# Thread: How to integrate 2^(4-x

1. ## How to integrate 2^(4-x

How do you integrate 2^(4-x) and $2^x$
thanks.

2. Originally Posted by Johnt447
How do you integrate 2^(4-x) and $2^x$
thanks.
$\int 2^{(4-x)}dx = \int e^{ln|2^{(4-x)}|} dx$

$= \int e^{(4-x)ln|2|} dx$

$= \int e^{(4ln|2|-xln|2|)} dx$

$= \int e^{(4ln|2|})e^{(-xln|2|)} dx$

Now the first e part is a constant, and the second is of the form $e^Cx$, where C is just some constant. You can integrate those, right?

$\int 2^{x}dx = \int e^{ln|2^{x}|} dx$

$= \int e^{xln|2|} dx$

See?

3. First, ${{2}^{4-x}}=16\cdot {{2}^{-x}},$ then ${{2}^{-x}}={{e}^{-x\ln 2}}$ and perform a substitution from there to integrate an exponencial function.

(This is what Mush did, just little algebra first after integrating.)