# Need confirmation on this integration problem!

1. Apr 23, 2005

### jzq

Here's the problem:
$$\int e^{(5x)}$$

This is what I got (Correct me if I am wrong.):
$$\frac{1}{5}e^{(5x)}$$

Or is it just the same:
$$e^{(5x)}$$

2. Apr 23, 2005

### OlderDan

You are sort of right. I think you mean

$$\int e^{(5x)}dx = \frac{1}{5}e^{(5x)} + c$$

3. Apr 23, 2005

### jzq

Yes, I forgot to add the constant, but that's what I meant.
So I am correct then?

4. Apr 23, 2005

### philosophking

Yeah. In general, if you want to check yourself, just take the derivative of what you just integrated. If you get back the integrand, then you know you solved it correctly.

5. Apr 23, 2005

### twoflower

Linearity of primitive functions:

$$\int f(x)\ dx = F(x)\ +\ C \Rightarrow \int f(ax)\ dx = \frac{1}{a} F(ax)\ +\ C,\ a \in \mathbb{R}\ \backslash \ \{0\}$$

6. Apr 23, 2005

### jzq

Thanks guys!

7. Apr 23, 2005

### OlderDan

You also forgot to include the variable of integration for your integral. You need to know what the integration variable is. It will not always be dx, so you should be careful with it.