Question

一道微积分题，求解，谢谢大家了。

这道题结果是什么啊？我总是算不对。谢谢大家了

Answer 1

用分部积分法，很简单的。结果为1/9[In（x)chengshang{x}dejucifang-{x}dejucifang/9]

Answer 2

原式=1/9∫lnxdx^9
=1/9*lnx*x^9-1/9∫x^9dlnx
=1/9*lnx*x^9-1/9∫x^8dx
=1/9*lnx*x^9-x^9/81
=x^9/9*(lnx-1/9) +C

Answer 3

∫x^8lnxdx
=1/9∫lnxdx^9
=1/9(x^9lnx-∫x^9dlnx)
=1/9(x^9lnx-∫x^9/xdx)
=1/9(x^9lnx-∫x^8dx)
=1/9(x^9lnx-x^9/9)+C