Integration of(1+x-1/x)e^(x+1/x)is?

1 Answer
Apr 6, 2018

I=ex+1xx+C

Explanation:

We want to solve

I=(1+x1x)ex+1xdx

Write this as two separate integrals

I=(x1x)ex+1xdx+ex+1xdx

Let's call

I1=(x1x)ex+1xdx

Such that

I=I1+ex+1xdx

Use integration by parts

udv=uvvdu

Let dv=1dxv=x and

And u=ex+1xdu=(11x2)ex+1xdx

I=I1+ex+1xxx(11x2)ex+1xdx

I=I1+ex+1xx(x1x)ex+1xdx

I=I1+ex+1xxI1

I=ex+1xx+C