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Solve the integral:x2exdx

Short Answer

Expert verified

The required answer is -xex-x2ex-12e-x+c.

Step by step solution

01

Step 1. Given information. 

We have given integral isx2exdx.

02

Step 2. Solve the integration by parts . 

We have,u=x2,dv=dxex

u=x2du=2xdxdu2=xdx

and

dv=dxexv=dxexv=-1ex

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

role="math" localid="1648713324601" x2exdx=x2-1ex-12x-1exdx=-xex+12xexdx=-xex+12x-1ex--1exdx=-xex+12-xex+e-xdx

03

Step 3. Integration by parts.  

We have, u=-xdu=-dx

-xex+12-xex+e-xdx=-xex+12-xex-e-x+c=-xex-x2ex-12e-x+c

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