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Solution assignment 04 Integration by parts

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Assignment 4

Calculate:

\displaystyle\int{x\sin(x)}dx

Solution

We can write this integral as:

\displaystyle\int{xd(-\cos(x))}=

=-x\cos(x)+\displaystyle\int{\cos(x)}dx=

=-x\cos(x)-\sin(x)+C

Verify the result by differentiation.

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