Need confirmation on this integration problem

[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:
$$e^{(5x)}$$

 

[OlderDan]

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:
$$e^{(5x)}$$

You are sort of right. I think you mean

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

 

[jzq]

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

 

[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.

 

[twoflower]

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:
$$e^{(5x)}$$

Linearity of primitive functions:

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

 

[jzq]

Thanks guys!

 

[OlderDan]

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

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.