((1+x^2)^(3/2))dy/dx=1 求y等于多少

题目

((1+x^2)^(3/2))dy/dx=1 求y等于多少

答案

∵((1+x²)^(3/2))dy/dx=1==>dy=dx/(1+x²)^(3/2)∴y=∫dx/(1+x²)^(3/2)=∫sec²tdt/sec³t (令x=tant ,则sint=x/√(1+x²))=∫dt/sect=∫costdt=sint+C (C是积分常数)=x/√(1+x²)+C....