# Anti Derivative (making sure its right)

1. Dec 2, 2007

### kevinr

[SOLVED] Anti Derivative (making sure its right)

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

Find anti derivative of:

2 cos(x) - SQRT(e^2x)

2. Relevant equations

-

3. The attempt at a solution

- 2 sin (x) - (2/6)e^2x^(3/2)

Is this correct? I just want to make sure!

2. Dec 2, 2007

### hotcommodity

The first part of your answer is correct, but you've integrated $$\sqrt{e^{2x}}$$ incorrectly. Keep in mind that $$\sqrt{e^{2x}}$$ is just another way of saying $$e^{2x}^{\frac{1}{2}}$$. What does this simplify to?

3. Dec 2, 2007

### kevinr

So $$\sqrt{e^{2x}}$$ isnt e^2x^(1/2) ?? (since 2x is inside the sqrt)

4. Dec 2, 2007

It is $$(e^{2x})^{\frac{1}{2}}$$

Now power to power rule that.

Casey

5. Dec 2, 2007

### kevinr

o ok so than $$(e^{2x})^{\frac{1}{2}}$$ means $$(e^{x})$$ since 2 and 1/2 cancel.

So is the anti derivative just e^x since derivative of e^x = e^x * 1.

-2 sin(x) - e^x ?

6. Dec 2, 2007

Yes but watch your sign on the first term and don't forget your constant of integration +C. And just so you know, when you post a question, it helps us to help you if you post it exactly as stated in the text. i.e., don't forget dx. You don't need to use latex, but don't forget the dx, dy, dz and so on, as different problem statements require different solutions.

Something like integral of [2 cos(x) - SQRT(e^2x)]dx would work perfectly!

Welcome aboard!
Casey

7. Dec 2, 2007

### kevinr

O ok. Thank you very much! The first term should be positive!

Also sorry about that, it does say dx!

Thanks a lot!

8. Dec 2, 2007