How can we integrate a^(x)e^(x) dx using the conversion of ax to e^x?

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Homework Help Overview

The discussion revolves around the integration of the function a^(x)e^(x) with respect to x. The participants are exploring methods to simplify the integration process, particularly through conversions involving exponential functions.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • The original poster expresses uncertainty about using integration by parts and mentions difficulties with u-substitution. They have attempted taking natural logs without success. Other participants suggest converting the expression into a different form, specifically relating ax to an exponential function.

Discussion Status

Participants are actively discussing possible approaches to the integration problem. Some guidance has been offered regarding the conversion of the base a into an exponential form, but there is no clear consensus on the best method to proceed.

Contextual Notes

The original poster notes a lack of familiarity with integration techniques such as integration by parts and u-substitution, which may influence their approach to the problem.

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integrate a^(x)e^(x) dx

We haven't done integrations by part so I am not sure if that would be helpful for this question. I do not see any u substituion so I am not sre where to begin. I have tried taking natural logs and have gotten nowhere. Any infomation that could lead me in the right direction would be greatly appreciated
 
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Try converting to a different form, then see what you notice from there.
 
what type of form, I don't really know how to go about making it easier
 
Try converting ax to e to the appropriate power.

a = eln a, as long as a > 0 and not equal to 1.
 

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