How do I integrate u^-1 with new limits after substitution?

[markyp23]

Homework Statement

Homework Equations

None. Well, dx=du/cosx

The Attempt at a Solution

I've substituted it in, got new values for the limits but I have u^-1 on the bottom and so can't integrate it from my current knowledge. Basically I'm stuck with:

Integration of u^(-1) du with limits of 1 and 2.

Any help appreciated. Apologies for not being able to work the Latex system.

 

[arildno]

Seriously, you haven't encountered the derivative of the natural logarithm yet?

 

[markyp23]

I have but I thought it had to be a linear expression to use the natural log. It did cross my mind though - this is what to do, then?

 

[arildno]

What do you mean by a "linear expression"??

 

[markyp23]

Something of the form (ax+b).

Decided to assume that (u) is in that form and so worked it through. Is ln(2) the final answer?

 

[arildno]

Ask yourself:
May we write u=1*u+0?

Sure, the answer is ln2

 

[markyp23]

Thanks for your help! :)