Integration

👨🏻‍🏫 學術台數學

John

2009-05-17 9:00 pm

Integrate x(cscx^2)^2

更新1:

Actually I solved it quickly after I raised this question. Can I ask, why you can use only a few steps? I need to let u=cotx^2, but you don't need to! u=cotx^2 du=-2x(cscx^2)^2 dx

回答 (1)

STEVIE-G™

2009-05-17 9:50 pm

✔ 最佳答案

As follows:

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2009-05-17 14:12:52 補充：
其實原理同你設u的一樣,只不過做得呢d多就好似唔使設u呢d野...

2009-05-17 14:15:16 補充：
用你個方法做多次:

Let u=cotx^2
du=-2x(cscx^2)^2 dx

int x(cscx^2)^2 dx
=int x(cscx^2)^2 du/[-2x(cscx^2)^2]
=(-1/2) int du
=(-1/2)u+c
=(-1/2)cotx^2+c

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