Integral Help: 1/((4x^2)+(4x)+5)

  • Thread starter Thread starter tmclary
  • Start date Start date
  • Tags Tags
    Integral
Click For Summary
SUMMARY

The discussion focuses on integrating the function 1/((4x^2)+(4x)+5). Participants confirm that the denominator does not factor into linear components and suggest completing the square for simplification. The expression can be rewritten as 1/((2x+1)^2 + 4), leading to a u-substitution that results in an arctangent integral. This method is validated by multiple contributors, ensuring a clear path to the solution.

PREREQUISITES
  • Understanding of indefinite integrals
  • Knowledge of completing the square in quadratic expressions
  • Familiarity with u-substitution techniques
  • Basic concepts of arctangent integrals
NEXT STEPS
  • Practice integrating functions involving completing the square
  • Explore u-substitution in more complex integrals
  • Study arctangent integrals and their applications
  • Review techniques for handling non-factorable polynomials in integration
USEFUL FOR

Students studying calculus, particularly those focusing on integration techniques, as well as educators seeking to enhance their teaching methods in advanced mathematics.

tmclary
Messages
13
Reaction score
0

Homework Statement



Integrate the indefinite integral of 1/((4x^2)+(4x)+5)

Homework Equations





The Attempt at a Solution

 
Physics news on Phys.org
tmclary said:

Homework Statement



Integrate the indefinite integral of 1/((4x^2)+(4x)+5)
I assume you mean find the indefinite integral. You also forgot to fill in the following two sections, in particular the final one:
tmclary said:

The Attempt at a Solution

 
Sorry, I have no clue how to get started. The denominator won't factor (at least to linear factors w/ integral coefficients) and the discriminant is complex anyway. So if it's a partial fraction type solution, how do you get started? Thanks.
 
Try completing the square of the denominator.
 
So 1/(4x^2)+4x+5 =1/((2x+1)^2)+4 and I make a u-sub. Looks like tan^-1 type integral. Correct?
 
tmclary said:
So 1/(4x^2)+4x+5 =1/((2x+1)^2)+4 and I make a u-sub. Looks like tan^-1 type integral. Correct?
Looks good to me :approve:. Choose your substitution carefully.
 
Thanks for your help, Def & Hoot!
 
tmclary said:
Thanks for your help, Def & Hoot!
A pleasure :smile:
 
http://www.4nw.net/s_thumbnailer-6-2008/hb6z6g1g.JPG
 
Last edited by a moderator:

Similar threads

Solving x+3y=4-kz & 4x-2y=5+10z: Find the Solution Here
  • · Replies 6 ·
Replies
6
Views
2K
Integrating (4x+1)^1/2 | Homework Help
  • · Replies 5 ·
Replies
5
Views
3K
Obtain a nonzero solution of ##y''-4y'+x^2(y'-4y)=0## by inspection
  • · Replies 7 ·
Replies
7
Views
2K
Applying integration to math problems
  • · Replies 5 ·
Replies
5
Views
1K
A differential equation with undetermined coefficients
  • · Replies 5 ·
Replies
5
Views
2K
Solving for y in a logarithmic equation involving |y|
  • · Replies 12 ·
Replies
12
Views
2K
Solve the given second order differential equation
  • · Replies 14 ·
Replies
14
Views
1K
Verify Green's Theorem in the given problem
  • · Replies 10 ·
Replies
10
Views
2K
Find the PDF in terms of another variable
  • · Replies 2 ·
Replies
2
Views
2K
Math problem integration by partial fractions
  • · Replies 6 ·
Replies
6
Views
2K