求积分:∫x+5/x²-6x+13 dx
1个回答

∫x+5/x²-6x+13 dx

=∫(x-3+8)/(x²-6x+13) dx

=∫(x-3)/(x²-6x+13)dx+8∫1/[(x-3)²+2²]dx

=1/2ln(x²-6x+13)+8/2 arctan(x-3)/2+c

=1/2ln(x²-6x+13)+4 arctan(x-3)/2+c