Question

What is `int (e^(ix)+e^(-ix))/(2i)dx`?

Answer 1

`-i\sin x+C`

Explanation:

Given that

`\int \frac{e^{ix}+e^{-ix}}{2i}\ dx`

`=\int \frac{\cos x+i\sin x+\cos x-i\sin x}{2i}\ dx`

`=\int \frac{2\cos x}{2i}\ dx`

`=1/i\int \cos x\ dx`

`=-i\sin x+C`