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Solve the integral:xexdx

Short Answer

Expert verified

The required answer is-xex-ex+c.

Step by step solution

01

 Step 1. Given information 

We have given integral is xexdx.

02

Step 2. Solve the integration by parts .  

We have, u=x,dv=dxex

u=xdu=dx

and

dv=dxexv=dxexv=-1ex

The formula of integration by parts is udv=uv-vdu

xexdx=x-1ex--1exdx=-xex+e-xdx

03

Step 3. Integration by parts. 

We have, u=-xdu=-dx

So,

-xex+e-xdu=-xex-e-x+c=-xex-ex+c

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