Integrate dx/(x^(1/2)(x+1)) | 1 to 3

  • Thread starter Thread starter Aerosion
  • Start date Start date
  • Tags Tags
    Integration
Click For Summary
SUMMARY

The discussion centers on the integration of the function dx/((x^(1/2))(x+1)) from 1 to 3. Participants suggest using the substitution x = u^2 to eliminate the radical, followed by integration by parts for further simplification. The confusion arises from choosing the correct substitution to handle both the radical and the linear term in the denominator. The integration process requires careful manipulation of variables to achieve the correct limits and form.

PREREQUISITES
  • Understanding of definite integrals and limits
  • Familiarity with substitution methods in integration
  • Knowledge of integration by parts technique
  • Basic proficiency in LaTeX for mathematical notation
NEXT STEPS
  • Practice integration techniques involving radicals and linear terms
  • Learn about integration by parts with examples
  • Explore advanced substitution methods in calculus
  • Review LaTeX formatting for mathematical expressions
USEFUL FOR

Students studying calculus, particularly those tackling integration problems involving radicals and linear expressions, as well as educators looking for effective teaching strategies in integration techniques.

Aerosion
Messages
52
Reaction score
0

Homework Statement



(integrate: upper limit 3; lower limit 1)(dx/((x^(1/2))(x+1))

Homework Equations


The Attempt at a Solution



First of all, somebody needs to show me how to get the actual integration sign to show up on the forums.

Anyway, I was pretty confused with this one. I tried making u be x+1 and du=dx, but I was afraid this wouldn't solve for the radical x that I also had. Than I tried making u be x and du be dx, but then that wouldn't solve for the x+1 that I had. I don't think I can break this up into two different equations, so I'd like some help.
 
Physics news on Phys.org
First line of attack in such cases: Remove the radical with a "square". Try x = u2.

Btw, making the "substitution" x = u does nothing more than change the letter denoting the dummy variable.

As for getting LaTeX to work, see this thread: https://www.physicsforums.com/showthread.php?t=8997
 
After trying that x=u^2 substitution, try integration by parts.
 

Similar threads

Solving the Integral ∫dx/(1-x)
  • · Replies 3 ·
Replies
3
Views
2K
I'm getting the wrong answer for the Indefinite Integral of: (x^2+2x)/(x+1)^2
  • · Replies 3 ·
Replies
3
Views
2K
Calculating radius of gyration of plane figure about x-axis
  • · Replies 5 ·
Replies
5
Views
3K
Solve ##\int\frac{e^{-x}}{x^2}dx## and ##\int \frac{e^{-x}}{x}dx##
  • · Replies 7 ·
Replies
7
Views
2K
Volume between a region (above x-axis and below parabola) and a surface
  • · Replies 4 ·
Replies
4
Views
3K
Prove that the integral is equal to ##\pi^2/8##
  • · Replies 105 ·
4
Replies
105
Views
11K
Integrals that keep me up at night
  • · Replies 22 ·
Replies
22
Views
3K
Integrate [cosec(30°+x)-cosec(60°+x)] dx in terms of tan x
  • · Replies 3 ·
Replies
3
Views
2K
How To Integrate 1/[sqrt (x^2 + 3x + 2)] dx?
  • · Replies 44 ·
2
Replies
44
Views
6K
Integral using substitution x = -u
  • · Replies 12 ·
Replies
12
Views
2K