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A little help on trig substituiton

  • Thread starter vande060
  • Start date
  • #1
186
0

Homework Statement



∫ x/(x^2 + x+ 1)dx






Homework Equations





The Attempt at a Solution



∫ x/(x^2 + x+ 1)dx

not really sure where to start on this one, i feel like i should factor the denominator in such a way that i have an expression whose derivative is some constant times x. help please
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
6,230
31
Try completing the square for x^2 + x+ 1 and then make an appropriate substitution.
 
  • #3
186
0
Try completing the square for x^2 + x+ 1 and then make an appropriate substitution.
∫ x/√(x^2 + x + 1 -3/4 + 3/4)

√((x + 1/2)^2 + 3/4)

u = (x+1/2)
u = dx

√((u)^2 + 3/4)

u = (√3/2)tanϑ du = √3/2sec^2ϑdϑ

√(u^2 + 3/4) = √3/2secϑ


- pi/2 < ϑ < pi/2

then substituting things back in

((√3/2)tanϑ - 1/2)/ √3/2secϑ)* √3/2sec^2ϑdϑ

im weary of that square root in the numerator
 
Last edited:
  • #4
tiny-tim
Science Advisor
Homework Helper
25,832
250
hi vande060! :smile:
√((u)^2 + 3/4)

u = (√3/2)secϑ
oooh :cry: … learn all your trigonometric identities …

sec2 = tan2 + 1, not t'other way round :redface:
 
  • #5
186
0
hi vande060! :smile:


oooh :cry: … learn all your trigonometric identities …

sec2 = tan2 + 1, not t'other way round :redface:
fixed, if this is correct so far, i can finish it out myself
 

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