求根号下(1-x^2)*x的不定积分
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求根号下(1-x^2)*x的不定积分
![求根号下(1-x^2)*x的不定积分](/uploads/image/z/18905816-56-6.jpg?t=%E6%B1%82%E6%A0%B9%E5%8F%B7%E4%B8%8B%EF%BC%881-x%5E2%EF%BC%89%2Ax%E7%9A%84%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86)
原式=(1/2)∫√(1-x^2)d(x^2)
=-(1/2)∫√(1-x^2)d(1-x^2)
=-(1/2)×(2/3)(1-x^2)^(3/2)+C
=-(1/3)(1-x^2)√(1-x^2)+C
=-(1/2)∫√(1-x^2)d(1-x^2)
=-(1/2)×(2/3)(1-x^2)^(3/2)+C
=-(1/3)(1-x^2)√(1-x^2)+C