求下列不定积分.(1)∫[(1-x)²/³√x]dx;(6) ∫[3x²/(1﹢x
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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;
(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﹢x](/uploads/image/z/13921608-48-8.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%2317)
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
=∫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