# Homework Help: Integrating 3cos[SUP]5[/SUP]3xdx

1. Feb 10, 2012

### bobsmith76

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

If you look at the answer you will see that they integrate sin43x into (sin53x)/5. well, if you can do that why not just integrate 3cos53xdx into (cos63xdx)/2? why go through all the trouble of dividing it into parts? it is true that (cos63xdx)/2 = 0 but i still don't see why you can integrate sin43x and not 3cos53xdx.

2. Feb 10, 2012

### Staff: Mentor

No, they do not. They integrate sin4(3x)*cos(3x)*3dx to get (1/5)sin5(3x).
Because that's not the right answer. IOW, (cos63xdx)/2 is not an antiderivative of 3cos53x.
To make a relatively difficult problem amenable to solution by a very simple technique. Do you recognize what type of integration they did for the 2nd and 3rd integrals? I'm guessing you don't.
???
No, this is not generally true.

3. Feb 10, 2012

### Gallagher

They don't integrate sin43x into sin53x/5 but rather, they integrate sin43xcos3x into sin53x/5.

Thinking about sin53x/5 this makes sense as if you were to differentiate that function you would get nfn-1 per the power rule which is sin43x times the derivative of the inner function per the chain rule, cos3x.

You couldn't integrate 3cos53xdx into (cos63xdx)/2 as you would need a -sin3x with it so as to fullfil the chain rule.

I hope that I'm not totally wrong on this and if not, that it helps you understand.

4. Feb 10, 2012

### Staff: Mentor

Bob, I have to question the reasonableness of your study strategy. I've read your blog, so I understand a little of your situation and what you're trying to do, which is laudable. However, mathematics is not something that is amenable to cramming X number of pages into Y hours of study time. You will not learn very well by merely looking at worked problems and trying to understand the steps they show. You'll learn better by actually working the problems - then things will stick in your mind.

Also, in a fair number of your posts, I've noticed a lack of understanding of basic algebra and trig concepts. You will continue beating your head against the wall, unless you revisit those parts of mathematics and reinforce these foundational subjects.

Unlike some other disciplines, mathematics is not made up of discrete, unrelated areas, but instead builds on previous areas. The old saying is, if you build your house on sand, it will collapse.