 1 - exp((- 5) ftsw)
(%i6) f_lebon(ftsw) := ftsw/0.4;
                                              ftsw
(%o6)                        f_lebon(ftsw) := ----
                                              0.4
(%i7) fh_vanL(psi)  := f_vanL(hex(psi));
(%o7)                  fh_vanL(psi) := f_vanL(hex(psi))
(%i8) fh_lebon(psi) := f_lebon(hex(psi));
(%o8)                 fh_lebon(psi) := f_lebon(hex(psi))
(%i9) g_vanL(psi)  := fh_vanL(psi)  / dhex(psi);
                                         fh_vanL(psi)
(%o9)                     g_vanL(psi) := ------------
                                          dhex(psi)
(%i10) g_lebon(psi) := fh_lebon(psi) / dhex(psi);
                                         fh_lebon(psi)
(%o10)                   g_lebon(psi) := -------------
                                           dhex(psi)
(%i11) g_vanL(-1.0);
(%o11)                         0.87559357230093
(%i12) g_lebon(-1.0);
(%o12)                          0.4416961130742
(%i13) plot2d([f_lebon,f_vanL],[ftsw,0,0.4]);
plotplot2d([f_lebon,f_vanL],[ftsw,0,0.4]);plot2d([g_lebon,g_vanL],[psi,-1.5,-0.33]);
plotplot2d([g_lebon,g_vanL],[psi,-1.5,-0.33]);
Run Example
integrate(exp(-x+sqrt(x)),x);
                                                      2
                                       (1 - 2 sqrt(x))                  2
                %i gamma_incomplete(1, ----------------) (1 - 2 sqrt(x))
        1/4                                   4
(%o1) %e    %i (---------------------------------------------------------
                                                   2
                                    (2 sqrt(x) - 1)
                                                            2
                                          1  (1 - 2 sqrt(x))
                      %i gamma_incomplete(-, ----------------) (1 - 2 sqrt(x))
                                          2         4
                    - --------------------------------------------------------)
                                        2 abs(2 sqrt(x) - 1)
(%i2) 

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