Help with Integral: \int \frac{\(x+9}{x^2+9} dx

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Homework Help Overview

The discussion revolves around the integral \(\int \frac{x+9}{x^2+9} dx\), which falls under the subject area of calculus, specifically focusing on integration techniques.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster expresses uncertainty about how to begin solving the integral and considers the possibility of needing multiple substitutions. Another participant suggests breaking the integral into two parts, which prompts a realization about the potential use of logarithmic and inverse tangent functions.

Discussion Status

The discussion has seen participants exploring different approaches to the integral, with one participant indicating a significant shift in understanding after receiving a suggestion. However, there is no explicit consensus on the final solution, as one participant claims to have solved it independently.

Contextual Notes

The original poster's uncertainty highlights a potential lack of familiarity with integration techniques, and the discussion reflects varying levels of confidence and insight among participants.

laker88116
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[tex]\int \frac{\(x+9}{x^2+9} dx[/tex]

I am not sure where to start. I have a feeling that I need to subsitute twice, but I just don't know what to use first. Any help is appreciated.
 
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[tex]\int \frac{x dx}{x^{2}+9} + 9 \int \frac{dx}{x^{2}+9}[/tex]
 
Wow, that changes everything, ln and tan inverse I think just looking at it, let me try this, I can't believe I overlooked that.
 
Yea, I solved it, thank you for the help.
 

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