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Simple Integration using U Substitution 
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#1
Jan2808, 01:42 PM

P: 13

1. The problem statement, all variables and given/known data
Find the indefinite integral. The antiderivative or the integral of (x^21)/(x^21)^(1/2)dx 2. Relevant equations 3. The attempt at a solution Tried using (x^21)^(1/2) as u and udu for dx and I solved for x but I am still left with a 1 on top not sure how to deal with it. 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution 


#3
Jan2808, 02:05 PM

P: 13

Sorry made a mistake in typing the denominator (2x1)^(1/2) Im slightly displexic



#4
Jan2808, 02:05 PM

P: 13

Simple Integration using U Substitution
How did you type that exactly.



#5
Jan2808, 02:08 PM

P: 1,754

Check my thread again, I editted it. Is it correct now? 


#6
Jan2808, 02:12 PM

P: 13

Yes thank you, that command latex is complicated I'll try to learn it.



#7
Jan2808, 02:13 PM

P: 1,633

well try to use this substitution:
2x1=u^2, try to defferentiate and substitute back what u get for dx, you also get for x=(u^2 + 1)/2, from 2x1=u^2 the rest is pretty simple after u substitute! Can you go from here? 


#8
Jan2808, 02:15 PM

P: 1,754

First, I would break up the numerator. [tex]\int\frac{x^2}{\sqrt{2x1}}dx\int\frac{dx}{\sqrt{2x1}}[/tex] 


#9
Jan2808, 02:17 PM

P: 1,633




#10
Jan2808, 02:22 PM

P: 13

Ok ill try stupid maths method I would get the integral of (((u^2+1)/2)^21)/(u) what would my du be



#11
Jan2808, 02:43 PM

P: 13

I guess I will attempt this on my own thats for the help.



#12
Jan2808, 03:57 PM

P: 1,633

You do not need to know what the du will be, you need just to plug in the value of the dx that you get after differentiating 2x1=u^2, so it obviously will be dx=udu, and when you plug this in the u here and that one that you will get on the denominator will cancel out so you are left with somehting like this:
[tex]\int\frac{((\frac{u^{2}+1}{2})^{2}1)udu}{u}[/tex], now you can go from here right? 


#13
Jan2808, 04:02 PM

P: 1,633




#14
Jan2808, 05:15 PM

P: 13

thx stupidmath. I knew I got the right udu for dx.



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