SOLUTION: please help me on the following assignment questions .how do i differentiate xcos3x with respect to x .how do i intergrate xcos3x with respect to x

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Question 411547: please help me on the following assignment questions
.how do i differentiate xcos3x with respect to x
.how do i intergrate xcos3x with respect to x
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
To differentiate x%2Acos%28x%29, use the product rule:

%28d%2Fdx%29x%2Acos%28x%29+=+cos%28x%29+-+x%2Asin%28x%29.

To integrate int%28x%2Acos%28x%29%2C+dx%29, use integration by parts. Let u+=+x, dv+=+cos%28x%29dx. Then, du+=+dx and v+=+sin%28x%29. Hence,

int%28x%2Acos%28x%29%2C+dx%29+=+x%2Asin%28x%29+-+int%28sin%28x%29dx%29

int%28x%2Acos%28x%29%2C+dx%29+=+x%2Asin%28x%29+%2B+cos%28x%29+%2B+C where C is any constant.