试求 $$ex I=int_2^4frac{sqrt{ln (9-x)}}{sqrt{ln(9-x)}+sqrt{ln(x+3)}} d x. eex$$
解答: $$eex ea I&=int_4^2 frac{sqrt{ln(t+3)}}{sqrt{ln(t+3)}+sqrt{ln(9-t)}}(- d t)quadsex{9-x=t+3}\ &=int_2^4 frac{sqrt{ln (x+3)}}{sqrt{ln(9-x)}+sqrt{(x+3)}} d xequiv J\ &=frac{1}{2}(I+J) =frac{1}{2}int_2^4 d x=1. eea eeex$$