How do I integrate (e^3lnx + e^3x)dx without a calculator?

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Homework Help Overview

The problem involves integrating the expression (e^3lnx + e^3x)dx, which includes both exponential and logarithmic components. The subject area is calculus, specifically focusing on integration techniques.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the interpretation of the expression, questioning whether it is e^3*lnx or e^(3*lnx). There are attempts to simplify the expression, particularly focusing on the relationship between exponential and logarithmic functions.

Discussion Status

Some participants have provided hints and guidance on how to approach the integration, particularly regarding the simplification of e^(3*lnx) to ln(x^3). There is an ongoing exploration of the problem without a clear consensus on the final approach.

Contextual Notes

One participant expresses uncertainty about how to proceed without a calculator, indicating a potential constraint in their understanding of the integration process.

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Homework Statement


I have to integrate (e^3lnx + e^3x)dx


Homework Equations





The Attempt at a Solution


I have the answer and its (1/4)x^4 + (e^3x)/3 + C.
I don't know how to get to the answer without the help of my calculator.
 
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boardinchic said:
I don't know how to get to the answer without the help of my calculator.

I'm not surprised.
 
Do you mean e^[3ln(x)]?

Try and simplify that. Remember ln(y) is the inverse operation to e^y
 
boardinchic said:
I have to integrate (e^3lnx + e^3x)dx

So, is this e^3*lnx or e^(3*lnx)?

First, you can separate them into two integrals of e^(3*lnx) and e^3x. I assume you can solve the second one.

So, for the integral of e^(3*lnx), I'll give you a hint.

3*lnx = ln(x^3)
 
Thank you. I got that the e^lnx = x, but didn't know what to do with the 3. I get it now.
 

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