∫dx/(1+√(1-x^2))
x=sinu dx=cosudu √(1-x^2)=cosu
tan(u/2)=sinu/(1+cosu)=x/(1+√(1-x^2))
=∫cosudu/(1+cosu)
=∫[1-1/(1+cosu)]du
=u-∫du/(1+cosu)
=u-∫d(u/2)/(cos(u/2))^2
=u-tan(u/2)+C
=arcsinx - x/(1+√(1-x^2)) +C
∫9(cosx)^3)dx=9∫(cos 2;x*cosx)dx =9∫(（1-sin 2;x）*cosx）dx =9∫(cosx-（sin 2;x*cosx)）dx =9∫cosxdx-∫（sin 2;x*cosx)
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