Integrating e^7x using U-Substitution | Step-by-Step Guide

[Cacophony]

Homework Statement

S e^7x

Homework Equations

no

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?

 

[Bohrok]

Try treating ∫e^u du just as if it were ∫e^x dx

 

[Mark44]

Homework Statement

S e^7x

Homework Equations

no

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?

This is one of the easiest integrations!

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

 

[Cacophony]

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

 

[Bohrok]

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

 

[RoshanBBQ]

Homework Statement

S e^7x

Homework Equations

no

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?

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
$$\int e^u \frac{du}{7}=\frac{1}{7} \int e^u \, du$$