SOLUTION: Please help me with this question. Integrate with respect to the variable: x Sin x dx

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Question 469480: Please help me with this question.
Integrate with respect to the variable:
x Sin x dx

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


x+Sin%28x%29+dx

For the integrand x+Sin%28x%29+, integrate by parts, ∫f+dg = f+g- ∫+g+df, where

+f+=+x,

dg+=+sin%28x%29+dx,

+df+=+dx,

g+=+-cos%28x%29:

cos%28x%29+dx-x+cos%28x%29

The ∫ of cos%28x%29 is sin%28x%29:so,

x+Sin%28x%29+dx=+sin%28x%29-xcos%28x%29%2Bconstant

+graph%28+500%2C+500%2C+-6%2C+6%2C+-10%2C+10%2C+sin%28x%29-x%2Acos%28x%29%29%29+