高数不定积分题,求详解,∫1/(x+√(1+x^2)) dx,
问题描述:
高数不定积分题,求详解,∫1/(x+√(1+x^2)) dx,
答
∫1/(x+√(1+x^2)) dx=∫(x-√(1+x^2))/(x+√(1+x^2))(x-√(1+x^2)) dx
=∫(√(1+x^2)-x)/(x+√(1+x^2))(√(1+x^2)-x) dx
=∫(√(1+x^2)-x)dx=x/2*√(1+x^2)+1/2*ln|√(1+x^2)+x|-x^2/2+c