导函数是y=(1-x^2)^(1/2) 求原函数?

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导函数是y=(1-x^2)^(1/2)求原函数?导函数是y=(1-x^2)^(1/2)求原函数?导函数是y=(1-x^2)^(1/2)求原函数?令x=sinadx=cosada(1-x^2)^(1/2

导函数是y=(1-x^2)^(1/2) 求原函数?
导函数是y=(1-x^2)^(1/2) 求原函数?

导函数是y=(1-x^2)^(1/2) 求原函数?
令x=sina
dx=cosada
(1-x^2)^(1/2)=cosa
所以原式=∫cos²ada
=∫(1+cos2a)/2da
=1/2∫da+1/4∫cos2ad2a
=a/2+sin2a/4+C
=(arcsinx)/2+sin2(arcsinx)/4+C
=(arcsinx)/2+2x*(1-x^2)^(1/2)/4+C