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assume-exp-inf-integrate

assume (t>0);

assume (T>0);

erfflag=0;

Calculate

assume-diff-ode2

assume(m>0,k>0,...

ode2(m*'diff(z,t,2)=-...

Calculate

assume-define-exp-integrate-kill-min-ratsimp-sqrt-subst

kill(all);

assume(k>0);

define(A(x),(2*exp(-a...

Calculate

assume-solve-sqrt

assume(a<0);

solve(sqrt(a)=-2,a);

Calculate

assume-diff-integrate-plot2d
plot2d ([yexa(x),yvar(x)], [x, 0, 10],[legend,"exacta","variacional"],[style,lines]);

/* [wxMaxima batch fi...

dy(x):=diff(y(x),x);

ddy(x):=diff(dy(x),x);

Calculate

assume-diff-linsolve-ode2

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

eq2:x+2=y;

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

Calculate

assume-display2d-exp-false-inf-integrate-lambda

display2d: false;

assume(lam>0);

lambda: lam;

Calculate

assume-display2d-exp-false-inf-integrate

display2d: false;

assume(lambda>0);

integrate(lambda^3/2*...

Calculate

assume-define-exp-sqrt

assume(k>0);

define(A(x),(2*exp(-a...

define(C(x),(exp(-a*x...

Calculate

assume-exp-quad_qag

assume(t>0);

quad_qag (x^3/(exp(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] [apply1,assume,defrule,diff,ev,ident,inf,integrate,load,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,cons,eliminate,ev,fpprintprec,map,plot2d,solve] [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,solve] [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]

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