∫(x+5)/(x²-6x+13)dx
=∫(x+5)/[(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∫1/[(x-3)²+4]dx
=(1/2)ln[(x-3)²+4]+4arctan[(x-3)/2]+C
∫sin³xcos²xdx
=-∫sin²xcos²xd(cosx)
=∫(cos²x-1)cos²xd(cosx)
=∫[(cosx)^4-cos²x]d(cosx)
=(cosx)^5/5-(cosx)^3/3+C