Can the Indefinite Integral of sqrt(2x+1)dx be Expressed as 1/3(2x+1)^3/2 + C?

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Homework Help Overview

The discussion revolves around evaluating the indefinite integral of the function sqrt(2x+1) with respect to x. Participants are exploring the correctness of a proposed final expression for the integral.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of substitution methods for evaluating the integral, with one participant questioning the steps taken by another. There is also a mention of an alternative substitution that could lead to the same result.

Discussion Status

The discussion includes confirmations of correctness, requests for clarification on the steps involved, and an acknowledgment of different substitution methods. There is an ongoing exploration of the reasoning behind the integral evaluation.

Contextual Notes

Some participants express confusion about the steps taken in the integration process, indicating a need for further explanation of the substitution method used.

sapiental
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evaluate the indefinite integral sqrt(2x+1)dx

I let u^2 = 2x+1

then

indefinite integral u^2du

1/3u^3 + C

1/3(sqrt(2x+1))^3 + C is my finals answer

can this also be written like this 1/3(2x+1)^3/2 + C?


Thanks
 
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yes you are correct
 
Your answer is right, but I have no idea what you just did. Would you mind explaining it to me?
 
sure,

I skipped a few steps in my previous post.

evaluate the indefinite integral sqrt(2x+1)dx

u = sqrt(2x+1)

du = dx/sqrt(2x+1)

sqrt(2x+1)du = dx

or

udu = dx

rewriting the integral

indefinite integral u x udu

= indefinite integral u^2du

then just take antiderivative of u^2 and substitute sqrt(2x+1) back into it
 
oooh, I see now, thx!
 
Probably Quasar987 was used the substitution u= 2x+1 which gives the same answer.
 

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