Integral of (1 + x - 1/x) e^(x + 1/x)

The same question, asked 2 times: 4 May 2023 S1, 15 May 2023 S2. Every wording below, oldest first.

Try each one first, then open its answer.

Question 1
4 May 2023 S1
108 $\int\!\left(1+x-\frac{1}{x}\right)e^{x+\frac{1}{x}}\,dx$
Tap an option to check your answer.
Question 2
15 May 2023 S2
119 $\int\left(1+x-\frac{1}{x}\right)e^{x+\frac{1}{x}}\,dx$
Tap an option to check your answer.