# Integrating e^7x

1. Mar 30, 2012

### Cacophony

1. The problem statement, all variables and given/known data

S e^7x

2. Relevant equations

no

3. The attempt at a solution

Ok so I am using U-substitution for this problem but I don't know what to do next.

u = 7x, du = 7dx

How do I integrate e^u*du?

2. Mar 30, 2012

### Bohrok

Try treating ∫eu du just as if it were ∫ex dx

3. Mar 30, 2012

### Staff: Mentor

This is one of the easiest integrations!

$\int e^u~du = e^u + C$

4. Mar 30, 2012

### Cacophony

What happen's to du? Why does it dissapear in the solution?

5. Mar 30, 2012

### Bohrok

It disappears for the same reason when integrating something like ∫2x dx to get x2 + C

6. Mar 30, 2012

### RoshanBBQ

I just want to point out, you are asking "how do I integrate"
$$\int e^u \,du$$

Which implies a bit you MAY think that will give you the answer (you could have just omitted the 1/7 to be brief).

But if you did miss it, since
$$du =7dx \rightarrow dx = \frac{du}{7}$$
When you replace dx in the original integral with du/7 and 7x in the original integral with u, you get
$$\int e^u \frac{du}{7}=\frac{1}{7} \int e^u \, du$$

Last edited: Mar 30, 2012