(%i1) residue(1/(1+z^2),z,%i)*%i*%pi;
residue(exp(%i*z)/(1+z^2),z,%i)*%i*%pi;

Result

(%i3) integrate(1/sqrt(x),x,0,10);

Result

(%i4) integrate(1/(sqrt(x)*(1+x)),x,0,inf);

Result

(%i5) ldefint(log(x)/(1-x^2),x,0,1);

Result

(%i6) integrate(exp(-x)*x/(1-exp(-2*x)),x,0,inf);

Result

(%i7) assume(p>0)$
integrate(exp(-x)*x^p,x,0,inf);

Result

(%i9) integrate(exp(-x^2),x,-inf,inf);

Result

(%i10) integrate(exp(-x^2)*cos(x),x,0,inf);

Result

(%i11) 'integrate(exp(-x^2)/(1+x^2),x,0,1);
changevar(%,y-erf(x),y,x);

Result

(%i13) integrate(integrate(exp(-x^2/2)/(1+y^2),x,-inf,inf),y,-inf,inf);

Result

(%i14) integrate(integrate(exp(-x^2/2)/(1+y^2),x,-10,10),y,-10,10);

Result

(%i15) integrate(exp(-x^2/2),x,-10,10);
integrate(1/(1+y^2),y,-10,10);

Result

(%i17) integrate(z^10*(1-z)^10,z,0,1);
beta(11,11);

Result

(%i19) integrate(integrate(integrate(exp(-x^2/2)/(1+y^2)*z^10*(1-z)^10,x,-10,10),y,-10,10),z,0,1);
beta(11,11)*sqrt(2);

Result

(%i21) assume(p>0,q>0)$
integrate(x^(p-1)*(1-x)^(q-1),x,0,1);

Result

(%i23) integrate((sin(x)/x)^2,x,0,inf);

Result

(%i24) integrate((sin(x)/x)^3,x,0,inf);

Result

(%i25) integrate((sin(x)/x)^4,x,0,inf);

Result

(%i26) integrate(integrate(r,r,0,1),theta,0,2*%pi);
integrate(integrate(1,x,-1,1),y,-1,1) - %;

Result


Created with wxMaxima.