積分極限:x=0，t =π/4；x=π/4，t=0
原公式= ∫ (0，π/4)(π/4-t)dt/[Costco(π/4-t)]
=∫(0，π/4)π/4dt/[Costco(π/4-t)]-∫(0，π/4)TDT/[Costco(π/4-t)]
因為不同的變量不影響最終的積分值，所以:
∫(0，π/4)TDT/[Costco(π/4-t)]=∫(0，π/4) xdx/[cosxcos(π/4-x)]
然後:∫ (0，π/4)xdx/[cosx cos(π/4-x)]= 1/2∫(0，π/4)π/4dt/[Costco(π/4-t)]
和∫(0，π/4)π/4dt/[Costco(π/4-t)]
=∫(0，π/4)π/4dt/[Costcoπ/4 cost+sinπ/4 Sint]
=√2π/4∫(0，π/4) dt/[cost(cost+sint)]
=√2π/4∫(0，π/4) d(tant)/(1+tant)
=√2π/4ln(1+tant)|(0，π/4)
=√2πln2/4
那麽:∫ (0，π/4)xdx/[cos xcos(π/4-x)]=√2πLN2/8。