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Question

How to integrate xex?


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Solution

Integrate the given expression :

Let I=xexdx

We will use the method of by parts to solve the integration.

We now that

u(x)v(x)dv=u(x)v(x)dx-du(x)dxv(x)dxdx

Let ,

  1. u(x)=x
  2. v(x)=ex

Therefore,

I=xexdx=xexdx-dxdxexdxdx=xex-dxdx·exdxex=ex+c=xex-exdxdxdx=1=xex-ex+c

xexdx=xex-ex+c

Hence, the value of the integrating xexdx is xex-ex+c


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