Integrating by Parts: Solving ∫r^3/(4+r^2)^(1/2) dr

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Homework Help Overview

The problem involves evaluating the integral ∫r^3/(4+r^2)^(1/2) dr, which falls under the subject area of calculus, specifically integration techniques.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to apply integration by parts but encounters difficulties, leading to uncertainty about their approach. Some participants suggest using substitution instead, questioning the necessity of integration by parts and offering alternative substitutions.

Discussion Status

The discussion is active, with participants exploring different methods for solving the integral. There are suggestions for both integration by parts and substitution, indicating a variety of interpretations regarding the best approach. No consensus has been reached yet.

Contextual Notes

Participants are discussing the appropriateness of different integration techniques, with some expressing confusion about the original poster's challenges. There is an emphasis on finding a simpler method to evaluate the integral.

AnnieF
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Homework Statement



∫r^3/(4+r^2)^(1/2) dr

Homework Equations



∫udv=uv-∫vdu

The Attempt at a Solution



I know that integration by parts must be used. I tried doing it with 4+r^2 as u, but kept running into issues..then I got an answer but it appears to be wrong. I guess I am not sure how to do this.
 
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First substitute r^2=t, then integrate by parts.ehild
 
I don't think it needs integration by parts. I'd do a simple u substitution. u=r^2+4, like AnnieF suggested. What 'issues' were you running into?
 
Dick said:
I don't think it needs integration by parts. I'd do a simple u substitution. u=r^2+4, like AnnieF suggested. What 'issues' were you running into?

The substitution u=r^2 would be significantly easier to deal with. One can then use parts or another substitution to make the integral elementary.
 

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