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anonymous
 5 years ago
How do you take the antiderivative of (2x1)^1/2???
anonymous
 5 years ago
How do you take the antiderivative of (2x1)^1/2???

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Is that (2x1)^(1/2) or (2x1)^1 which is divided by 2?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0O.k. Then you would let u = 2x1 Then du = 2 dx So your integral:\[\int\limits \frac{1}{\sqrt{2x+1}}dx\] becomes

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.01/2 times \[\int\limits \frac{2dx}{\sqrt{2x+1}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits \frac{du}{\sqrt{u}}=\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits u ^{1/2}du=\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{u ^{1/2 + 1}}{1/2+1}+C\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{(2x+1) ^{1/2}}{1/2}+C\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and dividing by 1/2 is the same as multiplying by the reciprocal 2/1

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0What about x/(2x1)^(1/2) with an upper of 5 and a lower of 1. My calculator is giving me a correcct answer of 5.333333. But I can work the problem out to be the same

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sorry, I "can't" work the problem out the same

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0o.k. well, you would want to plug 5 into \[2*\sqrt{2x+1}\] and then subtract what you get when you plug 1 into it.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0that would be 2 times the result of \[\sqrt{2(5)+1}  \sqrt{2(1)+1} = \sqrt{11}\sqrt{3}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0which turns out to be about 3.17

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh! I didn't notice you had an "x" in the numerator.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You would still use the same substitution

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but the x in the numerator can be rewritten in terms of "u"

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0since u = 2x+1 u1 = 2x and so you get that x = (.5)*(u  1)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so dividing that by \[\sqrt{u} = u^{1/2}\] you can use exponent rules to get

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{.5*(u1)}{u^{1/2}} \]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0which boils down to \[.5* (u^{11/2}u^{1/2})\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0which is\[.5* (u^{1/2}u^{1/2})\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and you can use the power rule for integrals to antidifferentiate

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[.5* (u^{3/2}u^{1/2})\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0or \[.5* ((2x+1)^{3/2}(2x+1)^{1/2})\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0does that make sense?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yes, but when I plug in the upper and lower I'm still not getting the correct answer.......

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The (2x+1) is suppose to be (2x1)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0right...it's 14.8511...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh! :) Well, I can guarantee you if you use 2x1 instead it should work but I'll check

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0My graphing calculator is giving me 5.333333

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[9^{3/2}9^{1/2}(1^{3/2}1^{1/2})\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Do you have a graphing cal on you?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Actually, you have to go back and change the substitution also so it is more work than this

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if u = 2x1 then x=.5*(u+1)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thanks for your help. I'm in FLorida and it's about 1am. I need to hit the hay. Thanks again......

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yeah, I did it by hand and it works out. Just use that substitution

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and also multiply by the reciprocal of the new exponent you get when you integrate. ;)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Your welcome...sorry I'm new to typing this out. It's a bit distracting ;) but I'll get used to it. Night!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yeah, it's a pain in the retrice Laters
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