1、∫ 1/(x²√x) dx
=∫ x^(-5/2) dx
=-(2/3)x^(-3/2) + C
2、∫ √x(x-3) dx
=∫ [x^(3/2)-3x^(1/2)] dx
=(2/5)x^(5/2) -2x^(3/2) + C
3、∫ 1/[x²(1+x²)] dx
=∫ [1/x² - 1/(1+x²)] dx
=- 1/x - arctanx + C
希望可以帮到你,如果解决了问题,请点下面的"选为满意回答"按钮.
求三题不定积分的过程,预习课本不太懂怎么做.
1、∫ 1/(x²√x) dx
=∫ x^(-5/2) dx
=-(2/3)x^(-3/2) + C
2、∫ √x(x-3) dx
=∫ [x^(3/2)-3x^(1/2)] dx
=(2/5)x^(5/2) -2x^(3/2) + C
3、∫ 1/[x²(1+x²)] dx
=∫ [1/x² - 1/(1+x²)] dx
=- 1/x - arctanx + C
希望可以帮到你,如果解决了问题,请点下面的"选为满意回答"按钮.