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Solve the integral:x2e3xdx.

Short Answer

Expert verified

The required answer isx2e3x3-29xe3x+227e3x+c.

Step by step solution

01

Step 1. Given information. 

We have given integral isx2e3xdx.

02

Step 2. Solve the integration by parts . 

We have, u=x2,dv=e3xdx

localid="1648652451162">u=x2du=2xdx

and

dv=e3xdxv=e3xdxv=e3x3

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

x2e3xdx=x2e3x3-2xe3x3dx=x2e3x3-23xe3xdx

03

Step 3. Integration by parts. 

We have, u=x,dv=e3xdx

u=xdu=dx

and

dv=e3xdxv=e3xdxv=e3x3

So,

13x2e3x-23xe3x3dx=13x2e3x-2313xe3x-13e3xdx=13x2e3x-29xe3x+227e3x+c

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