Integral [(1 - 2x) / (x^2 + x +3)] dx

i've been out too long. i dont remember any of the trig integrals personally.



This post was edited by carteblanche on Sep 3 2016 08:12pm

how can u tell its trig integrals without lookin at solutions?

dude, that looks nasty to solve lol wtf
btw this is just the right side of the differential equation that I have to solve... the left side of the Differntial equation is just Integral dx/x

This post was edited by FamilyGuyViewer on Sep 3 2016 08:44pm

Looks like you'll need arctan and ln

didn't you learn a chart in calc 1?



im too old for this. if it was a simple u substitution i would have done it (eg if top was 1+2x instead of 1-2x).

This post was edited by carteblanche on Sep 3 2016 09:45pm

that was years ago lol

so how the fck am i suppose to do this by hand

This post was edited by FamilyGuyViewer on Sep 4 2016 07:12am

have you tried integration by parts?

(1-2x) / (x² + x +3) = - (2x + 1) / (x² + x + 3) + 2 / (x² + x + 3)

Integrate the first term simply by using ∫ u'/u = ln |u|

(don't forget to show that the denominator is always positive).

For the second term, show that : x² + x + 3 = 11/4 [ ((2x + 1)/√11)² + 1]

(completing the square)

and change the variable :
t = (2x + 1) / √11
dt = 2 dx / √11

and you should recognize ∫ dt / ( t² + 1) , which is Arctan t.

thanks alot man. dam i woulda been stuck on this problem for forever if this was on my exam...

If this is not for an exam, just ask Wolfram