The integral is equal to: #02

• Integration

The integral ∫(1 + x - 1/x)e^{x + 1/x} dx  is equal to

1. xe^{x + 1/x} + c
2. (x + 1)e^{x + 1/x} + c
3. (x - 1)e^{x + 1/x} + c
4. -xe^{x + 1/x} + c

Answer

∫(1 + x - 1/x)e^{x + 1/x} dx 

∫(e^{x + 1/x})dx + ∫x(1 - 1/x²)e^{x + 1/x} dx

∫(e^{x + 1/x}) dx + xe^{x + 1/x} - ∫(e^{x + 1/x}) dx

The correct option is A.