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unimatix
 one year ago
Integral (3x+1)/(x^23x+2) dx
unimatix
 one year ago
Integral (3x+1)/(x^23x+2) dx

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unimatix
 one year ago
Best ResponseYou've already chosen the best response.0dw:1441664655453:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0did you try partial fractions?

unimatix
 one year ago
Best ResponseYou've already chosen the best response.0No hold I'll try that.

unimatix
 one year ago
Best ResponseYou've already chosen the best response.0Not sure how to do that in this case.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0factor the denominator to \((x1)(x2)\) Then the original fraction can be written as \[\frac{ A }{ x1 }+\frac{ B }{ x2 }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 3x+1 }{ (x1)(x2) }=\frac{ A }{ x1 }+\frac{ B }{ x2 }\]

unimatix
 one year ago
Best ResponseYou've already chosen the best response.0I'm watching a video on partial fractions because it's been so long since I've seen them.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3\[\frac{3x+1}{x^23x+2} = \frac{3x+1}{(x2)(x1)}\]\[\frac{3x+1}{(x2)(x1)} = \frac{A}{(x2)}+\frac{B}{(x1)}\]\[3x+1=A(x1)+B(x2)\]Yu could use a system of equations or the "zero" method to solve for the x's

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0add on the right then set thh denominators equal. \[A(x1)+B(x2)=3x+1\] Equate the coefficients and solve the system \[A+B=3\] \[A2B=1\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And then once you have A and B the integral becomes \[\int\limits \left( \frac{ A }{ x1 }+\frac{ B }{ x2 } \right)dx\]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3Let's say we took \(x=1\), then \[3(1)+1=A(11)+B(12)\]\[4=0B\]\[B=4\]\[3x+1=A(x1)+B(x2)\]\[3(2)+1=A(21)+0\]\[7=A\]

amistre64
 one year ago
Best ResponseYou've already chosen the best response.0not sure if partials are needed, what is the derivative of the bottom to start with? can we modify the top?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3Basically trying to find what makes A and B = 0... etc.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3\[\int \left(\frac{7}{x1}\frac{4}{x2}\right)dx\]... Trying to refresh my memory on Partial Fraction Decomposition as well. I found PFD easier because the polynomial at the bottom could be factored, and factoring leads me to partial fractions.. etc.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.02x3: 3x+1+(x+4+x4) 2x3: 2x3+(x+4) meh, would still need it for part of it i spose ...

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3\[7\int \left(\frac{1}{x1}\right)dx 4\int \left(\frac{1}{x2}\right)dx \] Im guessing?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3@unimatix Are you capable of continuing from here?

unimatix
 one year ago
Best ResponseYou've already chosen the best response.0I think so! Thanks for all your help everyone!

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3And can you show me how you would integrate this? Just want to make sure you do it right.
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