Integration of(1+x-1/x)e^(x+1/x)is?
1 Answer
Apr 6, 2018
Explanation:
We want to solve
I=∫(1+x−1x)ex+1xdx
Write this as two separate integrals
I=∫(x−1x)ex+1xdx+∫ex+1xdx
Let's call
I1=∫(x−1x)ex+1xdx
Such that
I=I1+∫ex+1xdx
∫udv=uv−∫vdu
Let
And
I=I1+ex+1xx−∫x(1−1x2)ex+1xdx
I=I1+ex+1xx−∫(x−1x)ex+1xdx
I=I1+ex+1xx−I1
I=ex+1xx+C