Integrating x^2e^-3lnx: Tips and Tricks for Solving Tricky Integrals

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Homework Help Overview

The discussion revolves around the integral of the function x^2e^-3lnx, which falls under the subject area of calculus, specifically integration techniques. Participants are seeking tips and insights on how to approach this integral.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to manipulate the expression involving the exponential and logarithmic functions. There are hints provided regarding the transformation of e^-3lnx and questions about the implications of these transformations.

Discussion Status

The discussion is ongoing, with some participants providing hints and questioning the correctness of certain transformations. There is no explicit consensus, but participants are exploring different interpretations of the integral.

Contextual Notes

Some participants are addressing potential misunderstandings regarding the properties of logarithms and exponentials, indicating a need for clarification on these concepts.

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Homework Statement


int((x^2)(e^-3lnx))

anyone tips for this?

Homework Equations


The Attempt at a Solution

 
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Hint:

<br /> e^{-3 \, \ln{(x)}} = e^{\ln{(x^{-3})}} = ?<br />
 
Dickfore said:
Hint:

<br /> e^{-3 \, \ln{(x)}} = e^{\ln{(x^{-3})}} = ?<br />

now I get int (x^2)(e^(1/x^3)) then? stuck here
 
You are wrong. What does e^{\ln{y}} equal to? Use the property that the (natural) logarithm is the inverse function of the (natural) exponential function.
 

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