# Simple Integration using U Substitution

by anon413
Tags: integration, simple, substitution
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 P: 13 1. The problem statement, all variables and given/known data Find the indefinite integral. The antiderivative or the integral of (x^2-1)/(x^2-1)^(1/2)dx 2. Relevant equations 3. The attempt at a solution Tried using (x^2-1)^(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
 P: 1,754 $$\int\frac{x^2-1}{\sqrt{2x-1}}dx$$ Yes?
 P: 13 Sorry made a mistake in typing the denominator (2x-1)^(1/2) Im slightly displexic
 P: 13 Simple Integration using U Substitution How did you type that exactly.
P: 1,754
 Quote by anon413 How did you type that exactly.
LaTeX http://physicsforums.com/showthread.php?t=8997

Check my thread again, I editted it. Is it correct now?
 P: 13 Yes thank you, that command latex is complicated I'll try to learn it.
 P: 1,633 well try to use this substitution: 2x-1=u^2, try to defferentiate and substitute back what u get for dx, you also get for x=(u^2 + 1)/2, from 2x-1=u^2 the rest is pretty simple after u substitute! Can you go from here?
P: 1,754
 Quote by anon413 Yes thank you, that command latex is complicated I'll try to learn it.
Gets easier as you use it on a daily basis.

First, I would break up the numerator.

$$\int\frac{x^2}{\sqrt{2x-1}}dx-\int\frac{dx}{\sqrt{2x-1}}$$
P: 1,633
 Quote by rocophysics Gets easier as you use it on a daily basis. First, I would break up the numerator. $$\int\frac{x^2}{\sqrt{2x-1}}dx-\int\frac{dx}{\sqrt{2x-1}}$$
It might work this way also, but by immediately taking the substitution that i suggested he will get to the result pretty fast.
 P: 13 Ok ill try stupid maths method I would get the integral of (((u^2+1)/2)^2-1)/(u) what would my du be
 P: 13 I guess I will attempt this on my own thats for the help.
 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 2x-1=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: $$\int\frac{((\frac{u^{2}+1}{2})^{2}-1)udu}{u}$$, now you can go from here right?
P: 1,633
 Quote by anon413 Ok ill try stupid maths method I would get the integral of (((u^2+1)/2)^2-1)/(u) what would my du be
By the way it is not stupid math, but instead sutupidmath! NOt that i mind it, but it feels good to be correct! NO hard feelings, ok?
 P: 13 thx stupidmath. I knew I got the right udu for dx.

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