14-December-2021 Homework
Find the integrals. (You can use any method you learned from the course. Not all problems require integration by parts.)
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- %20%5C%2C%20dx%20%3D%20%5Cint%20%5Ctan%5E%7B-1%7D(x)%5C%2C%20dx#card=math&code=%5Cint%20%5Carctan%28x%29%20%5C%2C%20dx%20%3D%20%5Cint%20%5Ctan%5E%7B-1%7D%28x%29%5C%2C%20dx&id=T1vIT)
- %5C%2C%20dx#card=math&code=%5Cint%20x%20%5Csin%282x%29%5C%2C%20dx&id=V9LDV)
- %5C%2C%20dx#card=math&code=%5Cint%20x%20%5Ccos%282x%29%5C%2C%20dx&id=xbJQF)
- %20%5C%2C%20dx%2C%20%5Cquad%20I_2%20%3D%20%5Cint%20%5Ccos(%5Cln%20x)%5C%2C%20dx#card=math&code=I_1%20%3D%20%5Cint%20%5Csin%20%28%5Cln%20x%29%20%5C%2C%20dx%2C%20%5Cquad%20I_2%20%3D%20%5Cint%20%5Ccos%28%5Cln%20x%29%5C%2C%20dx&id=jR3Ii) (Hint: let , or you can use integration by parts and simultaneously solve out these two integrals)
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- %5C%2C%20dx%20%3D%20%5Cint%20x%20%5Ctan%5E%7B-1%7D%20(x)%20%5C%2C%20dx#card=math&code=%5Cint%20x%20%5Carctan%28x%29%5C%2C%20dx%20%3D%20%5Cint%20x%20%5Ctan%5E%7B-1%7D%20%28x%29%20%5C%2C%20dx&id=a11Jk)
Derive recursive formulas for the following integrals using the technique of integration by parts. Assume that is a positive integer.
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- %5C%2C%20dx#card=math&code=%5Cint%20%5Ctan%5En%28x%29%5C%2C%20dx&id=nDjbC) (Hint: , and hence .)
Please write down the numbering.
Email your homework to: yqfeng@stu.edu.cn with subject “hw141221”. You can submit a picture or a scanned copy. Due date: Thursday 23-December, 23:59 (GMT+8).