# Simple integration problem:help!

1. Oct 27, 2013

### Wonderland

Hi everyone,

I just started to study Physics and I have a very simple question about integration. I'm blocked on this for a while. I'm trying to solve a differential equation for which I need to integrate the expression:
∫(e^2lnx)(10x)dx

Does someone can tell me how to do it? I can't find this exact expression in formulas, and I've tried substitution with u = e^2lnx or with u = 2lnx and I've also tried to use ∫u'v = uv - ∫ uv' ... doesn't seem to work. Any idea?

Thanks a lot!

2. Oct 27, 2013

### arildno

$$e^{2\ln(x)}$$
In that case, use the fact that ln(x) is the inverse function of e^x

3. Oct 27, 2013

### Wonderland

Thank you, so e^2ln(x) = 2x?? I know the rule e^lna = a but here it is e^blna that makes me confused. Is the rule here e^(bln(a)) = ba?

4. Oct 27, 2013

### arildno

How can you rewrite, by rules for exponentiation for real numbers:
$$(a^{b})^{c}=??$$

5. Oct 27, 2013

### Wonderland

a^bc of course

6. Oct 27, 2013

### arildno

Of course!

So, if you have e^(2*ln(x)), can you utilize the above identity in a clever way to simplify your expression, say by starting with: e^(2*ln(x))=e^(ln(x)*2)

7. Oct 27, 2013

### Wonderland

so here, it would be (e^2)(e^lnx) = x(e^2), you mean I should just see e^2 as a constant and taking it out of the integration?

8. Oct 27, 2013

### arildno

Eeh, no.
Think again.

9. Oct 27, 2013

### Wonderland

Would it be (e^2)(e^lnx) = x^2??? It doesn't seem right...

10. Oct 27, 2013

### Wonderland

it would mean that e^blna = a^b

11. Oct 27, 2013

### arildno

Yup!

12. Oct 27, 2013

### arildno

Would it be (e^2)(e^lnx) = x^2??? It doesn't seem right.
Your LHS is wrong, due to a faulty application of the rule.

e^(2*ln(x))=x^2

13. Oct 27, 2013

### Wonderland

Phewww! Thanks!!:-):-)

14. Oct 27, 2013

### arildno

You're welcome!

15. Oct 27, 2013