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Solve the integral:3-xe2xdx

Short Answer

Expert verified

The required answer ise2x2-x+3+14e2x+c.

Step by step solution

01

Step 1. Given information. 

We have given integral is3-xe2xdx.

02

Step 2. Solve the integration by parts .  

We have, u=-x+3,dv=e2xdx

u=-x+3du=-dx

and

dv=e2xdxv=e2xdxv=e2x2

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

3-xe2xdx=-x+3e2x2--e2x2dx=(-x+3)e2x2+12e2xdx

03

Step 3. Integration by parts. 

We have,

u=2xdu=2dxdu2=dx

So,

e2x2(-x+3)+12e2x2du=e2x2(-x+3)+14e2xdu=e2x2(-x+3)+14e2x+c

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