Is This Integral Calculation Correct?

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Homework Help Overview

The discussion revolves around the integration of the expression (5x^2 + √x - 4/x^2) with respect to x. Participants are exploring the correct interpretation and approach to solving the integral.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to integrate the expression and has provided their current solution. Some participants question the clarity of the original expression due to the lack of parentheses, suggesting multiple interpretations of the integral. Others inquire about fundamental concepts related to integration, such as the properties of integrals and the meaning of "differentiating by parts."

Discussion Status

The discussion is ongoing, with participants seeking clarification on the original problem and exploring different interpretations of the integral. There is an exchange of questions aimed at deepening understanding of integration concepts, but no consensus has been reached regarding the correct approach or interpretation.

Contextual Notes

Participants are navigating potential ambiguities in the mathematical expression due to formatting issues, which may affect the interpretation of the integral. The original poster expresses difficulty in simplifying their solution, indicating a need for further guidance.

lemon26
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Hi, can anyone help please as I'm getting tied up in knots...

Homework Statement



Integrate (5x^2 + √x - 4/x^2) dx

Homework Equations



I think this is differentiating by parts...

The Attempt at a Solution



So far I've got to: 5x^3 / 3 + 2x^3/2 / 3 + 4 / x +c

I can't think how I can make it any tidier so any tips would be really appreciated!
 
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Two questions for you:

(1) What is:
[tex]\int( f(x) + g(x)) dx[/tex]
(2) What is:
[tex]\int x^k dx[/tex]
 
Question (3): What is 'differentiating by parts'?
 
lemon26 said:
Hi, can anyone help please as I'm getting tied up in knots...

Homework Statement



Integrate (5x^2 + √x - 4/x^2) dx

Homework Equations



I think this is differentiating by parts...

The Attempt at a Solution



So far I've got to: 5x^3 / 3 + 2x^3/2 / 3 + 4 / x +c

I can't think how I can make it any tidier so any tips would be really appreciated!

Because you do not use parentheses, I cannot figure out whether you mean
[tex](1) \; \int \left(5 x^2 + \sqrt{x} - \frac{4}{x^2} \right) \, dx \leftarrow \text{ what you wrote}[/tex]
or
[tex](2) \; \int \left( 5 x^2 + \sqrt{x - \frac{4}{x^2}} \right) \, dx[/tex]
or
[tex](3) \;\int \left(5 x^2 - \frac{ \sqrt{x-4}}{x^2} \right)\, dx[/tex]
or
[tex](4) \;\int \left(5 x^2 - \sqrt{ \frac{x-4}{x^2} } \right)\, dx[/tex]
 

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