(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]\int \frac{2x}{3x^{2}+10x+3} dx[/tex]

2. Relevant equations

3. The attempt at a solution

I can't think of a U-substitution that would work, nor a trigonometric substitution, or integration by part.

[tex]\int \frac{2x}{3x^{2}+10x+3} dx[/tex]

[tex]\int \frac{2x}{(x+3)(3x+1)} dx[/tex]

I factored the denominator out thinking that I could somehow substitute for one product, but that doesn't work clearly. How do you integrate functions like these??

I popped it into wolfram and it had a step about fractional decomposition, but I am having a hard time understanding it and we have not covered it yet in my course.

Here is my go at it:

It has to be in this form right?

[tex]\frac{2x}{(3+x)(3x+1)} = \frac{A}{3+x} + \frac{B}{3x+1}[/tex]

So now I would multiply the LCD through the equation leaving:

[tex]2x = A(3x+1) + B(3+x)[/tex]

I don't understand what to do now though?

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# Homework Help: Integral I don't understand?

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