Integral of 1/(x^2+sqrt(x)) - Step by Step Solution

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Homework Help Overview

The discussion revolves around finding the integral of the function 1/(x^2+sqrt(x)) with respect to x. Participants are exploring various substitution methods and approaches to tackle the integral.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts a substitution with u=sqrt(x) and transforms the integral accordingly. Some participants question the effectiveness of this approach, particularly when dealing with partial fractions and an irreducible quadratic that arises during the process.

Discussion Status

The discussion is ongoing, with some participants offering guidance on completing the square and suggesting trigonometric substitution, while others express uncertainty due to a lack of familiarity with trigonometric methods. There is a recognition that the problem may not be essential for the current learning stage.

Contextual Notes

Participants note that trigonometric substitution has not yet been covered in their coursework, which affects their ability to proceed with the problem. The original poster indicates that this problem was not required, suggesting a level of optionality in the discussion.

cragar
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Homework Statement


Integral of 1/(x^2+sqrt(x)) dx

The Attempt at a Solution



i tried u=sqrt(x)
so then 2udu=dx
u^2=x

so then 2 integral u/(u^4+u) du

then integral 2/(u^3+1)du then i factored it with sum of cubes then i did partial fraction's
on it is this the right approach.
 
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Seems fine to me so far.
 
but when i do the partial fractions after i factor the sum of cubes i get an unfactorable quadratic and i can't get the terms to cancel out without the other cancilind out to find out the leading co-effiecients of the numertors of the partial fractions.
 
Yes, you do get an irreducible quadratic. Complete the square in the denominator and use a trig substitution.
 
we havn't learned trig substitution yet.
 
I guess I don't see any other way to do it. There's an arctan in there I don't see how to get around.
 
ok this wasn't a required problem my teacher said some of us could maybe do it
so ill just wait till we learn trig sub.
 

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