求不定积分第31题？
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let
x= (3/2) sinu
dx=(3/2) cosu du
∫ (1-x)/√(9-4x^2) dx
=(1/8)∫ -8x/√(9-4x^2) dx +∫dx/√(9-4x^2)
=(1/4)√(9-4x^2) +∫dx/√(9-4x^2)
=(1/4)√(9-4x^2) +∫(3/2) cosu du/( 3cosu)
=(1/4)√(9-4x^2) +(1/2)u + C
=(1/4)√(9-4x^2) +(1/2)arcsin(2x/3) + C
x= (3/2) sinu
dx=(3/2) cosu du
∫ (1-x)/√(9-4x^2) dx
=(1/8)∫ -8x/√(9-4x^2) dx +∫dx/√(9-4x^2)
=(1/4)√(9-4x^2) +∫dx/√(9-4x^2)
=(1/4)√(9-4x^2) +∫(3/2) cosu du/( 3cosu)
=(1/4)√(9-4x^2) +(1/2)u + C
=(1/4)√(9-4x^2) +(1/2)arcsin(2x/3) + C
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