Stuck on vector integral, Calc III log_2

[mr_coffee]

Hello everyone I'm stuck on this problem its an integral but i don't know how to integrate the log_2 part, i converted it to natural log:
Here is what I have:
http://img278.imageshack.us/img278/1158/integral9lo.jpg
Thanks.

 

[TD]

As you say

$$\log _2 t = \frac{{\ln t}}{{\ln 2}}$$

So

$$\int {\log _2 tdt = } \int {\frac{{\ln t}}{{\ln 2}}} dt = \frac{1}{{\ln 2}}\int {\ln tdt}$$

So now it's just integrating ln(t)dt. If you don't remember how, think integration by parts with f = lnt and dg = dt.

 

[quicknote]

Hello, it looks like you are trying to integrate a vector integral involving a logarithmic function. In order to integrate the log_2 part, you can use the change of base formula to convert it to natural log. This will allow you to use the rules of integration for natural log. However, please keep in mind that when working with vector integrals, you may need to use vector calculus techniques such as line integrals or path integrals. I suggest consulting your textbook or seeking help from your professor or a tutor for further guidance on how to approach this problem. Good luck!