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anonymous
 4 years ago
Need help integrating (x+1)/(x^3 + x).
anonymous
 4 years ago
Need help integrating (x+1)/(x^3 + x).

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slaaibak
 4 years ago
Best ResponseYou've already chosen the best response.0\[{x+1} \over {x(x^2 + 1)}\] Use partial fractions.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I tried using partial fractions, and got A(x^2 + 1) + (Bx + C)x, but I'm not sure how to get the values of the coefficients.

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.2\[A(x^2+1)+(Bx+C)x=x+1\to (A+B)x^2+Cx+A\]just looking at the coefficients it looks like A=1, C=1, and A+B=0 wich leads to B=1

slaaibak
 4 years ago
Best ResponseYou've already chosen the best response.0\[x + 1 = A(x^2 + 1) + (Bx + C) x\] \[x + 1 = (A+B)x^2 + Cx + A\] Therefore A + B = 0 C=1 A=1 damn turing beat me :/

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.2sorry, you got your medal though ;)

slaaibak
 4 years ago
Best ResponseYou've already chosen the best response.0We will continue this battle in another question ;)

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.2indeed! did you get the idea Xylienda?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Yeah. So its more like a trial and error thing, right?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.2Not really in this case when you spell it out and look at the coefficient on the right side you get\[(A+B)x^2+Cx+A=x+1\]the coefficient of x^2 on the right is zero, so\[A+B=0\]the coefficient on x is 1, so\[C=1\]and the constant term is just 1, so\[A=1\]now that we know A=1 we can go back and solve the first one\[A+B=0\to B=1\]so no, it's not trial and error. It is making a system from by setting the coefficients on each side equal. See?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Oh! I think i really get it now. So you kind of begin by, more or less, matching up the forms on both sides of the equation and compare the coefficients, then work from there.

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.2exactly collect like terms on the left and set each coefficient equal to that on the right. Sometimes the systems will be more complex, but here it is pretty easy.
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