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integrate-log-ratsimp-sqrt

integrate(x*log(b/a/s...

F[x]:=2*(log(b/a/sqrt...

ratsimp(F[b^2/a^2]-F[...

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integrate(integrate((...

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integrate(integrate(2...

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f: x^2 ;

integrate ( f, x, 0, ...

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integrate(x-5,x);

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integrate((7^1-x),x);

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p > 0;

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integrate(x+x,x);

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Run Example
(%i1)plot2d ([cos(x),cos(x)^2,/*sin(x)^2,*/cos(x)-cos(x)^2], [x,0,2*%pi]);
plotplot2d ([cos(x),cos(x)^2,/*sin(x)^2,*/cos(x)-cos(x)^2], [x,0,2*%pi]);i:A*sin(2500*t);
(%o2)                            sin(2500 t) A
(%i3) v:diff(i,t)*L;
(%o3)                        2500 cos(2500 t) A L
(%i4) integrate(v,t);
(%o4)                           sin(2500 t) A L
(%i5) 
Run Example
f1(xi):= 1-xi^2;
                                               2
(%o1)                          f1(xi) := 1 - xi
(%i2) f2(xi):= log(1/xi);
                                             1
(%o2)                          f2(xi) := log(--)
                                             xi
(%i3) integrate(xi*f1(xi),xi,k,1);
                                  4      2
                                 k  - 2 k  + 1
(%o3)                            -------------
                                       4
(%i4) integrate(xi*f2(xi),xi);
                                 2     2
                               xi    xi  log(xi)
(%o4)                          --- - -----------
                                4         2
(%i5) 
Run Example
integrate((x+3)*(x-1)^(1/3),x,1,2);
                                      24
(%o1)                                 --
                                      7
(%i2) integrate(1/(x^2 -4*%e^2),x,0,%e);
                              - 1     - 1
                            %e      %e    log(3 %e)
(%o2)                       ----- - ---------------
                              4            4
(%i3) integrate(1/(x^2 -4),x,-1,0);
                                     log(3)
(%o3)                              - ------
                                       4
(%i4) integrate(1/(1-sin(x)),x,-%pi/2,0);
Principal Value
(%o4)                                  1
(%i5) 

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