求(x^2)/(a^2-x^2)^(1/2)Dx的不定积分详解,一个解答是a²arcsin(x/a）-(x/2)√(a²-x²)+C

求(x^2)/(a^2-x^2)^(1/2)Dx的不定积分详解,一个解答是a²arcsin(x/a）-(x/2)√(a²-x²)+C
求(x^2)/(a^2-x^2)^(1/2)Dx的不定积分
详解,
一个解答是a²arcsin(x/a）-(x/2)√(a²-x²)+C

求(x^2)/(a^2-x^2)^(1/2)Dx的不定积分详解,一个解答是a²arcsin(x/a）-(x/2)√(a²-x²)+C
∫[x²/√(a²-x²)]dx
=∫[(a²/√(a²-x²))-1]dx
=∫[a²/√(a²-x²)]dx-∫dx
=∫a[1/√(1-(x/a)²)]d(x/a)-∫dx
=aarcsin(x/a)-x+C

x^2\(a^2-x^2)^(1\2)
=-(a^2-x^2)^(1\2)+a^2\(a^2-x^2)^(1\2)
∫x^2\(a^2-x^2)^(1\2)dx
=-(x\2)(a^2-x^2)^(1\2)-(a^2\2)arcsin(x\a)+a^2arcsin(x\a)+c
=(a^2\2)arcsin(x\a)-(x\2)(a^2-x^2)^(1\2)+C