求计算定积分ln(x+√(x^2+1))dx ,上限1,下限0

2025-04-26 08:56:12
推荐回答(1个)
回答1:

∫ln(x+√(1+x^2))dx=xln(x+√(1+x^2))-∫xdln(x+√(1+x^2)
=xln(x+√(1+x^2)-√(1+x^2)+C
∫[0,1]ln(x+√(1+x^2)dx=ln(1+√2)-√2+1