积分arcsin根号x
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∫arcsin√xdx
=arcsin√x *x -∫xdarcsin√x
(arcsin√x )' =1/(2√x)*√[1-(√x)^2]=(1/2)(1/√(x-x^2)
=xarcsin√x-(1/2)∫xdx/√(x-x^2)
=xarcsin√x+(1/2)∫[(1/2-x)-1/2]dx/√(x-x^2)
=xarcsin√x+(1/4)∫d(x-x^2)/√(x-x^2)-(1/4)∫dx/√(x-x^2)
=xarcsin√x +(1/2)√(x-x^2) +(1/4)∫dx/√[1/4-(x-1/2)^2]
=xarcsin√x+(1/2)√(x-x^2)+(1/2)∫dx/√[1-(4x-2)^2]
=xarcsin√x+(1/2)√(x-x^2)+(1/8)arcsin(4x-2)+C
=arcsin√x *x -∫xdarcsin√x
(arcsin√x )' =1/(2√x)*√[1-(√x)^2]=(1/2)(1/√(x-x^2)
=xarcsin√x-(1/2)∫xdx/√(x-x^2)
=xarcsin√x+(1/2)∫[(1/2-x)-1/2]dx/√(x-x^2)
=xarcsin√x+(1/4)∫d(x-x^2)/√(x-x^2)-(1/4)∫dx/√(x-x^2)
=xarcsin√x +(1/2)√(x-x^2) +(1/4)∫dx/√[1/4-(x-1/2)^2]
=xarcsin√x+(1/2)√(x-x^2)+(1/2)∫dx/√[1-(4x-2)^2]
=xarcsin√x+(1/2)√(x-x^2)+(1/8)arcsin(4x-2)+C
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