| (%i1) |
residue(1/(1+z^2),z,%i)*%i*%pi; residue(exp(%i*z)/(1+z^2),z,%i)*%i*%pi; |
| (%i3) | integrate(1/sqrt(x),x,0,10); |
| (%i4) | integrate(1/(sqrt(x)*(1+x)),x,0,inf); |
| (%i5) | ldefint(log(x)/(1-x^2),x,0,1); |
| (%i6) | integrate(exp(-x)*x/(1-exp(-2*x)),x,0,inf); |
| (%i7) |
assume(p>0)$ integrate(exp(-x)*x^p,x,0,inf); |
| (%i9) | integrate(exp(-x^2),x,-inf,inf); |
| (%i10) | integrate(exp(-x^2)*cos(x),x,0,inf); |
| (%i11) |
'integrate(exp(-x^2)/(1+x^2),x,0,1); changevar(%,y-erf(x),y,x); |
| (%i13) | integrate(integrate(exp(-x^2/2)/(1+y^2),x,-inf,inf),y,-inf,inf); |
| (%i14) | integrate(integrate(exp(-x^2/2)/(1+y^2),x,-10,10),y,-10,10); |
| (%i15) |
integrate(exp(-x^2/2),x,-10,10); integrate(1/(1+y^2),y,-10,10); |
| (%i17) |
integrate(z^10*(1-z)^10,z,0,1); beta(11,11); |
| (%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); |
| (%i21) |
assume(p>0,q>0)$ integrate(x^(p-1)*(1-x)^(q-1),x,0,1); |
| (%i23) | integrate((sin(x)/x)^2,x,0,inf); |
| (%i24) | integrate((sin(x)/x)^3,x,0,inf); |
| (%i25) | integrate((sin(x)/x)^4,x,0,inf); |
| (%i26) |
integrate(integrate(r,r,0,1),theta,0,2*%pi); integrate(integrate(1,x,-1,1),y,-1,1) - %; |
