∫(x+5)/(x平方-6x+13)dx=
1个回答

∫(x+5)/(x^2-6x+13)dx

=∫(x+5)/((x-3)^2+4)dx

=∫(x-3+8)/((x-3)^2+4)dx

=∫(x-3)/((x-3)^2+4)dx+∫8/((x-3)^2+4)dx

=(1/2)∫1/((x-3)^2+4)d(x-3)^2+∫8/((x-3)^2+4)dx

=(ln(4+(x-3)^2)/2)+4∫1/(((x-3)/2)^2+1)d((x-3)/2)

=(ln(4+(x-3)^2))/2+4arctg((x-3)/2)+C