Calculus Post

First off, happy valentine's day to all :o

So this week in Calculus....wait, I wasn't there all week! So unfortunately I came down with a pretty nasty sickness that included things such as coughing blood and not being able to move for hours...but anyway, let's not talk about that.

I did go to school on Friday and worked on an integration worksheet for a few minutes, but we got called out to an assembly.

But anyway, I wanted to point out a few things that I think I remember that a lot of you were having problems with.

When working an integration problem, a lot of times you need to use substitution. Substitution is useful (at least in my eyes) ESPECIALLY when you see an item in the problem and it's derivative is in the problem somewhere else...let me elaborate a bit more.

In the following problem, you should quickly recognize what your u is and that the derivative of it is in the problem also.

Integral of (1/xln(x)).

Now, when we did this problem in class, a lot of people started to try to go to the log base a of u rule and all of that. First, with these types of problems I always try to think if I can split it up...well in this one you can...so let's do that in our head really quick...well since you can't see it, it is

(1/x)(1/ln(x)). So in this problem you should notice two things. The derivative of ln(x) is (1/x). So really we can rewrite this problem as 1/u where u is lnx. So to integrate 1/u, it's ln|u| + c so the answer to our problem is ln|ln(x)| + c.

If you split up problems visually so that you can better recognize the u and the derivative of u, the problems become way easier.

Anyway, hope that helps someone.