根号(4-x平方)的一个原函数是多少

已知y=√（x^2±a^2),
若x在前,后面是减号,
则设x=asect,若后面是加号,则设x=atant,
已知y=√（a^2-x^2),则设x=asint,
∫√（4-x^2)dx,a=2,
则设x=2sint,dx=2costdt,
√（4-x^2)=2cost,
cost=(1/2)√（4-x^2),
t=arcsinx/2,
sin2t=2sintcost=(x/2)√(4-x^2)
原式=∫2cost*2costdt
=4*(1/2)∫（1+cos2t)dt
=2∫dt+∫cos2t d(2t)
=2t+sin2t+C
=2arcsin(x/2)+(x/2)√(4-x^2)+C.