How to Integrate - Understand Integration Factors

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how to integrate?

can anybody let me know how to integrate?

and

about integration factor?
 
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that's an absurdly large question. you either don't know this, or expect people here to write whole chapters out of textbooks for you
 
kesh said:
...or expect people here to write whole chapters out of textbooks for you

...which they won't do, so you'll browse through the tutorial section or get some instructing material somewhere on the internet, or, consult a book. :wink:
 
radou said:
...which they won't do, so you'll browse through the tutorial section or get some instructing material somewhere on the internet, or, consult a book. :wink:
well i was feeling good humoured enough to check the maths tutorials index before posting my reply. nothing on integration
 
Integration and an integration factor are two very different things. One is your basic anti-derivative, and the other is used for exact differentials.

Integration is easy. Just like addition has its inverse law of subtraction, derivatives have its inverse law of integration. So if you want to find an integral you just figure out what function F(x) would give you the function you are given f(x) when you take its derivative. In other words, find a function F(x) such that F'(x)=f(x).

You are a long way off from integration factors.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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