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assume-integrate

assume(N>=0);

integrate( ((%e**(-x*...

Calculate

assume-diff-factor-integrate-log-ratsimp

/* vz (superposition)...

assume(k < 1);

Vz_nondim: (G)*(1 - (...

Calculate

assume-draw-draw3d-explicit-kill-load
draw3d(key = "U",color = blue,contour = both , /* rzutowanie na p3aszczyzne */explicit(y,x1, 1, 100, x2,1, 100));

load(draw);

kill(all);

assume(x1>0,x2>...

Calculate

assume-dim-integrate-log-ratsimp

/* vz (superposition)...

assume(k < 1);

Vz: G*(1 - (xi^2) - (...

Calculate

assume-integrate-sqrt

f:R-sqrt(R^2 - x^2);

assume(a>0);

assume(a<R);

Calculate

assume-is

assume(x>0);

assume(y>0);

f(x,y):= 3*x*y;

Calculate

assume-constant-cos-declare-diff-expandwrt-let-letsimp-sin-solve-trigsimp

x(t) := r(t) * sin(th...

y(t) := r(t) * cos(th...

declare (slope,consta...

Calculate

assume-diff-ev-expand-float-fullratsimp-integrate-rhs-solve

f(m):=m+t;

eq1:''integrate(f(m),...

sol1:solve(eq1,t);

Calculate

assume-integrate

assume(r0>0,h>0);

integrate(2*%pi*r0,z,...

r1:(r0/h)*(h-z);

Calculate

assume-declare-exp-integrate

declare(lambda, scalar);

assume(lambda > 0);

mu:exp(-lambda*x*x);

Calculate

assume

Run Example
(%i1)assume(A>
0,d>
0,y>
0,%lambda>
0,D>
0);
(%o1)              [A > 0, d > 0, y > 0, %lambda > 0, D > 0]
(%i2) test:4*A^2*cos(%pi*d*y/(%lambda*D))^2;
                                2    2  %pi d y
(%o2)                        4 A  cos (---------)
                                       %lambda D
(%i3) l:diff(test,y,1);
                             2      %pi d y        %pi d y
                    8 %pi d A  cos(---------) sin(---------)
                                   %lambda D      %lambda D
(%o3)             - ----------------------------------------
                                   %lambda D
(%i4) solve(l=0,y);

