Question

How to integrate? `int 2e^x+2e^-x dx`

Answer 1

`2(e^x - e^(-x)) + c`

Explanation:

I don't see the "dx" in there, I'm going to assume your problem as given to you has it.

`int(2e^x + 2e^(-x))dx = 2inte^xdx + 2inte^(-x)dx`

...for the first term, you know that the antiderivative of `e^x = e^x`

for the second term, remember that `int(e^u du) = e^u`. In this case, `u = -x`, so du = -1dx. So you can convert the second term to a form you can readily integrate by multiplying by `(-1)(-1)`, which turns your second integral term into:

`-2inte^(-x) (-dx)`

so, your original problem's integral evaluates to:

`2e^x - 2e^(-x) + c`

`= 2(e^x - e^(-x)) + c`

GOOD LUCK