Question

How do you find the indefinite integral of `int (7cosx+4e^x)dx`?

Answer 1

`7sinx+4e^x+c`

Explanation:

`"using standard integrals"`

`•color(white)(x)intcosxdx=sinx" and "inte^xdx=e^x`

`int(7cosx+4e^x)dx`

`=7sinx+4e^x+c`

`"where c is the constant of integration"`

Answer 2

`7sin(x) + 4e^x + C`

Explanation:

Since they're a sum, you can break it apart and integrate each part separately...

`int(7cos(x) + 4e^x)dx = int7cos(x)dx + int4e^xdx`

`= 7intcos(x)dx + 4inte^xdx`

`= 7sin(x) + 4e^x + c`