$$eex ea int_0^frac{pi}{4}ln (1+ an x) d x &=int_0^frac{pi}{4} ln frac{cos x+sin x}{cos x} d x\ &=int_0^frac{pi}{4} ln sez{sqrt{2}sin sex{x+frac{pi}{4}}}-ln cos x d x\ &=frac{pi}{8}ln 2 +int_frac{pi}{4}^frac{pi}{2}ln sin sex{x+frac{pi}{4}} d x -int_0^frac{pi}{4}ln cos x d x\ &=frac{pi}{8}ln 2 +int_frac{pi}{4}^frac{pi}{2}ln sin t d t -int_{-frac{pi}{4}}^0 ln cos s d squadsex{x+frac{pi}{4}=t, x=-s}\ &=frac{pi}{8}ln 2quadsex{s+frac{pi}{2}=t}. eea eeex$$ 今天上课有个学生问的. 当时写出了第一步, 没写下去了...