设f（x）在（0,π/2(为闭区间)上连续,f(x)=xcosx+∫ f(t)dt 则∫ f（x）dx 等于多少积分都有

记:∫[0,π/2]f(t)dt=k（常数）
则f(x)=xcosx+∫ [0,π/2]f(t)dt可化为
f(x)=xcosx+k
两边在[0,π/2]积分有
∫[0,π/2]f(t)dt=∫[0,π/2]tcostdt+k∫[0,π/2]dt【分部积分】
k=tsint[0,π/2]-∫[0,π/2]sintdt+kπ/2
k=π/2-1+kπ/2
解得k=-1