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?