# Integrating with logs

1. Jan 26, 2014

### rmiller70015

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

∫x(2^x^3)dx

2. Relevant equations

3. The attempt at a solution
I've tried using substitution using both x^3 and 2^x^3 as u.

I did get pretty far by using log_2 on each side.

∫log_2(x2^x^3)dx=∫(log_2(x)+log_2(2^x^3))dx=∫(log_2(x)+x^3)dx

At this point I'm not sure what to do, any help or hints would be appreciated.

2. Jan 26, 2014

### SteamKing

Staff Emeritus
3. Jan 26, 2014

### Dick

Two points. i) you can't take log inside an integral and get anything having anything to do with the original integral. ii) 2^x^3 doesn't mean anything. You mean either (2^x)^3 or 2^(x^3). They are very different. I suspect you mean (2^x)^3. That you can do with some work and integration by parts. 2^(x^3) leads to a nonelementary integral.

4. Jan 26, 2014

### rmiller70015

It was 2^(x^3) all multiplied by x.

5. Jan 26, 2014

### Dick

If your integrand is $x 2^{(x^3)}$ as opposed to $x (2^x)^3$ then you need some species of a gamma function to get an integral. Have you talked about those?