How to Integrate by Parts Twice for e^3x cos(x)?

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    Integrate parts
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Homework Help Overview

The discussion revolves around the integration of the function e^{3x} cos(x), specifically focusing on the technique of integration by parts. Participants are exploring the process and challenges associated with this integration method.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the necessity of integrating by parts twice and express uncertainty about their understanding of the technique. One participant shares their attempt at the integration and questions its correctness.

Discussion Status

The discussion is active, with participants providing feedback on attempts and expressing their learning process. Some guidance has been offered regarding the integration technique, but there is no explicit consensus on the correctness of the results presented.

Contextual Notes

One participant notes that they have not yet covered the relevant material in their coursework, indicating a potential gap in knowledge that may affect their understanding of the problem.

Klion
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I am studying for a midterm, was browsing over an old midterm and found this question


[tex] \int e^{3x} \cos{(x)}\; dx [/tex]

Can't figure it out, help would be appreciated
 
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Integrate by parts twice. Post back if you get stuck.
 
erm didn't think we'd gotten that far, assignment on that section isn't due until monday. No wonder I couldn't find it hehe.

O well I have 2 hrs to learn it I'm good! :)
 
hmm I ended up with

[tex] \int e^{3x} \cos{(x)}\; dx = \frac{e^{3x}\sin{(x)} + 3e^{3x} \cos{(x})} {10}[/tex]

that sound about right?
 
Looks good to me.
 

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