Question

I think I need someone to just give me a better explanation of integration by substitution. I may be limited by the way my professor explained it, or possibly I just didn't understand clearly

Answer 1

http://znd-search-test.khan-academy.appspot.com/math/calculus/v/indefinite-integration--part-iv

Answer 2

Do you want a better explanation of _how_ to do it, or are you not sure _why_ it works?

Answer 3

I was told that when you have du you replace it with + c and that du=f"(x) dx

Answer 4

Or maybe you're unsure _when_ you should be using it?

Answer 5

Excellent website for learning basically anything! I find his explanation very clear! If you don't get it, go back a video and back to basics if necessary!

Answer 6

in one solution du=8xdx then they say that du/8=xdx and then plug in the +c for xdx. Next example they say that du=2dx so du/2=dx and plug in +c for dx???????!!!!!!!

Answer 7

The +c has nothing to do with substitution. You add c after doing the integral, regardless of what technique you used.

Answer 8

that is where my confusion comes in. The professor said that to get the "+c" you had to relace it with du. To find du you had to solve for du using the technique du= f'(x)dx. Then you dolve for xdx. after you have xdx she said that you then have the du necesarry to replace du with "+c"

Answer 9

In my opinion, your professor has given an unintuitive method and you may want to find a better method instead.

Answer 10

Ok, I think there's two different things going on. When you substitute u for x you need to express dx in terms of du. To do that you take du=u'(x)dx, solve for dx and plug in the result. I'll give you an example later.

The other one is the whole issue with c. I've heard people say "the dx turns into c" or stuff like that. As far as I know it's just a way of reminding people not to forget about the integration constant.

Answer 11

that is what I am trying to do. my laptop is going dead but I will charge it when I get home I will check to read all your answers. thankyou for the help.

Answer 12

Tell me if any of the steps are unclear.