Question

6.4e^(−3x + 6) dx
take the integral

Answer 1

First, let's write 6.4 as a fraction to make it a bit easier to work with.

`\int\ {(32)/(5)e^(-3x+6)} \, dx`

`=(32)/(5) \int\ {e^(-3x+6)} \, dx`
Use u-substitution:

`u=-3x+6`

`du=-3dx`
So we now have

`(32)/(5)*-(1)/(3) \int {-3e^(-3x+6)} \, dx`

`=-(32)/(15) \int {e^(u)} \, du`

`=-(32)/(15)e^(u)+C`

`=-(32)/(15)e^(-3x+6)+C`

(If you want the answer to have a decimal, then
`-(32)/(15)` is -2.133333...)