((1+x^2)^(3/2))dy/dx=1 求y等于多少

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/29 00:39:31

∵((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.

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