solve: using arc-trig functions to get a solution.
Some solutions will be lost.
                                        %lambda D
(%o4)                       [y = 0, y = ---------]
                                           2 d
(%i5) 
Run Example
assume(r>
0);
(%o1)                               [r > 0]
(%i2) assume(d>
0);
(%o2)                               [d > 0]
(%i3) assume(b>
0);
(%o3)                               [b > 0]
(%i4) rr(t):=sqrt(r*r+rp*rp-2*r*rp*cos(t));
(%o4)           rr(t) := sqrt(r r + rp rp + (- 2) r rp cos(t))
(%i5) x(t):=rr(t)/(2*d);
                                         rr(t)
(%o5)                            x(t) := -----
                                          2 d
(%i6) f(t):=1/d*(6/5-2*x(t)^2+3/2*x(t)^3-5*x(t)^5);
                        1  6      2      3  3             5
(%o6)           f(t) := - (- - 2 x (t) + - x (t) + (- 5) x (t))
                        d  5             2
(%i7) expand(f(t)*sin(t));
                               2    2 5/2
        5 (- 2 r rp cos(t) + rp  + r )    sin(t)
(%o7) - ----------------------------------------
                             6
                         32 d
                          2    2 3/2                                 2
   3 (- 2 r rp cos(t) + rp  + r )    sin(t)   r rp cos(t) sin(t)   rp  sin(t)
 + ---------------------------------------- + ------------------ - ----------
                        4                              3                 3
                    16 d                              d               2 d
    2
   r  sin(t)   6 sin(t)
 - --------- + --------
        3        5 d
     2 d
(%i8) integrate(expand(f(t)*sin(t)),t);
                               2    2 7/2                          2    2 5/2
        5 (- 2 r rp cos(t) + rp  + r )      3 (- 2 r rp cos(t) + rp  + r )
(%o8) - --------------------------------- + ---------------------------------
                        6                                  4
                   224 d  r rp                         80 d  r rp
                                       2        2           2
                               r rp cos (t)   rp  cos(t)   r  cos(t)   6 cos(t)
                             - ------------ + ---------- + --------- - --------
                                      3             3           3        5 d
                                   2 d           2 d         2 d
(%i9) integrate(f(t)*sin(t),t);
                                2    2 7/2                          2    2 5/2
         5 (- 2 r rp cos(t) + rp  + r )      3 (- 2 r rp cos(t) + rp  + r )
(%o9) (- --------------------------------- + ---------------------------------
                         5                                  3
                    224 d  r rp                         80 d  r rp
                                    2        2           2
                          - r rp cos (t) + rp  cos(t) + r  cos(t)   6 cos(t)
                        + --------------------------------------- - --------)/d
                                              2                        5
                                           2 d
(%i10) 
Run Example
assume(x>
0);
(%o1)                               [x > 0]
(%i2) f(x):=integrate(1/sqrt(-1+exp(x)*erfc(sqrt(x)) + 2*sqrt(x/%pi)),x);
                                              1
(%o2) f(x) := integrate(----------------------------------------------, x)
                                                                  x
                        sqrt(- 1 + exp(x) erfc(sqrt(x)) + 2 sqrt(---))
                                                                 %pi
(%i3) define(f1(x),diff(f(x),x,1));
                                           1
(%o3)          f1(x) := ---------------------------------------
                                             x   2 sqrt(x)
                        sqrt(erfc(sqrt(x)) %e  + --------- - 1)
                                                 sqrt(%pi)
(%i4) f1(0.01);
                                      1
(%o4)                 ----------------------------------
                              0.2
                      sqrt(--------- - 0.10354302003087)
                           sqrt(%pi)
(%i5) 
[abs,assume,ceiling,declare,floor,max,tex] [abs,assume,if,is,ratsimp] [apply1,assume,defrule,diff,ev,ident,inf,integrate,load,matrix,sqrt,transpose] [assume,atvalue,diff,laplace,limit,solve] [assume,bessel_j,besselexpand,factor,inf,integrate,pi,print,quit,radexpand,true] [assume,binomial,simpsum] [assume,coeff,equal,expand,is,ratsimp] [assume,constant,cos,declare,diff,let,letsimp,sin,solve,trigsimp] [assume,constant,cos,declare,diff,let,letsimp,sin,subst,trigsimp] [assume,cos,expand,integrate,sin,sqrt,tex] [assume,cos,expand,integrate,sin,sqrt] [assume,cos,integrate,phi,sin,sqrt] [assume,cos,integrate,plot2d,sin,sqrt] [assume,cos,integrate,plot2d,sin,subst] [assume,cos,integrate,plot2d,sin] [assume,cos,integrate] [assume,declare,exp,facts,log,residue,sin,sinh] [assume,define,plot2d,sin,sqrt,subst] [assume,diff,ev,ic1,ic2,ode2,plot2d] [assume,diff,ev,integrate,linsolve,plot2d] [assume,diff,ev,integrate,plot2d,sin] [assume,diff,ev,integrate,plot2d] [assume,diff,exp,pade,taylor] [assume,diff,exp] [assume,diff,factor,integrate,log,ratsimp] [assume,diff,facts,forget,ode2] [assume,diff,integrate,plot2d] [assume,diff,integrate] [assume,diff,is,solve] [assume,diff,ode2] [assume,diff] [assume,dim,integrate,log,ratsimp] [assume,distrib,integrate,load] [assume,exp,inf,integrate] [assume,exp,inf,limit] [assume,exp,integrate,log] [assume,exp,integrate] [assume,exp,quad_qag] [assume,inf,limit] [assume,integrate,log,ratsimp] [assume,integrate,log] [assume,integrate,sin] [assume,integrate,sqrt] [assume,integrate] [assume,is] [assume,solve,sqrt] [assume,solve] [assume,sqrt,tan,taylor] [assume,taylor] [assume]

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