f(x) =ln [x+√(x²+1)]
f(-x)= ln[ -x+√(x²+1)]
=ln { [-x+√(x²+1)] [x+√(x²+1)] / [x+√(x²+1)] }
= ln 1/ [x+√(x²+1)]
= - ln [x+√(x²+1)]
= - f(x)
∴f(x)是奇函数
故P= ∫ f(x)dx =0
f(x) =ln [x+√(x²+1)]
f(-x)= ln[ -x+√(x²+1)]
=ln { [-x+√(x²+1)] [x+√(x²+1)] / [x+√(x²+1)] }
= ln 1/ [x+√(x²+1)]
= - ln [x+√(x²+1)]
= - f(x)
∴f(x)是奇函数
故P= ∫ f(x)dx =0