∫（x+5）/(x平方-6x+13)dx=
问题描述：
∫（x+5）/(x平方-6x+13)dx=
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