作业帮求下列不定积分.（1）∫[(1-x)²／³√x]dx;(6) ∫[3x²／(1﹢x²)]dx;(10) ∫[(x³-64)／(x﹣4)]dx;
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![求下列不定积分.（1）∫[(1-x)²／³√x]dx;(6) ∫[3x²／(1﹢x²)]dx;(10) ∫[(x³-64)／(x﹣4)]dx;](/uploads/image/z/8696719-55-9.jpg?t=%E6%B1%82%E4%B8%8B%E5%88%97%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86.%EF%BC%881%EF%BC%89%E2%88%AB%5B%281-x%29%26%23178%3B%EF%BC%8F%26%23179%3B%E2%88%9Ax%5Ddx%3B%286%29+%E2%88%AB%5B3x%26%23178%3B%EF%BC%8F%281%EF%B9%A2x%26%23178%3B%29%5Ddx%3B%2810%29+%E2%88%AB%5B%28x%26%23179%3B-64%29%EF%BC%8F%28x%EF%B9%A34%29%5Ddx%3B)
求下列不定积分.（1）∫[(1-x)²／³√x]dx;(6) ∫[3x²／(1﹢x²)]dx;(10) ∫[(x³-64)／(x﹣4)]dx;
求下列不定积分.
（1）∫[(1-x)²／³√x]dx;
(6) ∫[3x²／(1﹢x²)]dx;
(10) ∫[(x³-64)／(x﹣4)]dx;
求下列不定积分.（1）∫[(1-x)²／³√x]dx;(6) ∫[3x²／(1﹢x²)]dx;(10) ∫[(x³-64)／(x﹣4)]dx;
1.原式=∫(1-2x+x^2)/x^(1/3)dx
=∫x^(-1/3)dx-2∫x^(2/3)dx+∫x^(5/3)dx
=3/2x^(2/3)-6/5x^(5/3)+3/8x^(8/3)+C
2.原式=∫(3x^2+3-3)/(1+x^2)dx
=∫3dx-3∫dx/(1+x^2)
=3x-3arctanx+C
3.原式=∫(x^2+4x+16)dx
=x^3/3+2x^2+16x+C