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Solve the integral:x2+1exdx

Short Answer

Expert verified

The required answer is-2xex-x2+1ex-2e-x+C.

Step by step solution

01

Step 1. Given information. 

We have given integral isx2+1exdx.

02

Step 2. Solve the integration by parts .  

We have,

u=x2+1du=2xdx

and

role="math" localid="1648720139610" dv=e-xdxv=e-xdxv=-1ex

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

role="math" localid="1648720506794" x2+1exdx=x2+1-1ex--1exdx=-1exx2+1--2xexdx=-1exx2+1+2xexdx

03

Step 3. Integration by parts.

We have, u=xdu=dx

and dv=e-xdxv=e-xdxv=-1ex

==-1exx2+1+2e-xdx=-1exx2+1+2x-1ex--1exdx=-1exx2+1+2-xex--1exdx=-1exx2+1+2-xex-+e-xdx=-2xex-1exx2+1-2e-x+c

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